WO2024039809A1

WO2024039809A1 - Pancake direct capture substrate, device and method

Info

Publication number: WO2024039809A1
Application number: PCT/US2023/030517
Authority: WO
Inventors: Mansour Masoudi; IV Edward Benjamin TEGELER
Original assignee: Emissol, Llc
Priority date: 2022-08-17
Filing date: 2023-08-17
Publication date: 2024-02-22

Abstract

A capture device comprising: an inlet separated by an outlet along a flow path through a plurality of substrates; each substrate comprising a fluid inlet in fluid communication with a fluid outlet through a plurality of flow channels disposed therethrough, each of the plurality of flow channels having a flow channel length; and a sorbent disposed on or within at least one side of at least a portion of at least one flow channel; wherein the plurality of substrates are arranged along the flow path such that a fluid outlet of a first substrate is in fluid communication with, an immediately precedes a fluid inlet of a second substrate, and wherein the fluid outlet of the first substrate is separated from the fluid inlet of the second substrate by a space having a spacing distance.

Description

Patent Application Docket EMIS-1015PCT August 17, 2023 Page 1 of 44 TITLE: PANCAKE DIRECT CAPTURE SUBSTRATE, DEVICE AND METHOD INVENTORS: Mansour Masoudi Edward Tegeler STATEMENT OF GOVERNMENT SPONSORSHIP [0001] This invention was made with Government support under DE-SC0015946 awarded by DOE. The Government has certain rights in this invention. CROSS-REFERENCE TO RELATED APPLICATIONS [0002] This application claims benefit of United States provisional patent application serial number 63/398821, filed August 17, 2022, and to United States provisional patent application serial number 63/457738, filed April 6, 2023, and to United States provisional patent application serial number 63/441141, filed January 25, 2023, the entirety of which are herein incorporated by reference. FIELD [0003] The instant disclosure is generally directed to substrates and devices for treatment of a fluid. In particular, the instant disclosure is directed to so-called direct air capture substrates suitable for use treatment of a fluid by removal of a material present in the fluid by absorption, adsorptions, sequestering, containment, and/or by chemical reaction resulting in treatment of a fluid flowing through the substrate, and the like. BACKGROUND [0004] Direct Air Capture (DAC) is typically conducted using some sort of substrate coated with an adsorbent or absorbent to sorb or otherwise sequester CO₂, followed by desorbing and releasing CO2 periodically. The substrate preferably has a large amount of ‘surface area’ per unit area ideal for CO₂ adsorption / desorption while yielding very low pressure drop and hence reducing the power consumption required to pump the air or other fluid to be treated through the device. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 2 of 44 [0005] As shown in prior art FIG. 1, conventional capture substrates comprise a plurality of straight channels through which air (or in general any fluid) flows. This fluid flow is typically at a Reynolds number or other such index in the regime of laminar flow (due to operational needs to sustain its low pressure drop or flow resistance resulting in essentially straight streamlines as opposed to turbulent flow. In such a flow, for CO₂ to be adsorbed to the sorbent-coated walls or by a sorbent present along the walls of the channel, the CO2 species must travel across the flow streamlines driven by diffusion resulting from higher CO₂ concentration at the channel flow centerline vs. its lower concentration near the channel wall. The base flow or convection flow itself has essentially no role in CO2 transport from the fluid being treated into the sorbent. Diffusion, the dominant process for straight channels is known to be a slow process as compared to convection and other motive forces present. [0006] The capture substrate, e.g., a honeycomb or other arrangement, also includes significant barriers to use including the cost due to the energy required to pump or otherwise draw the air through the capture substrate due to the need to overcome the backpressure or resistance due to air passing through the channels, as well as the power requirements in the form of electrical heating or steam, and/or pressure required to switch the CO₂ adsorption process into a desorption or a separation process to effectively capture CO2. [0007] There is a need in the art to improve the contactor substrate and process useful in DAC and/or other fluid treatment devices. SUMMARY [0008] In embodiments, a capture device comprising: an inlet separated by an outlet along a flow path through a plurality of substrates; each substrate comprising a fluid inlet in fluid communication with a fluid outlet through a plurality of flow channels disposed therethrough, each of the plurality of flow channels having a flow channel length; and a sorbent disposed on or within at least one side of at least a portion of at least one flow channel; wherein the plurality of substrates are arranged along the flow path such that a fluid outlet of a first substrate is in fluid communication with, an immediately precedes a fluid inlet of a second substrate, and wherein the fluid outlet of the first substrate is separated from the fluid inlet of the second substrate by a space having a spacing distance. [0009] In one or more embodiments, a fluid treatment device comprises a capture device according to one or more embodiments disclosed herein. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 3 of 44 [0010] In one or more embodiments, method to treat a fluid comprises directing the fluid comprising a target compound present at an initial concentration through an inlet of the capture device according to claim 1, at a flow rate and at a temperature sufficient to produce a treated fluid exiting the capture device through the fluid outlet having a treated concentration of the target compound which is less than the initial concentration. In one or more embodiments, the method further comprises a desorption step wherein the target compound is released and recovered. Preferably, the fluid is air and the target compound is or includes carbon dioxide. BRIEF DESCRIPTION OF THE DRAWINGS [0011] FIG.1 shows a prior art substrate of a capture device having a linear absorption channel. [0012] FIG.2 is side perspective view of a capture device according to embodiments disclosed herein. [0013] FIG.3 is a perspective view of a substrate according to embodiments disclosed herein. [0014] FIG.4 is a perspective view of a flow channel according to embodiments disclosed herein. [0015] FIG.5 is a graphical representation showing the effect of spacing of the substrates vs Sherwood number, according to embodiments disclosed herein. [0016] FIG.6 is a side perspective view of a capture device according to embodiments disclosed herein. [0017] FIG.7 is a single substrate according to embodiments disclosed herein. [0018] FIG.8 is a portion of a capture device according to embodiments disclosed herein. [0019] FIG.9 is a substrate according to embodiments disclosed herein. [0020] FIG.10 is a capture device according to embodiments disclosed herein. [0021] FIG.11 is another capture device according to embodiments disclosed herein. [0022] FIG.12a shows is a flow path of a capture device having a uniform sorbent coating according to embodiments disclosed herein. [0023] FIG.12b shows is a flow path of a capture device having a non-uniform sorbent coating according to embodiments disclosed herein. [0024] FIG.12c shows is a flow path of a capture device having a non-uniform sorbent coating according to embodiments disclosed herein. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 4 of 44 [0025] FIG.12d shows is a flow path of a capture device having a non-uniform sorbent coating according to embodiments disclosed herein. [0026] FIG.13 is a portion of a substrate according to embodiments disclosed herein. [0027] FIG 14 is a portion of substrate according to embodiments disclosed herein. [0028] FIG.15 is another portion of a substrate according to embodiments disclosed herein. [0029] FIG.16 is a partially assembled substrate of the portions shown in FIG.14 and FIG.15 according to embodiments disclosed herein. [0030] FIG.17 shows the flow channel produced by the combination shown in FIG.16. [0031] FIG.18 shows a partially assembled substrate of a plurality of the portions shown in FIG.14 with the portion shown in FIG.15 according to embodiments disclosed herein. [0032] FIG.19 shows a partially assembled substrate of a plurality of the portions shown in FIG.14 with a plurality of the portions shown in FIG.15 according to embodiments disclosed herein. [0033] FIG.20 shows a side view of the substrate according to embodiments disclosed herein. DETAILED DESCRIPTION [0034] At the outset, it should be noted that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developer's specific goals, such as compliance with system related and business related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time consuming but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. In addition, the composition used/disclosed herein can also comprise some components other than those cited. [0035] In the summary and this detailed description, each numerical value should be read once as modified by the term "about" (unless already expressly so modified), and then read again as not so modified unless otherwise indicated in context. Also, in the summary and this detailed description, it should be understood that a physical range listed or described as being useful, suitable, or the like, is intended that any and every value within the range, including the end points, is to be considered as having been stated. For example, "a range of from 1 to Patent Application Docket EMIS-1015PCT August 17, 2023 Page 5 of 44 10" is to be read as indicating each and every possible number along the continuum between about 1 and about 10. Thus, even if specific data points within the range, or even no data points within the range, are explicitly identified or refer to only a few specific, it is to be understood that inventors appreciate and understand that any and all data points within the range are to be considered to have been specified, and that inventors possessed knowledge of the entire range and all points within the range. [0036] The following definitions are provided in order to aid those skilled in the art in understanding the detailed description, listed embodiments, and the appended claims. [0037] As used in the specification and claims, "near" is inclusive of "at." For purposes herein, a capture device substrate may also be referred to interchangeably as a capture device substrate, a capture substrate, a honeycomb, a contactor, or simply as a substrate. [0038] For purposes herein, unless specifically noted otherwise, the terms sequestration, sorption, adsorption and/or absorption are used interchangeably to indicate the retention and/or sequestration of a chemical species, e.g., carbon dioxide, from a fluid by a material employed for that purpose. [0039] For purposes herein, Reynolds number (Re) is a dimensionless quantity determined according to the equation: ^^^ ^^ = _^ ^ wherein : ρ is the density of the fluid (e.g., kg/m³); v is the velocity or flow speed of the fluid (e.g., m/s); Dh is the hydraulic diameter of the channel (opening size) μ is the dynamic viscosity of the fluid, also referred to herein as the fluid viscosity (e.g., Pa·s or N·s/m² or kg/(m·s)). [0040] For purposes herein, the range of Reynolds numbers for CO2 capture from ambient air or flu gas is in the range of 10 to 1000, with a typical range from about 100 to 500, with from about 100 to 200 being preferred for a flow channel having a hydraulic diameter on the order of about 1mm, and proportional to this range for both larger and smaller flow channels. [0041] For purposes herein, the Prandtl number (Pr) is a dimensionless quantity defined as the ratio of momentum diffusivity to thermal diffusivity, and is determined according to the equation: Patent Application Docket EMIS-1015PCT August 17, 2023 Page 6 of 44 ^_^^ ^^ = ^ wherein : C_p is the heat capacity of the

pressure; μ is the dynamic viscosity of the fluid, also referred to herein as the fluid viscosity (e.g., Pa·s or N·s/m² or kg/(m·s)); and k is the thermal conductivity of the fluid. For purposes herein, the Prandtl number of air “Prair“ is assumed to be ~ 0.7. [0042] For purposes herein, the Schmidt number (Sc) is a dimensionless quantity defined as the ratio of momentum diffusivity to mass diffusivity, and is determined according to the equation: ^ ^^ = ^^_^^ wherein : μ is the dynamic viscosity of the fluid, also referred to herein as the fluid viscosity (e.g., Pa·s or N·s/m² or kg/(m·s)); ρ is the density of the fluid (e.g., kg/m³); and DAB is the mass diffusivity of the fluid (m²/s). [0043] For purposes herein, the channel hydraulic diameter Dh, also referred to herein simply as the hydraulic diameter, is determined according to the equation: ^ℎ^^^^^ ^^^^^ ^^^^^^^^^ ^^^^ ^_^ = 4 ( ) [0044]

of side length “a” , the hydraulic diameter D_h, = a; for a channel having a rectangular square cross section of side length “a” and side length “b”, the hydraulic diameter Dh, = 4(ab)/(2a + 2b); for a channel having a circular cross section of diameter “d”, the hydraulic diameter Dh, = d. It is noted that the hydraulic diameter is not the same as the geometrical equivalent diameter of non- circular ducts or pipes, but is instead proportional to the wetted perimeter of the channel. [0045] For purposes herein, hydraulic diameter (D_h) is calculated with the generic equation: D_h= 4 A / p Patent Application Docket EMIS-1015PCT August 17, 2023 Page 7 of 44 wherein: Dh = hydraulic diameter (m); A = area section of the duct or pipe (m²); p = "wetted" perimeter of the duct or pipe (m) [0046] For purposes herein, the “Development Length” also referred to herein and in the art as the “entry length” of a fluid flowing through a channel, refers to the length determined from the channel entrance along the flow path over which the incoming flow boundary layer, thermal boundary layer and/or diffusion, or sorption boundary layer (CO2) becomes fully developed, e.g., essentially uniform and/or steady state. Flow development length may, or may not, be the same length as thermal development flow length and/or mass transfer development flow length. [0047] For purposes herein, the flow development length L1, which is the length determined from the inlet of the flow channel along the flow path of the flow channel, over which the flow profile of the fluid flowing through the flow channel becomes fully developed, is estimated via the equation: (!_"/^ℎ)/^^ ≅ 0.05; accordingly: L₁ ≈ 0.05Re / D_h. [0048] For purposes herein, the thermal development flow length L2 , over which thermal profile becomes fully developed, is estimated via the equation: (!2 / ^ℎ)/(^^ ^^) ≅ 0.05; accordingly: L2 ≈ 0.05RePr/ Dh. [0049] For purposes herein, the mass transfer development length L_3, which is the length determined from the inlet of the flow channel along the flow path of the flow channel, over which the mass transfer profile of the fluid flowing through the flow channel becomes fully developed, is estimated via the equation: (!₎/ ^ℎ)/(^^ ^^) ≅ 0.05; accordingly: L3 ≈ 0.05ReSc/ Dh. [0050] A capture device comprises an inlet separated by an outlet along a flow path through a plurality of substrates; each substrate comprising a fluid inlet in fluid communication with a fluid outlet through a plurality of flow channels disposed therethrough, each of the plurality of flow channels having a flow channel length; Patent Application Docket EMIS-1015PCT August 17, 2023 Page 8 of 44 and a sorbent disposed on or within at least one side of at least a portion of at least one flow channel; wherein the plurality of substrates are arranged along the flow path such that a fluid outlet of a first substrate is in fluid communication with, an immediately precedes a fluid inlet of a second substrate, and wherein the fluid outlet of the first substrate is separated from the fluid inlet of the second substrate by a space having a spacing distance. The capture device may further include each of the flow channels comprising a cross-sectional shape comprising a plurality of sides defining a cross-sectional area, determined orthogonal to the flow path, having a hydraulic diameter Dh equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel, wherein a flow channel length is from about 0.1 to about 100 times a hydraulic diameter of the flow channel. [0051] The capture device may further include a flow channel length of at least one flow channel which is from about 0.005*Re * Dh to about 0.5*Re *Dh, or from about 0.005*R_e * P_r * D_h to about 0.5*R_e * P_r *D_h, or from about 0.005*R_e * S_c * D_h to about 0.5*Re * Sc *Dh; wherein: Re is a Reynolds number of the fluid flowing there through; P_r is a Prandtl number of the fluid flowing there through; S_c is a Schmidt number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel when determined under operational conditions. [0052] The capture device may further include substrates in which at least one of the plurality of substrates has an aspect ratio from about 0.01 to about 100, wherein the aspect ratio is equal to the flow channel length divided by the larger of a total width of the substrate and a total height of the substrate. [0053] The capture device may further include substrates in which a cross sectional area of each flow channel is greater than or equal to about 0.01 mm² and less than or equal to about 500 mm². [0054] The capture device may further include substrates in which a cross sectional area of each flow channel present within each of the plurality of substrates is essentially equal. The capture device may further include substrates in which a flow channel length of each flow channel present within each of the plurality of substrates is essentially equal. The capture device may further include substrates in which a cross sectional area and/or a flow channel length of a flow channel present within one of the plurality of substrates is different than a cross sectional area and/or Patent Application Docket EMIS-1015PCT August 17, 2023 Page 9 of 44 a flow channel length of a flow channel present within another of the plurality of substrates. The capture device may further include substrates in which a center axis of a flow channel present within the first substrate is colinear with a center axis of a flow channel present within the second substrate. The capture device may further include substrates in which a center axis of a flow channel present within the first substrate is not colinear with a center axis of a flow channel present within the second substrate. The capture device may further include substrates in which each side of a flow channel present within the first substrate is essentially colinear with each side of a flow channel present within the second substrate. The capture device may further include substrates in which each side of a flow channel present within the first substrate is not colinear with each side of a flow channel present within the second substrate. [0055] The capture device may further include substrates in which a first flow channel present within the first substrate comprises a plurality of sides disposed about a center axis of the first flow channel, and a second flow channel present within the second substrate comprises a plurality of sides disposed about a center axis of the second flow channel, wherein the center axis of the first flow channel is colinear with the center axis of the second flow channel, and wherein the sides of the first flow channel are not colinear with the sides of the second flow channel. [0056] The capture device may further include the spacing distance between the first substrate and the second substrate is from about 0.2 to about 200 times a hydraulic diameter of a flow channel present within the second substrate, the hydraulic diameter equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. The capture device may further include substrates in which the spacing distance between a first substrate and a second substrate is from about 1 mm to about 100 mm. [0057] The capture device may further include a spacing distance between a first and a second consecutive substrate is different than a spacing distance between the second and a third consecutive substrate. [0058] The capture device may further include substrates in which at least a portion of at least one flow channel comprises an essentially sinusoidal shape, an essentially helical shape oriented radially about a center axis of the flow channel, an Patent Application Docket EMIS-1015PCT August 17, 2023 Page 10 of 44 essentially helical shape radially arranged about an essentially sinusoidal shape, an essentially sinusoidal shape arranged within an essentially helical shape oriented radially about a center axis of the flow channel, or a combination thereof. [0059] The capture device may further comprise one or more fluid inlets in direct fluid communication with the space between two or more consecutive substrates. [0060] The capture device may further include substrates in which a first flow channel present within a substrate is in fluid communication with a second flow channel present within the same substrate through at least one side of the first and second flow channels. The capture device may further include substrates in which a concentration of the sorbent disposed within a flow channel of the first substrate is different than a concentration of the sorbent disposed within a flow channel of the second substrate. The capture device may further include substrates in which a composition of the sorbent disposed within a flow channel of the first substrate is different than a composition of the sorbent disposed within a flow channel of the second substrate. As shown in FIGs.12a-12d, the sorbent may be uniform or non-uniform within each of the flow channels. Likewise, different sorbents may be utilized within the same flow channel or within different flow channels, and/or within different substrates along the flow path of the capture device. [0061] A method to treat a fluid may comprise directing the fluid comprising a target compound present at an initial concentration through an inlet of the capture device according to one or more of the capture devices disclosed herein, at a flow rate and at a temperature sufficient to produce a treated fluid exiting the capture device through the fluid outlet having a treated concentration of the target compound which is less than the initial concentration. [0062] As shown by way of example in prior art FIG.1, a capture device substrate, generally referred to as 5, includes an inlet end 6 separated from an outlet end 7 by a body length 8 wherein the inlet end 6 is in fluid communication with the outlet end 7 through at least one flow channel 21 disposed through the body 14 of the substrate 5. Substrates according to one or more embodiments of the instant disclosure may further comprise a sorbent 15 disposed in or present on a wall of the channel 21 suitable for removing CO2 or other materials from a fluid 13 flowing through the channel 21 from an inlet opening 9 to and exiting at outlet opening 10. As shown in FIG.1, capture devices utilize a Patent Application Docket EMIS-1015PCT August 17, 2023 Page 11 of 44 honeycomb type substrate typically have a single substrate extending from the inlet to the outlet. [0063] Other types of capture devices include those using a stack or assembly of frames in which a particulate absorbent and/or adsorbent is disposed between two barriers that are permeable to the fluid but which retain the absorbent, e.g., a flexible mesh, screen, or other such barrier (See US9751039). [0064] As shown in FIG.2, in contrast to the prior art, applicant has discovered a capture device according to one embodiment of the instant disclosure, generally indicated as 100, comprising an inlet 110 separated from an outlet 112 along a flow path 114 through a plurality of substrates 116a, 116b, 116c, 116d. As shown in FIG. 3, each of the plurality of substrates 116 comprises a fluid inlet 118 in fluid communication with a fluid outlet 120 through a plurality of flow channels 124 which may have a sorbent 123 disposed therein, only one being indicated for clarity, each having a flow channel length 122, which as shown in FIG.3 is typically the length or depth of the substrate 122 along the flow path 114. As shown in FIG.2, in embodiments the substrates 116 are arranged sequentially, e.g., such that a fluid outlet 120 of a first substrate 116a is separated from a fluid inlet 118 of a second substrate 116b by a spacing distance 126, e.g., d₁. [0065] As shown in FIG.4, Each of the flow channels 124 of the substrates 116 comprise a cross-sectional shape 128 comprising a plurality of sides 130 defining a cross-sectional area 132, determined orthogonal to the flow path 114. In embodiments, the flow channel length 122 (e.g., the substrate depth along the flow path, is from about 0.5 to about 10 times a development length of the flow channel 124. The development length is defined as the length from the fluid inlet 118 over which a flow profile of an incoming fluid flowing therethrough e.g., along flow path 114, becomes uniform. [0066] In embodiments, the capture device further comprises a sorbent effective to absorb, adsorb, sequester, and/or undergo a chemical reaction with one or more components present in the fluid flowing through at least a portion of the flow channel, which in embodiments, comprises a sorbent effective to absorb, adsorb, sequester, and/or undergo a chemical reaction with carbon dioxide. [0067] In embodiments, the flow channel length of at least one flow channel is Patent Application Docket EMIS-1015PCT August 17, 2023 Page 12 of 44 from about 0.1 to about 100 times the development length of the flow channel, when in operation under a particular set of conditions at which the capture device is to be operated, also referred to herein as operational conditions, e.g., the flow rate of a particular fluid such as air under ambient or operational conditions. Accordingly, depending on the intended operational conditions, the actual values may change in proportion to the flow channel length. [0068] In embodiments, the flow channel length of at least one flow channel is greater than or equal to about 0.01, or 0.5, or 1, or 5, or 10 times the development length of the flow channel under a particular set of conditions, and/or is less than or equal to about 100, or 50, or 10, or 5 times the development length of the flow channel under the particular set of conditions intended for operation. In embodiments, the development length is the flow development length, and/or the thermal development length, and/or the mass diffusion development length. [0069] In embodiments, the flow channel length of at least one flow channel is from about 0.005*Re * Dh to about 5*Re *Dh. In embodiments, the flow channel length of at least one flow channel is greater than or equal to about 0.005*R_e * D_h, or 0.01*Re * Dh, or 0.05*Re * Dh, or 0.1*Re * Dh, and/or is less than or equal to about 5*R_e * D_h, or 1*R_e * D_h or 0.5*R_e * D_h, or 0.1*R_e * D_h, wherein R_e is the Reynolds number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel equal to about 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. [0070] In embodiments, the flow channel length of at least one flow channel is from about 0.005*Re *Pr * Dh to about 5*Re *Pr *Dh. In embodiments, the flow channel length of at least one flow channel is greater than or equal to about 0.005*Re *P_r * D_h, or 0.01*R_e *P_r * D_h, or 0.05*R_e *P_r * D_h, or 0.1*R_e *P_r * D_h, and/or is less than or equal to about 5*Re *Pr * Dh, or 1*Re *Pr * Dh or 0.5*Re *Pr * Dh, or 0.1*Re *P_r * D_h, wherein R_e is the Reynolds number of the fluid flowing there through; P_r is a Prandtl number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel equal to about 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. [0071] In embodiments, the flow channel length of at least one flow channel is from about 0.005*Re *Sc * Dh to about 5*Re *Sc *Dh. In embodiments, the flow Patent Application Docket EMIS-1015PCT August 17, 2023 Page 13 of 44 channel length of at least one flow channel is greater than or equal to about 0.005*R_e *Sc * Dh, or 0.01*Re *Sc * Dh, or 0.05*Re *Sc* Dh, or 0.1*Re *Sc* Dh, and/or is less than or equal to about 5*R_e *S_c* D_h, or 1*R_e *S_c* D_h or 0.5*R_e *S_c* D_h, or 0.1*R_e *Sc* Dh, wherein Re is the Reynolds number of the fluid flowing there through; Sc is a Schmidt number of the fluid flowing there through; and D_h is the hydraulic diameter of the flow channel equal to about 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. [0072] In embodiments, at least one of the substrates has an aspect ratio of less than 1, wherein the aspect ratio is equal to the flow channel length 122 divided by the larger of a total width of the substrate 136 or a total height 138 of the substrate. In embodiments, at least one of the substrates has an aspect ratio of less than about 1, or less than or equal to about 0.7, or less than or equal to about 0.5, or less than or equal to about 0.3, or less than or equal to about 0.2, or less than or equal to about 0.1, or less than or equal to about 0.05, or less than or equal to about 0.01, wherein the aspect ratio is equal to the flow channel length 122 divided by the larger of a total width of the substrate 136 or a total height 138 of the substrate and/or a diameter of the substrate for a substrate having a circular cross section. [0073] In embodiments, a cross sectional area of the flow channel is greater than or equal to about 0.01 mm², or greater than or equal to about 0.05 mm², or greater than or equal to about 0.1 mm², or greater than or equal to about 0.5 mm², or greater than or equal to about 1 mm², or greater than or equal to about 5 mm², or greater than or equal to about 10 mm², and less than or equal to about 500 mm², or less than or equal to about 100 mm², or less than or equal to about 50 mm², or less than or equal to about 20 mm², or less than or equal to about 10 mm². [0074] In embodiments, the flow channel length is less than or equal to about 100mm, or less than or equal to about 50mm, or less than or equal to about 20mm, or less than or equal to about 10mm. In embodiments, the flow channel length is greater than or equal to about 0.1 mm, or greater than or equal to about 1 mm, or greater than or equal to about 3 mm, or greater than or equal to about 5mm. [0075] In embodiments, the cross sectional area of each flow channel present within a particular substrate is essentially the same. In embodiments, the cross sectional area of each flow channel present within a particular substrate is essentially Patent Application Docket EMIS-1015PCT August 17, 2023 Page 14 of 44 the same. [0076] In embodiments, a cross sectional area of a first flow channel present within the same substrate is different than a cross sectional area of a second flow channel. In embodiments, a cross sectional area of a first flow channel present within a first substrate is different than a cross sectional area of a second flow channel present within a second substrate. [0077] In embodiments, at least one center axis of a first flow channel (i.e., the geometric center of the cross sectional shape) present within a first substrate is colinear with a center axis of a second flow channel present within a second substrate. [0078] In embodiments, at least one center axis of a first flow channel present within a first substrate is not colinear with a center axis of a second flow channel present within a second substrate. [0079] In embodiments, a plurality of sides of a first flow channel present within a first substrate are colinear with a plurality of sides of a second flow channel present within a second substrate. [0080] In embodiments, a plurality of sides of a first flow channel present within a first substrate are not colinear with a plurality of sides of a second flow channel present within a second substrate. [0081] In embodiments, a straight through flow path- i.e., a line of site flow path, from the capture device inlet to the capture device outlet exists. In other embodiments, less than about 10%, or less than 5%, or less than 1% of the cross sectional area of the capture device inlet possesses a straight through flow path to the capture device outlet. Preferably, there is essentially no straight through flow path from the capture device inlet to the capture device outlet. [0082] In embodiments, a first flow channel present within a first substrate comprises a plurality of sides disposed about a center axis of the first flow channel, a second flow channel present within a second substrate comprises a plurality of sides disposed about a center axis of the second flow channel, wherein the center axis of the first flow channel is colinear with the center axis of the second flow channel, and wherein the sides of the first flow channel are not colinear with the sides of the second flow channel. In other words the cross sectional shapes of the flow channels Patent Application Docket EMIS-1015PCT August 17, 2023 Page 15 of 44 may be different between at least one substrate and another, and/or the orientation of the cross sectional shapes of the flow channels may be rotated and/or offset relative to one-another along the flow path from the capture device inlet to the capture device outlet. [0083] In embodiments, the spacing distance 126 between a first substrate 116a and a second substrate 116b is from about 0.1 to about 1000 times a hydraulic diameter of a flow channel of the second substrate, wherein the hydraulic diameter is equal to about 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. In embodiments wherein the hydraulic diameter of the flow channels present within a particular substrate are not essentially identical, the spacing distance 126 between a first substrate 116a and a second substrate 116b is from about 0.1 to about 1000 times a hydraulic diameter of the flow channel of the second substrate having the smallest hydraulic diameter present within the substrate. [0084] In embodiments, the spacing distance 126 between a first substrate 116a and a second substrate 116b is greater than or equal to about 0.1 times, or 0.5 times, or 1 times, or 5 times, or 10 times, or 50 times, a hydraulic diameter of a flow channel of the second substrate, and less than or equal to about 1000 times, or 500 time, or 100 times the hydraulic diameter of a flow channel of the second substrate. [0085] In embodiments, the spacing distance (126) between a first substrate (116a) and a second substrate (116b) is from about 0.01mm to about 100 mm. In embodiments, the spacing distance 126 between a first substrate 116a and a second substrate 116b is greater than or equal to about 0.01mm, or 0.05 mm, or 0.1mm, or 0.5mm, or 1mm, or 5mm, or 10mm, or 50mm, or 100mm, when determined from the outlet of the first substrate which immediately precedes the inlet of the second substrate immediately following the first substrate along the flow path. [0086] In embodiments, the spacing distance between each substrate is essentially equal. In other embodiments, a spacing distance between a first and a second consecutive substrate is different than a spacing distance between a second and a third consecutive substrate. It is to be clear that the first, second, third, and fourth substrates do not indicate actual order along the flow path, but only indicate the position relative to one other substrate along the flow path. For example, a first substrate may immediately precede a second substrate along the flow path, and a Patent Application Docket EMIS-1015PCT August 17, 2023 Page 16 of 44 third substrate may immediately precede a fourth substrate, but the first substrate may not necessarily precede the third and the fourth substrate along the flow path. [0087] In embodiments, the substrate comprises a first flow channel disposed proximate to a second flow channel, wherein at least a portion of at least one side of the first flow channel forms at least one common sidewall between at least a portion of at least one side of the second flow channel. [0088] In embodiments, at least a portion of the flow channel comprises an essentially sinusoidal shape, an essentially helical shape oriented radially about a center axis of the flow channel, an essentially helical shape radially arranged about an essentially sinusoidal shape, an essentially sinusoidal shape arranged within an essentially helical shape oriented radially about a center axis of the flow channel, or a combination thereof. In such embodiments, the flow path length is determined as the absolute distance from the inlet of the substrate to the outlet of the substrate. [0089] In embodiments, at least one flow channel has a cross-sectional shape comprising at least 3 sides. In embodiments, at least one flow channel has a cross- sectional shape comprising at least 4 sides. In embodiments, at least one flow channel has a cross-sectional shape comprising at least 6 sides. In embodiments, at least one flow channel has a cross-sectional shape comprising an infinite number of sides. [0090] In embodiments, at least a portion of the substrate is formed from one or more ceramics, metals, sorbents, thermoplastic polymers, thermoset polymers, or a combination thereof. In embodiments, the substrate is formed from a material comprising a sorbent effective to absorb, adsorb, sequester, and/or undergo a chemical reaction with carbon dioxide. [0091] In embodiments, the sorbent is present in a liquid, gel and/or slurry mobile phase flowing through one or more of the plurality of channels, preferably the sorbent flows counter-current to the fluid flowing therethrough. [0092] As shown in FIG.2, in embodiments, the capture device 100 may further comprise additional fluid inlets and/or fluid outlets 140 and/or 142 in direct fluid communication with the space between one or more of the substrates 116a, 116b, 116c, 116d. In such embodiments, the fluid to be treated, e.g., air or flu gas, is injected in between at least one pair of substrates bypassing at least one proceeding Patent Application Docket EMIS-1015PCT August 17, 2023 Page 17 of 44 substrate. [0093] For purposes herein the capture device substrates are not so limited to absorption or adsorption of an analyte, but they may be, or may also be suitable for conducting chemical reactions with the analyte present in the fluid flowing therethrough, e.g., the sorbent may be or may include a catalytic component disposed on or in a wall of the flow channel. Accordingly, the capture device substrates according to the instant disclosure may be used to accomplish other physical processes such as filtering, reactive filtering, heat transfer, chemical conversion or synthesis, and/or the like. In embodiments, one or more reactants may be introduced into the additional fluid inlets 140 in direct fluid communication with the space between one or more of the substrates 116a, 116b, 116c, 116d (See FIG.2). [0094] It is to be understood that for purposes herein, discussion of a fluid flowing through a capture device substrate refers to the fluid flow having a mass flowrate, a pressure, a temperature and under conditions consistent with the intended purpose of the capture device substrate. For example, fluid flow through a capture device substrate employed for direct air capture of CO₂ for treatment of ambient air may be at a first set of conditions having a mass flow rate, a temperature, and under conditions consistent with DAC, while treatment of an exhaust stream generated by combustion or some other source refers to a fluid flow and composition having a mass flow rate, a temperature, and under conditions consistent with a typical exhaust stream as readily understood by one of minimal skill in the art. [0095] It is to be understood that for purposes herein, a channel having an “essentially” helical shape or channel flow path refers to a channel that is generally represented by a helix. Accordingly, for purposes herein it is to be understood that an essentially helical shape includes a helical shape. However, the channel need not be strictly defined by a helix, but may approximate a helix as would be readily understood by one of minimal skill in the art. In addition, a channel having an “essentially” helical shape according to the instant disclosure includes a shape that results from a mathematical superposition, transform, or other mathematical operation of two or more essentially helical, which for purposes herein includes helical shapes and/or an essentially helical shape with another shape. [0096] For purposes herein, a flow channel having a flow path with an essentially sinusoidal shape ( an essentially sinusoidal flow channel) refer to a flow channels having a shape which is essentially described by the mathematical sine function, i.e., a sine wave Patent Application Docket EMIS-1015PCT August 17, 2023 Page 18 of 44 or sinusoid, according to the mathematical sine function. However, the channel need not be strictly defined by a sine wave or sinusoid, and for purposes herein includes a shape defined by a periodic oscillation, preferably a smooth periodic oscillation, according to understanding common to the skilled artisan. Other similar descriptions of an essentially sinusoidal shape include “wavy” or wave-like, herringbone, pseudo essentially sinusoidal, pseudo wavy, saw tooth, stepped, serpentine, and/or variations and combination thereof. In addition, a channel having an “essentially” sinusoidal shape according to the instant disclosure includes a shape that results from a mathematical superposition, transform, or other mathematical operation of two or more essentially sinusoidal shapes and/or an essentially sinusoidal shape with another shape. Accordingly, for purposes herein it is to be understood that an essentially sinusoidal shape includes a sinusoidal shape. [0097] In embodiments, flow path through the capture device may be curved or have a U-shape flow path. Accordingly, the channel flow path need not be along a longitudinal axis of the substrate body, but may follow along any line connecting the inlet of the substrate body to the outlet of the substrate body that is disposed within the substrate body. [0098] For purposes herein, a flow channel may have a single inlet, multiple inlets, a single outlet, multiple outlets, or any combination thereof. [0099] For purposes herein, a direct capture substrate which is formed from, and/or which comprises a thermoplastic polymer, a thermoset polymer, and/or any combination thereof, for brevity may be simply referred to as comprising a “plastic”, unless specifically stated otherwise. [0100] For purposes herein, a thickness of a flow channel sidewall (or wall) is defined as the distance between an inner side of a first flow channel and an inner side of a directly adjacent flow channel such that the flow channel sidewall is the barrier between the two adjacent flow channels. In embodiments, the thickness of the flow channel sidewall is greater than or equal to about 0.1 mm, or greater than or equal to about 1 mm, or greater than or equal to about 5 mm, and less than or equal to about 10 mm. [0101] As used herein, Sherwood number (Sh), which is also referred to in the art as the mass transfer Nusselt number, is a dimensionless number used in mass-transfer operation. It represents the ratio of the convective mass transfer to the rate of diffusive mass transport and is defined as follows: Patent Application Docket EMIS-1015PCT August 17, 2023 Page 19 of 44 ℎ ^^^^^^^^^^ ^^^^ ^^^^^^^ ^^^^ ^ℎ = = ^^⁄ ! ^^^^+^^^^ ^^^^ wherein: L is a characteristic length (m); D is mass diffusivity (m^2*s⁻¹); and h is the convective mass transfer film coefficient (m*s⁻¹). [0102] In particular, for purposes herein, the Sherwood number is defined as a function of the Reynolds and Schmidt numbers depending on the operation, including the ratio of the mass transfer to frictional losses of a system at varying Reynolds number in which the Friction coefficient: C_f, is multiplied by the flow Reynolds number Re, according to the relationship Sh/CfRe. [0103] In embodiments, at least one flow channel has a cross-sectional shape comprising 3 or more sides. In some embodiments, at least a portion of the substrate is formed from one or more ceramics, metals, sorbents, thermoplastic polymers, thermoset polymers, or a combination thereof. In embodiments, the substrate comprises or is formed from one or more metal sheets, polymeric sheets, or a combination thereof, disposed about at least one axis of the body. In some of such embodiments, at least a portion of the substrate comprises or is formed from a plurality of corrugated sheets separated from one another by a corresponding number of flat sheets wherein contact between the corrugated sheet and the flat sheet forms the cross-sectional shape of the flow channels; a plurality of corrugated sheets having a first cross- sectional shape separated from one another by a corresponding number of corrugated sheets having a second cross-sectional shape, wherein contact between the corrugated sheets forms the cross-sectional shape of the flow channels; or a combination thereof. Sorbents [0104] In embodiments, the direct capture substrate further comprises one or more sorbents. As used herein, a sorbent is effective to absorb, adsorb, sequester, and/or undergo a chemical reaction with a target compound in the fluid being treated. In one embodiment, the target compound is carbon dioxide. [0105] For purposes herein a sorbent refers to a substance which has the property of collecting and/or retaining molecules of another substance. This may be accomplished by sorption, including adsorption, absorption, sequestration, trapping and/or the like. This may also be accomplished by the occurrence of reversible or non-reversable chemical reactions, and/or combinations thereof. For purposes herein, sorbents also include multipurpose Patent Application Docket EMIS-1015PCT August 17, 2023 Page 20 of 44 materials that utilize any number of processes to remove the target analyte from the fluid being treated. Sorbents may be solids, liquids and/or gels under the conditions at which they are utilized. Sorbents may also undergo phase transitions as a result of removing the target analyte from the fluid being treated and/or as a result of releasing the target analyte or a material derived therefrom. For purposes herein a sorbent present in a liquid phase refers to substances which readily flow under the force of gravity, having a viscosity of less than or equal to about 10,000 cps, preferably less than or equal to about 5000 cps, with less than or equal to about 1000 cps or less than or equal to about 100 cps being more preferred. [0106] For purposes herein a sorbent may also be a catalyst depending on the intended use of the substrate. While a catalyst may not generally be considered a sorbent, for purposes herein it is to be understood that unless expressly stated otherwise, a sorbent may also refer to a catalyst even though the catalyst does not retain a target analyte, but instead facilitates a reaction to convert that target analyte to something else, e.g., for purposes herein a substrate that comprises a sorbent includes a substrate comprising a catalyst present in or on the substrate which converts CO2 into a hydrocarbon. In this example, the “sorbent” is the catalyst. [0107] Suitable sorbents include, but are not limited to oligomeric amines e.g., polyethyleneimine (PEI), and tetraethylenepentamine,(TEPA), functionalized mesoporous silica capsules, e.g., MC400/10 nano capsules, zeolites, (e.g., 5A, 13X, NaY, NaY-10, H-Y-5, H-Y-30, H-Y-80, HiSiv 1000, H-ZSM-5-30, H-ZSM-5-50, H-ZSM-5-80, H-ZSM-5-280, and HiSiv 3000, and the like, hierarchical silica monoliths, mesoporous silica SBA‐15 (SBA(P)) with tetraethylenepentamine (TEPA) and/or polyethyleneimine (PEI), carbon nanotubes, metal–organic frameworks, M2(dobpdc) (M = Zn (1), Mg (2); dobpdc^4–= 4,4′-dioxido-3,3′- biphenyldicarboxylate), adopting an expanded MOF-74 structure types, amine-grafted silicas, aqueous amine solutions, polyamines in porous polymer networks, pore-expanded silica (e.g., MCM-41) with diethanolamine and/or 3-[2-(2-aminoethylamino) ethylamino]propyl trimethoxysilane (TRI) and/or the like, high-silica zeolites TNU-9, IM-5, SSZ-74, ferrierite, ZSM-5 and/or ZSM-11, Y-type zeolite with a Si/Al molar ratio of 60 (abbreviated as Y60) modified with amines including PEI and TEPA, mesoporous silica (e.g., SBA‐15) modified with 3-trimethoxysilylpropyl diethylenetriamine, beta zeolites, activated carbon, activated carbon with ammonia or other amines, mesoporous silica foam comprising tethered amines, hollow fibers comprising amine impregnated silica, aqueous amines e.g., mono, di and tri alkyl amines and mono, di and tri alkanol amines e.g., monoethanolamine (MEA), activated carbon Patent Application Docket EMIS-1015PCT August 17, 2023 Page 21 of 44 with carbonates e.g., potassium carbonate, sorb NX35, olivine, modified alumina with KAl(CO3)(OH)2, combinations thereof, and the like. [0108] In embodiments, the sorbent is disposed on or at least partially within walls of the flow channels. In some embodiments, the substrate is at least partially constructed from the sorbent and/or the substrate is functionalized with the sorbent. In some embodiments, the sorbent is present in a liquid, gel and/or slurry mobile phase flowing through one or more of the plurality of channels, which in an embodiment may be a counter-current flow to the fluid to be treated flowing therethrough. In some embodiments, the mobile phase flowing sorbent is directed into the one or more flow channels through one or more channels laterally disposed into the body at an angle to the flow path of the flow channel. [0109] In embodiments, a method to remove a target compound from a fluid comprises the steps of directing the fluid comprising a first concentration of the target compound through a capture device comprising a capture device substrate according to one or more embodiments disclosed herein at a flow rate, a temperature, and for a period of time sufficient to produce a treated stream having a second concentration of the target compound, wherein the first concentration of the target compound is greater than the second concentration of the target compound. In some embodiments, the method further comprises a desorption step wherein the capture device substrate is subjected to conditions suitable to release the target compound. [0110] In embodiment, the sorbent is disposed on or at least partially within the flow channels of the substrate. Suitable methods include various coating procedures wherein the sorbent is used alone or in combination with a support material e.g., mesoporous alumina, silica, and/or the like. The sorbent such as PEI, used as a viscous liquid or in solvent is directed through the flow channels as a slurry or a solution depending on the sorbent used. Various solvents and binders may be employed and the solvents are then removed. [0111] In other embodiments, the direct capture substrate is functionalize using wet impregnation wherein the sorbent is combined with a solvent and optionally a support which is directed through the flow channels. The solvent is then evaporated. This can also be done without solvent. [0112] In other embodiments, the substrate is produced via binder jetting or other similar technologies to form a porous substrate which is then sintered. The sintered substrate is then functionalized with the sorbent, typically by combining the sorbent with solvent and directing the sorbent through the channels, e.g., immersing the substrate in the sorbent mixture with Patent Application Docket EMIS-1015PCT August 17, 2023 Page 22 of 44 agitation. After which the solvent is evaporated. This may be repeated over again using the same or a different sorbent. [0113] Accordingly, in embodiments the sorbent is disposed on or within the flow channel walls using wash coating, incipient wetness, impregnation, and variations thereof known in the art. In another embodiment, the substrate is composed of support material such as mesoporous silica or mesoporous alumina and then functionalized with a sorbent material, such as polyethyleneimine (PEI), via wet impregnation or some other method. This allows for a reduction in the thermal mass of the contactor relative to a baseline contactor that is composed of an inert material, such as cordierite, and then coated with a sorbent/support material. [0114] In another embodiment, the contactor is composed entirely of sorbent material, and/or sorbent material disposed on a support such as PEI on silica/alumina. This may allow for a further reduction in thermal mass. Capture Device Substrates [0115] In one embodiment, the capture device comprises a plurality of substrates, also referred to herein as honeycombs, each separated from one another by a distance along the flow path through the capture device. The capture device substrate may have a plurality of flow channels, each having essentially the same shaped flow path from an inlet to the outlet, or may have a plurality of flow channels having a plurality shapes of the individual flow paths. This plurality of shapes of the individual flow paths may be consistent from the inlet to the outlet of the substrate. In other embodiments, the flow path through the substrate may comprise a plurality of shapes arranged within the substrate in various sections and/or along the substrate from the inlet to the outlet of the substrate. The flow paths of the various flow channels may be oriented perpendicular to the overall flow path through the capture device, may be parallel to the overall flow path through the capture device, or may be oriented at various angles to the overall flow path from the inlet to the outlet of the capture device. [0116] Each of the flow channels may individually have a single inlet and a single outlet, multiple inlets and multiple outlets, a single inlet and multiple outlets, or multiple inlets and a single outlet. The number of flow channels and/or the average flow channel cross-sectional area present at a particular point in a cross section of the capture device substrate may be variable along the length of the capture device substrate or substrates. [0117] In embodiments, the capture device may have a substrate comprising a first number of channels per unit area present within a substrate at a point proximate to the inlet of the Patent Application Docket EMIS-1015PCT August 17, 2023 Page 23 of 44 capture device which is different from a second number of channels per unit area present in the substrate at a point proximate to the outlet of the capture device. In embodiments, the substrate present at a point proximate to the inlet of the capture device may have channels having a first cross-sectional area which is different from a second cross-sectional area of the same channels located at a point on the same substrate proximate to the outlet of the capture device. [0118] In embodiments, the capture device may have a first substrate comprising a first number of channels per unit area which is different from a second number of channels per unit area present in another substrate located at another point along the flow path of the capture device. In embodiments, a substrate present at a point proximate to the inlet of the capture device may have channels having a first cross-sectional area which is different from a second cross-sectional area of channels disposed through a second substrate located at a point proximate to the outlet of the capture device. [0119] Applicant has discovered that the capture device substrates disclosed herein, when compared to capture device substrates having linear flow channels as seen in prior art Figs.2 and 3, yield at least twice as much mass transfer, i.e., throughput, and/or Sherwood number, which is defined as a dimensionless number used in mass-transfer operation representing the ratio of the convective mass transfer to the rate of diffusive mass transport. Accordingly, capture devices according to the instant disclosure allow for downsizing, reduced sorbent, and/or much improved yield. [0120] Applicant has discovered that when employing the capture device substrates according to embodiments disclosed herein, the mass transfer increases faster than its frictional losses. As a result, the presently claimed invention yields a net gain in Sh/Cf.Re; that is, its required pumping power is reduced by downsizing, while still meeting its performance target. Additionally, it requires less energy for desorption due to the reduced capture device substrate thermal mass. Applicant has also discovered that a capture device substrate or honeycomb made of metal, a thermoplastic, a thermoset plastic, and/or a combination thereof, instead of ceramic or other non-conductive materials, permits efficient heating strategies such as joule heating, in lieu of the less efficient steam heating required by ceramic honeycombs, thus providing increased energy cost savings during desorption operations, in addition to having a reduced thermal mass allowing for much faster return to sorbet operation than devices known in the art. In addition, applicant has discovered that capture device substrates according to embodiments disclosed herein can be manufactured out of thermoplastic and/or thermoset Patent Application Docket EMIS-1015PCT August 17, 2023 Page 24 of 44 polymers e.g., alpha olefin, acrylics, polyesters, polyethers, polyimines, polyamides, and/or the like, and thus may be produced at greatly reduced cost relative to substrates known in the art. Applicant has further discovered that the capture device substrates may be produced at least partially from sorbents, e.g., PEI, and/or may be produced by additive manufacturing techniques, that simplify production and reduce cost. [0121] Suitable polymers, generally referred to herein as “plastics” include polyethylene, isotactic polypropylene, highly isotactic polypropylene, syndiotactic polypropylene, random copolymer of propylene and ethylene, and/or butene, and/or hexene, polybutene, ethylene vinyl acetate, LDPE, LLDPE, HDPE, ethylene vinyl acetate, ethylene methyl acrylate, copolymers of acrylic acid, polymethylmethacrylate or any other polymers polymerizable by a high- pressure free radical process, polyvinylchloride, polybutene-1, isotactic polybutene, ABS resins, ethylene-propylene rubber (EPR), vulcanized EPR, EPDM, block copolymer, styrenic block copolymers, polyamides, polycarbonates, PET resins, cross linked polyethylene, copolymers of ethylene and vinyl alcohol (EVOH), polymers of aromatic monomers such as polystyrene, poly-1 esters, polyacetal, polyvinylidine fluoride, polyethylene glycols, polyisobutylene, and/or combinations thereof. Impact of Spacing and Arrangement on Contactor Substrate Mass transfer. [0122] Applicant has discovered that when substrates are positioned in the vicinity of each other, e.g., in tandem, each contactor’s mass transfer may also depend on its spacing with other contactors. Mass transfer, often measured by Sherwood number, is a measure of a contactor CO2 capture or release. FIG.5 shows how spacing between contactors was found to impact a contactor mass transfer (Sherwood number), wherein the spacing between contactors X (normalized by channel opening or hydraulic diameter D, or X/D) impacts contactor mass transfer. [0123] Applicant has discovered that optimum CO₂ capture occurs in the channel entry region, wherein the CO2 concentration gradient is the largest, thus yielding the largest CO2 capture rate per channel unit surface area. Therefore, instead of using long contactors (i.e., substrates), applicant utilizes a series of short, thin or ‘pancake shape’ substrates (see FIG.6). This is achieved by forming the substrates having the required dimensions, and/or by cutting a longer substrate into several shorter ones (‘pancake’ shape). When put in tandem, as air or any fluid enters each downstream substrate, at each channel entrance the concentration (CO₂) boundary layer is freshly re-formed upon each entrance. As a result, optimum CO2 capture Patent Application Docket EMIS-1015PCT August 17, 2023 Page 25 of 44 rate is repeatedly achieved along the flow path [0124] Such short contactor’s length X can be estimated by setting ^{, / -^} ./ 01 2 0.05 or X 2 0.05 ^^ ^^ ^ℎ . Hence, for a given channel size (D_h) subject to

number Re and working fluid (air), the optimum contactor length X can be

which yields maximum CO₂ capture per unit adsorption surface area. Arranging several of such short (pancake shape) substrates in a series or series-like arrangement, one arrangement example shown in FIG.6. [0125] Furthermore, embodiments of the instant disclosure utilize substrates dimensioned and arranged according to various correlations for change in the local mass transfer (local Sherwood number). For example, utilizing the equation: ;

wherein: ; RΩ= D/4;

<u> = average fluid velocity; Dm = mass diffusivity; L = channel Length; x = position along channel (x = 0 at the inlet and L at the outlet); ShT = Sherwood number, constant concentration; wherein Sh_T∞ = Asymptotic Sherwood number, constant concentration, which represents the Sherwood number in a fully developed region (beyond the development length of the channel). The substrate aspect ratio (ratio thickness divided by total width or length, whichever is larger is also selected both to maximize capture and to minimize pressure drop, e.g., backpressure, or flow resistance, or pumping power). In embodiments, the substrate Aspect Ratio AR is less preferably less than 1. The shorter substrate flow path length results in a corresponding lower pressure drop. [0126] Short, pancake channels may be straight through and/or be non-straight, e.g., the channels may be helical or sinusoidal. Such channels have higher mass transfer than straight channels, often measured via channel’s Sherwood number. While a regular, straight channel Patent Application Docket EMIS-1015PCT August 17, 2023 Page 26 of 44 has a Sherwood number about 3, a channel of the same length comprising a plurality of short (pancake) substrates having the same straight channel, when dimensioned and arranged according to embodiments disclosed herein, yields a Sherwood number about 5.5 – 6.5 i.e., about 50 - 100% higher. Short (pancake) substrates comprising helical channels may have a Sherwood number about 10 – 15, well above that of straight channel. Accordingly, a plurality of short (pancake) substrates having helical channels, when dimensioned and arranged according to embodiments disclosed herein, yields an improved Sherwood number ideal for CO2 capture. [0127] Accordingly, capture devices according to embodiments disclosed herein may result in short channels, which may include helical and/or sinusoidal channels, and as such, reduce sorbent use and cost. It is noted that in many carbon capture operations sorbent cost is a substantial portion of the total capture cost, as it is often a major part of the capture plant capital expenses (see for example National Academies of Sciences, Engineering, and Medicine. 2019. Negative Emissions Technologies and Reliable Sequestration: A Research Agenda. Washington, DC: The National Academies Press. https://doi.org/10.17226/25259; H. Azarabadi and K. S. Lackner. A Sorbent-Focused Techno-Economic Analysis of Direct Air Capture. Applied Energy, Vol.250, 2019. Pages 959-975, ISSN 0306-2619.) [0128] In embodiments, as shown in FIG.7, the substrate’s center axis of each flow channel (i.e., its flow direction) is normal to second substrate’s center axis of channels. Accordingly, in such embodiments, flow travelling through the first substrate, when reaching a channel end, will turn to travel through the next substrate adjacent to it (or in its vicinity.) [0129] In another embodiment, as shown in FIG. 8a and FIG. 8b, the flow may enter a substrate in a first plane and exit the substrate on a second plane as shown in FIG. 8a, or in another direction e.g., orthogonal to the inlet flow as shown in FIG.8b. [0130] In another embodiment, shown in FIG.9, the substrates may be porous and arranged in a labyrinth, where the flow is continually forced to turn from one orientation through one substrate into another orientation in the next substrate(s), thus prolonging flow contact with substrate’s surface area where a suitable sorbent may be coated, hence maximizing CO2 capture. [0131] In yet another embodiment, as shown in FIG.10, the substrates may be arranged in a compacted labyrinth, where the flow is continually forced to pass through several substrates in various directions, into an open space, and then turning and flowing through another Patent Application Docket EMIS-1015PCT August 17, 2023 Page 27 of 44 substrate, thus further prolonging flow contact with substrate’s surface area where a suitable sorbent may be coated, hence maximizing CO2 capture. FIG. 11 shows an embodiment wherein at least a portion of the flow is perpendicular to the inlet and the outlet of the capture device. [0132] In embodiments, when utilizing such substrate arrangements, flow turning from one substrate into the next one would be a 90-degree (orthogonal) turn. However, consecutive substrates may be arranged so that flow turning from one substrate outlet into the next substrate inlet may attain angels less than, or higher than, 90 degrees. For instance, pancake contactors may be rotated relative to one another, hence allowing the flow to turn having non-orthogonal angels. [0133] In capture devices known in the art, an increase in Sherwood number is accompanied by increase in pressure drop, requiring excess pumping power and hence increased higher energy costs. However, applicant has discovered that by arranging substrates according to the instant disclosure in tandem, the first contactor will likely have the highest CO2 capture rate, then the second contactor, next the third, and so on. This pattern may however be improved upon by “feeding” fresh flow into the structure mid-way through the space between two of the substrates. [0134] When sufficient CO₂ is captured, per a per-determined process control, in embodiments, the capture device is operated to release its stored (adsorbed) CO2, known as unloading or regeneration. Such release may be induced via raising the contactor temperature (thermal swing). The exact unloading/ regeneration process depends on the type of the sorbent. It is also possible to use contactors made of metals. This could make thermal swings easier as metal contactors could be heated via Joule heating, i.e., via electrical resistivity. [0135] In embodiments, a pulsating or oscillatory flow may be utilized such that the flow rate is varied through the flow channels providing further enhancement in heat and/or mass transfer. In embodiments, a plurality of capture devices may be operated using a swing valve arrangement. In an embodiment, this variation in flow rate is created using a set of two valves, one located at the upstream and one at the downstream of each contactor. Two parallel contactors may be “in operation”. The upstream valve will close the flow on one contactor while the downstream valve will close the flow on the other one. Through oscillation of these valves, a flow pulsation will be created in the direction of the air flow which will enhance mass transfer and, consequently, facilitate CO2 capture. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 28 of 44 [0136] In embodiments, the cross sectional shape of the substrate comprises at least 3 sides, e.g., triangular, but may also be square, rectangular, or have any number of sides up to being circular or elliptical. The overall cross-sectional shape of the contactor may also change along the flow path from the inlet to the outlet. Formation of the Substrate [0137] At least a portion of the capture device substrates according to embodiments disclosed herein may be manufactured out of ceramics, metals, thermoplastic polymers, thermoset polymers, or a combination thereof. In embodiments, the capture device substrate body or core may be produced via extrusion molding. According to one or more embodiments, a process for manufacturing ceramic linear and non-linear channels includes extrusion of the soft (uncured or green) ceramic materials whose composition is carefully controlled. The ceramic is extruded through a die outlet having a pattern which produces the flow channels, e.g., a thin mesh or lattice, which results in the formation of the flow channels. In embodiments, the die is moved relative to the extruder output to form the channels as described herein. After extrusion, the extrudate is trimmed to a length appropriate for a catalyst application and heat cured to produce the capture device substrate. In some embodiments, the heat-cured capture device substrate is contacted with a catalyst, typically via washcoat, according to methods known in the art. The capture device substrate may then be mounted and packaged in a housing or shell. [0138] In other embodiments, at least a portion of the capture device substrate may be produced by additive manufacturing, e.g., 3-D printing. This includes ceramics, metals, thermoplastic polymers, thermoset polymers, or a combination thereof. For example, using a process referred to in the art as binder jetting, a polymeric or other type of sorbent may be directly printed to form at least a portion of the direct capture substrate. [0139] In other embodiments, at least a portion of the direct capture substrate comprises a support material such as mesoporous silica or mesoporous alumina, which is produced to a rigid support, e.g., sintered or cured, and then functionalized with a sorbent material, such as polyethyleneimine (PEI), via wet impregnation, incipient wetness, and/or the like. This allows for a reduction in the thermal mass of the direct capture substrate relative to a baseline contactor that is formed from an inert material, such as a ceramic, and then coated with a sorbent/support material e.g., washcoated. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 29 of 44 [0140] In some embodiments, the direct capture substrate is produced using materials and conditions selected to control the pore size, pore structure, and pore size distribution of the substrate material as well as the loading of sorbent mass on and/or within the substrate support material, internal mass transfer resistance may be decreased, further increasing the rate of transfer of CO₂ to the sorbent in the substrate. [0141] In embodiments, the formation of substrates having essentially helical channels may comprise the step of rotating the die at a given angular velocity along its longitudinal axis of symmetry to produce the capture device substrate having essentially helical channels disposed along a central axis parallel to the center axis of the substrate. The rotation of the die causes the extruded soft ceramic or thermoplastic material to form thin, narrow, long, and identically-sized tube-like channels wound along the die's longitudinal axis of symmetry in a manner similar to a helix. The speed of the rotation of the die is selected to produce the requisite number of essentially helical turns per given substrate length. [0142] In an alternative embodiment, to form a capture device substrate having essentially sinusoidal channels, the die is oscillated along a vertical axis and/or a horizontal axis relative to the extruder output according to the amplitude and arrangement of the sine-wave or sinusoids to be formed in substrate. The specified frequency and mass-output of the extruder are controlled to form thin, narrow, long, essentially sinusoidal channels or cells that rise and fall along the die's longitudinal axis of symmetry according to a sinusoid function. In yet another embodiment, capture device substrates having essentially helical sinusoids and essentially sinusoidal helices may be formed by both oscillating along one or more axes, and/or rotation in one or more directions relative to the extruder output. The frequency and angular speed of die's essentially sinusoidal motion, and the speed of its rotation, will determine wavelength, amplitude, and essentially helical turns for any specified design. [0143] In other embodiments, the extrudate flows through the die and into a form which supports the extrudate. This form is then moved relative to the extruder output i.e., via oscillation along one or more axes, rotations along one or more axes, or a combination thereof to form the channels according to embodiments disclosed herein, followed by curing of the ceramic to form the capture device substrates according to embodiments disclosed herein. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 30 of 44 [0144] The reaction substrate may be formed out of any suitable ceramic known in the art. Likewise, in embodiments, the capture device substrate may be formed from materials which further include one or more catalytic materials such that the capture device substrates comprise one or more catalytic materials disposed within the wall of the flow channels. Suitable ceramic materials include those disclosed in US Patent Nos.3489809, 5714228, 6162404, and 6946013, the content of which are fully incorporated by reference herein. [0145] In other embodiments, the capture device substrates are formed essentially from metal, preferably metal sheeting, or foil. In an embodiment, the metallic substrate is manufactured into a conventional shape with straight and parallel tube-like channels, and then essentially helically twisted into a suitable essentially helical shape. In other embodiments, the manufacture of a metallic substrate core with essentially sinusoidal- essentially helical channels comprising forming the metal sheet into an essentially sinusoidal shape and stacking sheets into a block, followed by brazing or otherwise permanently affixing the sheets into place which may be followed by essentially helically twisting the formation to form essentially sinusoidal-essentially helical channels. [0146] As shown in FIG.13, in embodiments, the substrate may comprise a surface formed from the intersection of two or more sinusoidal surfaces, which further increase contact between a fluid flowing over the surface with a sorbent disposed on the surface through secondary flow formation. These double sinusoidal trays can vary in frequency and amplitude. [0147] In embodiments, as shown in FIGs.14 – 20, the substate may comprise a plurality of helical flow channels formed from a plurality of intersecting corrugated sheets, which in embodiments may be corrugated metal (e.g., stainless-steel) foils. In embodiments, the intersection of two sets of sinusoidal sheets shown in FIG.14 and FIG.15 oriented at right angles to one another, as shown in FIG.16, form a helical flow channel shown in FIG.17. In an embodiment, both the vertical sheet 14 and the horizontal sheet 15 both define sin waves, which are out of phase with one another by pi (∏). In other words, when one sheet is defined as a sine wave, the other is a cosine wave. The projection of their intersection coincides naturally with the parametric equations describing a helix. The helical channel itself is comprised of the space between the two sheets in parallel, separated by some distance, intersected with two other sheets according to FIGs.14 and 15 in parallel also separated by the Patent Application Docket EMIS-1015PCT August 17, 2023 Page 31 of 44 same distance (see FIG.16), resulting in a channel of roughly square cross section as shown in FIG.17. Varying the distance will produce a rectangular cross section. In one embodiment, a series of parallel sinusoidal slots are machined into one sheet type, and the other sheet type is inserted through these slots. In the example shown in FIGs.18 and 19, the sheets are assembled to form the substrate. In embodiments, the sheet may then be spot welded, brazed, or otherwise affixed to one another, any extraneous material may be trimmed to produce the helical channel substrate shown in FIG.20. [0148] In embodiments, the geometry can be assembled from various sheets with having other geometries. In embodiments, the sheets may be formed from ceramic and/or printed, stamped, or cast in ceramic, assembled, and subsequently fired or sintering. The shape of the helical channel can be controlled by changing the amplitude and the frequency of the sine and cosine waves used to pattern the sheets, as well as the spacing of the sheets. [0149] In other embodiments, the capture device substrates are formed essentially from thermoplastic polymers, thermoset polymers, or a combination thereof (plastic), preferably as a thin sheet. They may also be cast, injection molded, or 3D printed to produce the capture device substrate. In an embodiment, the plastic substrate is manufactured into a conventional shape with straight and parallel tube-like channels, and then essentially helically twisted into a suitable essentially helical shape. In other embodiments, the manufacture of a plastic substrate core with essentially sinusoidal- essentially helical channels comprising forming the metal sheet into an essentially sinusoidal shape and stacking sheets into a block, followed by welding or otherwise permanently affixing the sheets into place which may be followed by essentially helically twisting the formation to form essentially sinusoidal-essentially helical channels. In other embodiments, the direct capture substrate is formed by extrusion of the thermoplastic and/or thermoset polymer according to one or more methods by which ceramic substrates may be formed, as disclosed herein. [0150] In one or more embodiments, a metallic and/or plastic capture device substrate may be manufactured from corrugated sheets folded first into a block, and then wound into a spiral, wherein a metal or plastic sheet is pressed or otherwise formed into a desirable corrugation, which is then formed into a channel shape. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 32 of 44 During this process, sheets of corrugated metal are stacked into blocks that are spirally wound and brazed, welded or permanently affixed into place. The blocks are then cut into individual substrate cores to form the channels. Once formed, the substrate may be washcoated with a slurry or solution comprising the catalyst and subsequently cured or fixed to bond or adhere the catalyst to the substrate. [0151] In other embodiments, the capture device substrate may be formed by a process comprising three-dimensional (3-D) printing of the substrate, from metal, ceramic, plastic, or a combination thereof, and/or by forming a mold and casting the substrate. [0152] 3-D printing is suitable for manufacturing capture device substrates having essentially helical channels, essentially sinusoidal channels, essentially helical- sinusoid channels, and essentially sinusoidal essentially helical channels. Manufacture using 3-D printing comprises programing the printer with an appropriate computer-aided design (CAD) or digital model of a capture device substrate. Still other technologies, and methods of manufacturing capture device substrates according to one or more embodiments disclosed herein are suitable. [0153] Accordingly, in embodiments, a method for manufacturing a ceramic capture device substrate comprises the steps of providing a die perforated with a lattice over an outlet of an extruder; extruding soft ceramic materials through the whilst the die is rotated along its axis of symmetry in a clockwise or counterclockwise manner in order to make a substrate having essentially helical channels of an essentially helical diameter, a channel length; and a winding number of essentially helical turns which is independent of the channel length. Preferably, the winding number is selected in order to optimize a pressure gradient across the selected essentially helical diameter and/or backpressure along the channel length in order to produce stable Dean vortical structures in a fluid flowing through the channel. In embodiments, the capture device substrate is adapted to increase heat- transfer and/or mass-transfer performance through formation of stable Dean vortical structures due to the winding number, pressure gradient, and/or backpressure, and further the channels are dimensioned and arranged to form stable Dean vortical structures which are exclusively operative under strictly non-turbulent flow conditions, to create secondary flow, lateral to a longitudinal channel base flow, and Patent Application Docket EMIS-1015PCT August 17, 2023 Page 33 of 44 enhance interactions with channel walls. The method may further include trimming a plurality of the extruded substrates and heat curing and/or crosslinking, the substrates to form the capture device substrates. [0154] In some embodiments the die is moved up and down along its axis of symmetry in order to superimpose an essentially sinusoidal channel into the essentially helical channel of the capture device substrate. In embodiments, the essentially sinusoidal waveforms formed in the channels are controlled by selecting a substrate length and selecting a frequency, amplitude, and wavelength of the up-and- down motion of the die during the extrusion process. [0155] In embodiments, the process further includes coating the capture device substrate with a washcoat that contains a sorbent formulation; and optionally installing the capture device substrate within a protective outer housing having a fluid inlet and a fluid outlet on opposite ends of the direct capture substate through which the fluid enters and exits the housing. [0156] In embodiments, the extrusion may further include controlling the winding number of essentially helical turns formed in the essentially helical substrate per a given substrate length by adjusting a frequency with which the die is rotated clockwise or counterclockwise around a center axis of the die, optionally combined with the up-and-down motion of the die. [0157] In other embodiments, a method for manufacturing a metallic and/or plastic capture device substrate comprises the steps of pressing a sheet of the material into a corrugated pattern having a plurality of identically-sized flow channels formed along a longitudinal axis of the pressed sheet, stacking a plurality of said pressed sheets all oriented along their longitudinal axes, permanently affixing each of the pressed sheets to each other into a block; and trimming the block into a length suitable for a capture device substrate. [0158] In some embodiments, the step of pressing the sheet forms identically- sized essentially helical grooves in a flow direction along the longitudinal axis of the pressed sheet in lieu of the corrugated pattern, wherein the identically-sized essentially helical grooves have groove axes that are non-coincident with each other, and wherein each of the identically-sized essentially helical groove have a selected essentially helical diameter, a selected channel length, and a selected winding Patent Application Docket EMIS-1015PCT August 17, 2023 Page 34 of 44 number of essentially helical turns, independent of the channel length. [0159] In other embodiments, a method for manufacturing a ceramic and/or plastic capture device substrate comprises the steps of providing the die perforated with a lattice over an outlet of an extruder, extruding the soften materials through said die whilst said die is moved up and down relative to its axis of symmetry of the die to form essentially sinusoidal shaped channels. The method may further include trimming and heat curing and wash coating as above. In such embodiments, the step of extruding may further include controlling a number of essentially sinusoidal waveforms formed in the substrate per substrate length by adjusting a frequency, the essentially sinusoidal amplitude, and/or the essentially sinusoidal wavelength of the up-and-down motion with which the die is moved. [0160] In other embodiments, at least a portion of the capture device substrates are produced using additive manufacturing techniques. [0161] Capture device substrates according to one or more embodiments disclosed herein provide improved cost savings since the enhanced efficiency allows for a reduction of substrate volume (downsizing), a reduction in the amount of sorbent and/or the like, which is of considerable economic importance since many sorbent formulations are expensive, particularly when their formulations include precious metals (platinum, palladium, and rhodium). Downsizing allows non-negligible, multi- layered savings in costs of: (a) substrate, (b) sorbent washcoat, (c) sorbent precious metal(s), (d) sorbent coating process, (e) substrate packaging and support materials, and the like. [0162] Capture device substrates according to one or more embodiments disclosed herein provide improved energy utilization since reduced size results in less energy expenditure due to a reduction in backpressure, a reduction in pumping power, weight reduction, and improved sorbent performance. [0163] Likewise, the capture device substrates disclosed herein are suitable for use in heat-exchangers, filters, and the like, wherein the shape, arrangement and other properties of the channels and the substrate are selected according to the operational conditions. Direct Capture Substrates having Permeable Flow Channels [0164] In some embodiments, the capture device substrate comprises a first flow channel disposed proximate to a second flow channel, wherein at least a portion of at Patent Application Docket EMIS-1015PCT August 17, 2023 Page 35 of 44 least one side of the first flow channel forms at least one common sidewall between at least a portion of at least one side of the second flow channel. In some of such embodiments, the capture device substrate includes at least a portion of the at least one common sidewall comprises a porosity, a conduit, a via, or a combination thereof, wherein the fluid inlet is in fluid communication with the fluid outlet through at least a portion of the at least one common sidewall. [0165] In some embodiments, substrate includes inlet channels which are open on the inlet end of the substrate and in direct fluid communication with the fluid inlet of the capture device, and which are blocked on the outlet end of the substrate and thus not in direct fluid communication with the fluid outlet of the capture device. Adjacent to these inlet channels are disposed outlet channels which are closed on the inlet end of the substrate and thus not in direct fluid communication with the fluid inlet of the capture device, and which are open on the outlet end of the substrate and thus in direct fluid communication with the fluid outlet of the capture device. The inlet of the capture device is in fluid communication with the outlet of the capture device through the sidewalls of the inlet flow channels and the outlet flow channels. [0166] This fluid communication between the inlet and the outlet of the capture device may include a porosity of the channel walls, via or holes disposed through the channel walls from an inlet channel to an outlet channel, valves or other gating mechanisms, or any combination thereof. [0167] One or more of embodiments include: E1. A capture device comprising: an inlet separated by an outlet along a flow path through a plurality of substrates; each substrate comprising a fluid inlet in fluid communication with a fluid outlet through a plurality of flow channels disposed therethrough, each of the plurality of flow channels having a flow channel length; and a sorbent disposed on or within at least one side of at least a portion of at least one flow channel; wherein the plurality of substrates are arranged along the flow path such that a fluid outlet of a first substrate is in fluid communication with, an immediately precedes a fluid inlet of a second substrate, and wherein the fluid outlet of the first substrate is separated from the fluid inlet of the second substrate by a space having a spacing distance. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 36 of 44 E2. The capture device according to embodiment E1, wherein each of the flow channels comprise a cross-sectional shape comprising a plurality of sides defining a cross-sectional area, determined orthogonal to the flow path, having a hydraulic diameter D_h equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel, wherein a flow channel length is from about 0.1 to about 100 times a hydraulic diameter of the flow channel. E3. The capture device according to one or more of embodiments E1-E2, wherein the flow channel length of at least one flow channel is: from about 0.005*Re * Dh to about 0.5*Re *Dh wherein: R_e is a Reynolds number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel when determined under operational conditions. E4. The capture device according to one or more of embodiments E1-E3, wherein the flow channel length of at least one flow channel is: from about 0.005*Re * Pr * Dh to about 0.5*Re * Pr *Dh; wherein R_e is a Reynolds number of the fluid flowing there through; Pr is a Prandtl number of the fluid flowing there through; and D_h is the hydraulic diameter of the flow channel when determined under operational conditions. E5. The capture device according to one or more of embodiments E1-E4, wherein the flow channel length of at least one flow channel is: from about 0.005*Re * Sc * Dh to about 0.5*Re * Sc *Dh; wherein: Re is a Reynolds number of the fluid flowing there through; S_c is a Schmidt number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel when determined under operational conditions. E6. The capture device according to one or more of embodiments E1-E5, wherein at least one of the plurality of substrates has an aspect ratio from about 0.01 to about 100, wherein the aspect ratio is equal to the flow channel length divided by the larger of a total width of the substrate and a total height of the substrate. E7. The capture device according to one or more of embodiments E1-E6, wherein a cross Patent Application Docket EMIS-1015PCT August 17, 2023 Page 37 of 44 sectional area of each flow channel is greater than or equal to about 0.01 mm² and less than or equal to about 500 mm². E8. The capture device according to one or more of embodiments E1-E7, wherein a cross sectional area of each flow channel present within each of the plurality of substrates is essentially equal. E9. The capture device according to one or more of embodiments E1-E8, wherein a flow channel length of each flow channel present within each of the plurality of substrates is essentially equal. E10. The capture device according to one or more of embodiments E1-E9, wherein a cross sectional area and/or a flow channel length of a flow channel present within one of the plurality of substrates is different than a cross sectional area and/or a flow channel length of a flow channel present within another of the plurality of substrates. E11. The capture device according to one or more of embodiments E1-E10, wherein a center axis of a flow channel present within the first substrate is colinear with a center axis of a flow channel present within the second substrate. E12. The capture device according to one or more of embodiments E1-E11, wherein a center axis of a flow channel present within the first substrate is not colinear with a center axis of a flow channel present within the second substrate. E13. The capture device according to one or more of embodiments E1-E12, wherein each side of a flow channel present within the first substrate is essentially colinear with each side of a flow channel present within the second substrate. E14. The capture device according to one or more of embodiments E1-E13, wherein each side of a flow channel present within the first substrate is not colinear with each side of a flow channel present within the second substrate. E15. The capture device according to one or more of embodiments E1-E14, wherein a first flow channel present within the first substrate comprises a plurality of sides disposed about a center axis of the first flow channel, and a second flow channel present within the second substrate comprises a plurality of sides disposed about a center axis of the second flow channel, wherein the center axis of the first flow channel is colinear with the center axis of the second flow channel, and wherein the sides of the first flow channel are not colinear with the sides of the second flow channel. E16. The capture device according to one or more of embodiments E1-E15, wherein the Patent Application Docket EMIS-1015PCT August 17, 2023 Page 38 of 44 spacing distance between the first substrate and the second substrate is from about 0.2 to about 200 times a hydraulic diameter of a flow channel present within the second substrate, the hydraulic diameter equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel. E17. The capture device according to one or more of embodiments E1-E16, wherein the spacing distance between the first substrate and the second substrate is from about 1 mm to about 100 mm. E18. The capture device according to one or more of embodiments E1-E17, wherein a spacing distance between a first and a second consecutive substrate is different than a spacing distance between the second and a third consecutive substrate. E19. The capture device according to one or more of embodiments E1-E18, wherein at least a portion of at least one flow channel comprises an essentially sinusoidal shape. E20. The capture device according to one or more of embodiments E1-E19, wherein at least a portion of at least one flow channel comprises an essentially helical shape oriented radially about a center axis of the flow channel. E21. The capture device according to one or more of embodiments E1-E20, wherein at least a portion of at least one flow channel comprises an essentially helical shape radially arranged about an essentially sinusoidal shape. E22. The capture device according to one or more of embodiments E1-E21, wherein at least a portion of at least one flow channel comprises an essentially sinusoidal shape arranged within an essentially helical shape oriented radially about a center axis of the flow channel. E23. The capture device according to one or more of embodiments E1-E22, further comprising one or more fluid inlets in direct fluid communication with the space between two or more consecutive substrates. E24. The capture device according to one or more of embodiments E1-E23, wherein a first flow channel present within a substrate is in fluid communication with a second flow channel present within the same substrate through at least one side of the first and second flow channels. E25. The capture device according to one or more of embodiments E1-E24, wherein a concentration of the sorbent disposed within a flow channel of the first substrate is different than a concentration of the sorbent disposed within a flow channel of the second substrate. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 39 of 44 E26. The capture device according to one or more of embodiments E1-E25, wherein a composition of the sorbent disposed within a flow channel of the first substrate is different than a composition of the sorbent disposed within a flow channel of the second substrate. E27. A method to treat a fluid comprising: directing the fluid comprising a target compound present at an initial concentration through an inlet of the capture device according to any one of embodiments E1 -E26, at a flow rate and at a temperature sufficient to produce a treated fluid exiting the capture device through the fluid outlet having a treated concentration of the target compound which is less than the initial concentration. [0168] Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus- function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures.

Claims

Patent Application Docket EMIS-1015PCT August 17, 2023 Page 40 of 44 CLAIMS 1. A capture device comprising: an inlet separated by an outlet along a flow path through a plurality of substrates; each substrate comprising a fluid inlet in fluid communication with a fluid outlet through a plurality of flow channels disposed therethrough, each of the plurality of flow channels having a flow channel length; and a sorbent disposed on or within at least one side of at least a portion of at least one flow channel; wherein the plurality of substrates are arranged along the flow path such that a fluid outlet of a first substrate is in fluid communication with, an immediately precedes a fluid inlet of a second substrate, and wherein the fluid outlet of the first substrate is separated from the fluid inlet of the second substrate by a space having a spacing distance. 2. The capture device of claim 1, wherein each of the flow channels comprise a cross- sectional shape comprising a plurality of sides defining a cross-sectional area, determined orthogonal to the flow path, having a hydraulic diameter D_h equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel, wherein a flow channel length is from about 0.1 to about 100 times a hydraulic diameter of the flow channel. 3. The capture device of claim 2, wherein the flow channel length of at least one flow channel is: i) from about 0.005*R_e * D_h to about 0.5*R_e *D_h; ii) from about 0.005*Re * Pr * Dh to about 0.5*Re * Pr *Dh; or iii) from about 0.005*R_e * S_c * D_h to about 0.5*R_e * S_c *D_h; wherein: R_e is a Reynolds number of the fluid flowing there through; Pr is a Prandtl number of the fluid flowing there through; S_c is a Schmidt number of the fluid flowing there through; and Dh is the hydraulic diameter of the flow channel when determined under Patent Application Docket EMIS-1015PCT August 17, 2023 Page 41 of 44 operational conditions. 4. The capture device of claim 1, wherein at least one of the plurality of substrates has an aspect ratio from about 0.01 to about 100, wherein the aspect ratio is equal to the flow channel length divided by the larger of a total width of the substrate and a total height of the substrate; and/or wherein a cross sectional area of each flow channel is greater than or equal to about 0.01 mm² and less than or equal to about 500 mm². 5. The capture device of claim 1, wherein a cross sectional area of each flow channel present within each of the plurality of substrates is essentially equal; and/or, wherein a flow channel length of each flow channel present within each of the plurality of substrates is essentially equal. 6. The capture device of claim 1, wherein a cross sectional area and/or a flow channel length of a flow channel present within one of the plurality of substrates is different than a cross sectional area and/or a flow channel length of a flow channel present within another of the plurality of substrates. 7. The capture device of claim 1, wherein a center axis of a flow channel present within the first substrate is colinear with a center axis of a flow channel present within the second substrate; and/or wherein each side of a flow channel present within the first substrate is essentially colinear with each side of a flow channel present within the second substrate. 8. The capture device of claim 1, wherein each side of a flow channel present within the first substrate is not colinear with each side of a flow channel present within the second substrate; and/or wherein a center axis of a flow channel present within the first substrate is not colinear with a center axis of a flow channel present within the second substrate. 9. The capture device of claim 1, wherein a first flow channel present within the first substrate comprises a plurality of sides disposed about a center axis of the first Patent Application Docket EMIS-1015PCT August 17, 2023 Page 42 of 44 flow channel, and a second flow channel present within the second substrate comprises a plurality of sides disposed about a center axis of the second flow channel, wherein the center axis of the first flow channel is colinear with the center axis of the second flow channel, and wherein the sides of the first flow channel are not colinear with the sides of the second flow channel. 10. The capture device of claim 1, wherein the spacing distance between the first substrate and the second substrate is from about 0.2 to about 200 times a hydraulic diameter of a flow channel present within the second substrate, the hydraulic diameter equal to 4 times a cross sectional area of the flow channel divided by a perimeter of the flow channel, and/or wherein the spacing distance between a first substrate and a second substrate is from about 1 mm to about 100 mm; and/or wherein a spacing distance between a first and a second consecutive substrate is different than a spacing distance between the second and a third consecutive substrate. 11. The capture device of any one of claims 1 -10, wherein at least a portion of at least one flow channel comprises an essentially sinusoidal shape, an essentially helical shape oriented radially about a center axis of the flow channel, an essentially helical shape radially arranged about an essentially sinusoidal shape, an essentially sinusoidal shape arranged within an essentially helical shape oriented radially about a center axis of the flow channel, or a combination thereof. 12. The capture device of any one of claims 1 -10, further comprising one or more fluid inlets in direct fluid communication with the space between two or more consecutive substrates. 13. The capture device of any one of claims 1 -10, wherein a first flow channel present within a substrate is in fluid communication with a second flow channel present within the same substrate through at least one side of the first and second flow channels. Patent Application Docket EMIS-1015PCT August 17, 2023 Page 43 of 44 14. The capture device of any one of claims 1 -10, wherein a concentration of the sorbent disposed within a flow channel of the first substrate is different than a concentration of the sorbent disposed within a flow channel of the second substrate; wherein a composition of the sorbent disposed within a flow channel of the first substrate is different than a concentration of the sorbent disposed within a flow channel of the second substrate; or a combination thereof. 15. A method to treat a fluid comprising: directing the fluid comprising a target compound present at an initial concentration through an inlet of the capture device according to any one of claims 1-14, at a flow rate and at a temperature sufficient to produce a treated fluid exiting the capture device through the fluid outlet having a treated concentration of the target compound which is less than the initial concentration.