WO2020247434A1 - Methods of redirecting droplets, and related systems and uses - Google Patents

Abstract

Method and article for redirecting droplets impinging on the article, the article (14, 18, 22) comprising a non-wetting surface (210) having a dynamic contact angle (9d) of at least 90 degrees, the non- wetting surface (210) comprising a plurality of macro-scale features (220) configured to induce momentum redirection of a droplet (20) impinging onto the non-wetting surface (210), thereby reducing an area of contact between the droplet (20) and the non-wetting surface (210).

Description

METHODS OF REDIRECTING DROPLETS. AND RELATED SYSTEMS AND

USES

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(e) of U.S. provisional application serial number 62/857,104 filed June 4, 2019, the disclosure of which is incorporated by reference in its entirety.

TECHNICAL FIELD

Methods of redirecting droplets and related systems and uses thereof are generally described.

SUMMARY

Methods of redirecting droplets are generally described. Inventive systems and uses thereof are also described. For example, in some embodiments, the methods comprise redirecting the momentum of an impinging droplet on a non- wetting surface, such that the area of contact between the droplet and the non-wetting surface is reduced. In some embodiments, the non-wetting surface and/or an article disclosed herein comprises a plurality of macro-scale features and a dynamic contact angle of at least 90 degrees. In some embodiments, the methods and systems disclosed herein are useful for reducing heat transfer ( e.g ., from a roof during rain), reducing salt deposition on a surface exposed to salt water spraying, restricting vapor diffusion into the pores of waterproof clothing, or inducing directional rebound of impinging droplets for rain collection. The subject matter of the present invention involves, in some cases, interrelated products, alternative solutions to a particular problem, and/or a plurality of different uses of one or more systems and/or articles.

Certain aspects are related to articles.

In some embodiments, the article comprises a non-wetting surface having a dynamic contact angle of at least 90 degrees, the non-wetting surface comprising a plurality of macro-scale features configured to induce momentum redirection of a droplet impinging onto the non- wetting surface, thereby reducing an area of contact between the droplet and the non-wetting surface. In certain embodiments, the article comprises a surface constructed and arranged to induce redirection of liquid droplets impinging onto it, comprising a plurality of ring like structures having average diameters between 1 and 10 times the average diameter of the droplets, the ring-like structures comprising a continuous or discontinuous ridge extending, from the remainder of the surface absent the ridge, a distance of greater than or equal to 0.5% of the average thickness of the droplets when a spreading lamella, and where discontinuous, the discontinuity or discontinuities defining no more than 30% of the shape of the ring-like structure.

In some embodiments, the article comprises a surface constructed and arranged to induce redirection of a spreading liquid lamella, comprising a plurality of structures comprising a continuous or discontinuous ridge extending, from the remainder of the surface absent the ridge, a distance of greater than or equal to 0.5% of the average thickness of the spreading liquid lamella, the discontinuity or discontinuities defining no more than 30% of the shape of the structure.

In certain embodiments, the article comprises a surface constructed and arranged to induce redirection of liquid droplets impinging onto it, comprising a plurality of ring like structures having average diameters between 1 and 10 times the average diameter (D) of the droplets and a ratio (h/D) of the average height (h) of the ring-like structures to the average diameter (D) of the droplets between 0.001 and 1, inclusive, the ring-like structures comprising a continuous or discontinuous ridge, and where discontinuous, the discontinuity or discontinuities defining no more than 30% of the shape of the ring-like structure.

Certain aspects are related to methods.

In some embodiments, the method comprises exposing a non-wetting surface to an impinging droplet; redirecting the momentum of the impinging droplet; and reducing an area of contact between the impinging droplet and the non- wetting surface; wherein the non- wetting surface comprises a plurality of macro-scale features and a dynamic contact angle of at least 90 degrees.

Other advantages and novel features of the present invention will become apparent from the following detailed description of various non-limiting embodiments of the invention when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and/or inconsistent disclosure, the present specification shall control. BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. In the figures:

FIG. 1A is a schematic side view of a droplet resting on a surface during a static contact angle measurement, according to an illustrative embodiment of the invention.

FIGS. IB and 1C are schematic side views of a liquid spreading and receding, respectively, on a surface, according to an illustrative embodiment of the invention.

FIG. ID is a schematic side view of a droplet resting on an angled surface, according to an illustrative embodiment of the invention.

FIG. 2A is, in accordance with certain embodiments, a schematic illustration of a top view of a surface comprising a macro-scale ring-like structure comprising a continuous perimeter.

FIG. 2B is, in accordance with certain embodiments, a cross-section of a side view of a surface comprising a macro-scale ring-like structure comprising a continuous perimeter.

FIG. 2C is, in accordance with certain embodiments, a schematic illustration of a side view of a surface comprising a macro-scale ring-like structure comprising a continuous perimeter with an impinging droplet that has not yet contacted the macro scale ring-like structure.

FIG. 2D is, in accordance with certain embodiments, a schematic illustration of the system of FIG. 2C after the impinging droplet has contacted the macro-scale ring-like structure, resulting in the droplet taking on a bowl ( e.g ., a waterbowl) shape.

FIG. 3 is, in accordance with certain embodiments, a schematic illustration of a top view of a surface comprising a macro-scale ring-like structure comprising a substantially continuous perimeter.

FIG 4 is, in accordance with certain embodiments, a schematic illustration of a top view of a surface comprising a plurality of macro-scale features. FIG. 5A shows, in accordance with certain embodiments, chronophotography of an impacting droplet on a flat superhydrophobic surface (top) and on a surface with a ring placed at d/D = 1.3 (bottom). Pictures at time t = 0, 0.8, 2.2, and 4ms after impact, respectively.

FIG. 5B shows, in accordance with certain embodiments, wet area, A, normalized by the maximum spreading area in the control case, Ao. Schematics of impacting droplet in two configurations: without a wall (left) and with a wall (right).

FIGS. 6A-6B show, in accordance with certain embodiments, the interaction parameter of an impacting droplet on a surface with a macroscopic ring texture of diameter d and height h, normalized by that obtained in the reference case of a regular superhydrophobic surface as a function of ring diameter (FIG. 6A) and Weber number of the impinging drop (FIG. 6B). The error bars represent the measurement uncertainty in the interaction parameter (y-axis) and the standard deviation of the drop diameter (x- axis).

FIG. 7A shows, in accordance with certain embodiments, a regime map showing whether the lamella of a drop impacting on a textured ring is ejected (all points to the right of the curve, labeled 2) or overruns the wall (all points to the left of the curve, labeled 1) as a function of normalized wall height and diameter.

FIG. 7B shows, in accordance with certain embodiments, pictures of an overrunning lamella and an ejected lamella. The ring diameter is 3.5 mm.

FIG. 7C shows, in accordance with certain embodiments, schematics of an overrunning lamella and an ejected lamella.

FIG. 7D shows, in accordance with certain embodiments, sine of the ejection angle as a function of the scaled height of the wall for a ring diameter such that d/D =

2.3. The cross shows the standard deviation of the ejection angle measurement and the uncertainty of the scaling factor.

FIG. 7E shows, in accordance with certain embodiments, schematics of the ejection of the lamella at different angles based on the wall height changing.

FIG. 7F shows, in accordance with certain embodiments, pictures of the ejection of the lamella at different angles based on the wall height changing. The drawn line highlights the ejection angle of the lamella.

FIG. 8 shows, in accordance with certain embodiments, contact time, t_c, and dimensionless Interaction parameter, Flo, as a function of offset between the center of the droplet and the center of the ring, e. The drop diameter, D, is 2.13mm, the ring diameter, d, is 5mm, and the ring height, h, is 200pm. The dashed lines are guides for the eye.

FIG. 9A shows, in accordance with certain embodiments, a schematic of the experimental setup facilitating the simulation of rain on a periodic substrate and the measure of the substrate temperature.

FIG. 9B shows, in accordance with certain embodiments, a picture of impacting rain droplets on the substrate with enhanced ring diameter.

FIG. 9C, left, shows, in accordance with certain embodiments, surface temperature drop, DT, normalized by the equilibrium temperature drop on a control superhydrophobic surface, DTo, on substrates with different textures, where the shaded areas represent the standard deviation between samples. FIG. 9C, right, shows, in accordance with certain embodiments, photographs of the different textures used in FIG. 9C, left, (the scale bar represents 5mm).

DETAILED DESCRIPTION

Disclosed herein are methods of redirecting droplets (and/or the momentum thereof) and related articles, systems, and uses thereof. In some embodiments, the articles described herein comprise a surface ( e.g ., a non-wetting surface). In certain embodiments, the article and/or surface comprises (or is part of) roofing, external building surfaces, siding, construction materials, aircraft wings, turbine blades, power cables, fabric, and/or a garment. In some embodiments, the surface has a dynamic contact angle of at least 90 degrees and comprises a plurality of features (e.g., macro scale features, such as macro-scale ring-like structures). In certain cases, the plurality of features (e.g., macro-scale features and/or ring-like structures) is configured such that an impinging droplet (e.g., a rain droplet), and/or the momentum thereof, is redirected upon contacting the features.

In some embodiments, the redirection of the droplet (and/or the momentum thereof) is accomplished by inducing a shape change of the spreading droplet, for example, into the shape of a bowl (e.g., a waterbowl). In some embodiments, the height, diameter, pattern, shape, and/or spacing of the features are selected such that the features can induce a change in the shape of a droplet of interest (e.g., a rain droplet) to that of a bowl (e.g., a waterbowl). For example, in some embodiments a ring-like structure with a diameter larger than that of the droplet of interest may be selected to induce a change in the shape of the droplet of interest to that of a bowl ( e.g ., a waterbowl) upon contacting an area of the surface within the ring-like structure. In some embodiments, arranging the features (e.g., the ring-like structures) in a periodic pattern amplifies the result, such that numerous droplets of interest are changed into the shape of a bowl (e.g., a waterbowl).

In some embodiments, this change in the shape of the spreading droplet into that of a bowl (e.g., a waterbowl) results in a reduction in contact area between the droplet and the surface. A reduction in contact area between a droplet and a surface can provide one or more of a variety of possible benefits. For example, reducing the contact area between a droplet and a surface could be useful in reducing heat transfer (e.g., reducing heat transfer from a home during a rainstorm), reducing salt deposition on a surface exposed to salt water spraying, restricting vapor diffusion into the pores of waterproof clothing, or inducing directional rebound of impinging droplets for rain collection.

Additional details regarding the properties and operation of the articles, systems, and methods are provided below.

Certain aspects are related to articles, systems, and methods for redirecting droplets. Non-limiting examples of such articles, systems, and methods are shown in FIGS. 1A-9C.

In certain embodiments, the article comprises a surface. For example, FIG. 2A comprises surface 210. In some embodiments, the surface has a dynamic contact angle of at least 90 degrees. For example, in some embodiments, the surface (e.g., a non wetting surface) has a dynamic contact angle of at least 100 degrees, at least 120 degrees, at least 140 degrees, or at least 160 degrees. In certain embodiments, the dynamic contact angle is less than or equal to 170 degrees, less than or equal to 150 degrees, less than or equal to 130 degrees, or less than or equal to 110 degrees. Combinations of these ranges are also possible (e.g., 90-130 degrees).

Referring to FIG. 1A, in certain embodiments, a static contact angle Q between a liquid and solid is defined as the angle formed by liquid drop 12 on solid surface 14 as measured between a tangent at the contact line, where the three phases— solid, liquid, and vapor— meet, and the horizontal. The term "contact angle" usually implies the static contact angle Q since the liquid is merely resting on the solid without any movement.

As used herein, dynamic contact angle, O_d, is a contact angle made by moving liquid 16 on solid surface 18. In the context of droplet impingement, 9_d may exist during either advancing or receding movement, as shown in FIGS. IB and 1C, respectively. In certain embodiments, the surface is a non-wetting surface. As used herein, a surface is "non-wetting" if it has a dynamic contact angle with a liquid of at least 90 degrees. Examples of non- wetting surfaces include, for example, superhydrophobic surfaces and superoleophobic surfaces.

As used herein, contact angle hysteresis (CAH) is:

CAM = q_a - 0_r,

where 0_a and 0_r are advancing and receding contact angles, respectively, formed by liquid 20 on solid surface 22. Referring to FIG. ID, the advancing contact angle 0_a is the contact angle formed at the instant when a contact line is about to advance, whereas the receding contact angle 0_r is the contact angle formed when a contact line is about to recede.

As used herein, "non-wetting features" are physical textures (e.g., random, including fractal, or patterned surface roughness) on a surface that, together with the surface chemistry, make the surface non-wetting. In certain embodiments, non-wetting features result from chemical, electrical, and/or mechanical treatment of a surface. In certain embodiments, an intrinsically hydrophobic surface may become

superhydrophobic when non- wetting features are introduced to the intrinsically hydrophobic surface. Similarly, an intrinsically oleophobic surface may become superoleophobic when non-wetting features are introduced to the intrinsically oleophobic surface. Likewise, an intrinsically metallophobic surface may become

supermetallophobic when non- wetting features are introduced to the intrinsically metallophobic surface.

In certain embodiments, non-wetting features are micro-scale or nano-scale features. For example, the non-wetting features may have a length scale L_n (e.g., an average pore diameter, or an average protrusion height) that is less than 100 microns, less than 10 microns, less than 1 micron, less than 0.1 microns, or less than 0.01 microns. Compared to a length scale L_m associated with macro-scale features, described herein, the length scales for the non- wetting features are typically at least an order of magnitude smaller. For example, when a surface includes a macro-scale feature that has a length scale L_m of 100 microns, the non-wetting features on the surface can have a length scale L_n that is less than 10 microns. In certain embodiments a ratio of the length scale for the macro-scale features to the length scale for the non-wetting features (i.e., L_m / L_n) is greater than 10, greater than 100, greater than 1000, or greater than 10,000.

In certain embodiments, the non-wetting surface is superhydrophobic, superoleophobic, and/or supermetallophobic. In some embodiments, the surface includes a non-wetting material. In some cases, the surface may be heated above the Leidenfrost temperature.

In certain embodiments, the surface (e.g., the non- wetting surface) includes an alkane (e.g., an alkane functionalization). In one embodiment, the surface includes a fluoropolymer. In certain embodiments, the surface includes at least one of teflon, trichloro(lH,lH,2H,2H-perfluorooctyl)silane (TCS), octadecyltrichlorosilane (OTS), heptadecafluoro-l,l,2,2-tetrahydrodecyltrichlorosilane, fluoroPOSS, a ceramic material, a polymeric material, a fluorinated material, an intermetallic compound, and a composite material. In certain embodiments, the surface includes a polymeric material, the polymeric material including at least one of polytetrafluoroethylene, fluoroacrylate, fluoroeurathane, fluorosilicone, fluorosilane, modified carbonate, chlorosilanes, and silicone. In certain embodiments, the surface includes a ceramic material, the ceramic material including at least one of titanium carbide, titanium nitride, chromium nitride, boron nitride, chromium carbide, molybdenum carbide, titanium carbonitride, electroless nickel, zirconium nitride, fluorinated silicon dioxide, titanium dioxide, tantalum oxide, tantalum nitride, diamond-like carbon, and fluorinated diamond-like carbon. In certain embodiments, the surface includes an intermetallic compound, the intermetallic compound including at least one of nickel aluminide and titanium aluminide.

As used herein, a "superhydrophobic" surface is a surface having a static contact angle with water of at least 120 degrees and a CAH of less than 30 degrees. In certain embodiments, an intrinsically hydrophobic material (i.e., a material having an intrinsic contact angle with water of at least 90 degrees) exhibits superhydrophobic properties when it includes non-wetting features. For superhydrophobicity, typically nano-scale non-wetting features are preferred. Examples of intrinsically hydrophobic materials that exhibit superhydrophobic properties when given non-wetting features include:

hydrocarbons, such as alkanes, and fluoropolymers, such as teflon,

trichloro(lH,lH,2H,2H-perfluorooctyl)silane (TCS), octadecyltrichlorosilane (OTS), heptadecafluoro- 1 , 1 ,2,2-tetrahydrodecyltrichlorosilane, and fluoroPOSS . As used herein, a "superoleophobic" surface is a surface having a static contact angle with oil of at least 120 degrees and a CAH with oil of less than 30 degrees. The oil may be, for example, a variety of liquid materials with a surface tension much lower than the surface tension of water. Examples of such oils include alkanes (e.g., decane, hexadecane, octane), silicone oils, and fluorocarbons. In certain embodiments, an intrinsically oleophobic material (i.e., a material having an intrinsic contact angle with oil of at least 90 degrees) exhibits superoleophobic properties when it includes non wetting features. The non-wetting features may be random or patterned. Examples of intrinsically oleophobic materials that exhibit superoleophobic properties when given non-wetting features include: teflon, trichloro(lH,lH,2H,2H-perfluorooctyl) silane (TCS), octadecyltrichlorosilane (OTS), heptadecafluoro-1,1,2,2- tetrahydrodecyltrichlorosilane, fluoroPOSS, and other fluoropolymers.

As used herein, a "supermetallophobic" surface is a surface having a static contact angle with a liquid metal of at least 120 degrees and a CAH with liquid metal of less than 30 degrees. In certain embodiments, an intrinsically metallophobic material (i.e., a material having an intrinsic contact angle with liquid metal of at least 90 degrees) exhibits supermetallophobic properties when it includes non-wetting features. The non wetting features may be random or patterned. Examples of intrinsically metallophobic materials that exhibit supermetallophobic properties when given non- wetting features include: teflon, trichloro(lH,lH,2H,2H-perfluorooctyl)silane (TCS),

octadecyltrichlorosilane (OTS), heptadecafluoro- 1 , 1 ,2,2-tetrahydrodecyltrichlorosilane, fluoroPOSS, and other fluoropolymers. Examples of metallophobic materials include molten tin on stainless steel, silica, and molten copper on niobium.

In certain embodiments, intrinsically hydrophobic materials and/or intrinsically oleophobic materials include ceramics, polymeric materials, fluorinated materials, intermetallic compounds, and composite materials. Polymeric materials may include, for example, polytetrafluoroethylene, fluoroacrylate, fluoroeurathane, fluorosilicone, fluorosilane, modified carbonate, chlorosilanes, silicone, and/or combinations thereof. Ceramics may include, for example, titanium carbide, titanium nitride, chromium nitride, boron nitride, chromium carbide, molybdenum carbide, titanium carbonitride, electroless nickel, zirconium nitride, fluorinated silicon dioxide, titanium dioxide, tantalum oxide, tantalum nitride, diamond-like carbon, fluorinated diamond-like carbon, and/or combinations thereof. Intermetallic compounds may include, for example, nickel aluminide, titanium aluminide, and/or combinations thereof.

As used herein, an intrinsic contact angle is a static contact angle formed between a liquid and a perfectly flat, ideal surface. This angle is typically measured with a goniometer. The following publications, which are hereby incorporated by reference herein in their entireties, describe additional methods for measuring the intrinsic contact angle: C. Allain, D. Aussere, and F. Rondelez, J. Colloid Interface Sci., 107, 5 (1985); R. Fondecave, and F. Brochard-Wyart, Macromolecules, 31, 9305 (1998); and A. W.

Adamson, Physical Chemistry of Surfaces (New York: John Wiley & Sons, 1976).

When a liquid droplet impacts a non-wetting surface, the droplet will spread out on the surface and then begin to recoil. For highly non-wetting surfaces, the droplet can completely rebound from the surface. Through the impact dynamics, the shape of the droplet is generally axisymmetric so that, at any point in time during recoil, the wetted area is substantially circular. By patterning the surface, however, the shape of the droplet may be altered or controlled, such that the contact area of the droplet with the surface may be increased or decreased. For example, by controlling or defining macro-scale features on the surface, the droplet may be shaped into a bowl (e.g., a waterbowl), such that the contact area of the droplet with the surface is reduced.

At points of contact between a droplet and a surface, heat, mass, and momentum diffuse between the droplet and the surface. By controlling the contact area between a droplet and the surface, this diffusion may be optimized both temporally and spatially. This can be done, for example, by including macro-scale features (e.g., ring-like structures) that induce redirection of an impinging droplet (and/or the momentum thereof). For example, in some embodiments, the use of macro-scale ring-like structures on a surface (e.g., a non- wetting surface) causes an impinging droplet to be shaped into a bowl (e.g., a waterbowl), such that it (and/or its momentum) is redirected, and the contact area between the droplet and the surface is reduced.

The shape in which an impinging droplet spreads depends not only on the material properties of the droplet, but also the properties of the surface the droplet contacts. On non-wetting surfaces, the contact area between the droplet and the surface can be reduced by the shape in which the droplet spreads. Variations in shape of the droplet may be achieved by changing the structure and/or chemistry of the surface patterns that form the non- wetting surface. For example, when the surface comprises macro-scale features ( e.g ., ring-like structures), the spreading droplet can be shaped into a bowl (e.g., a waterbowl). In some embodiments, this is affected by the diameter of the ring-like structures, the height of the ring-like structures, the spacing between the ring like structures, and/or the pattern of the ring-like structures.

In certain embodiments, surfaces (e.g., non-wetting surfaces) are designed that introduce a bowl (e.g., a waterbowl) shape into the spreading droplet. Using these designs, the surfaces are tailored so that the contact area between the surface and the droplets in certain regions is smaller than it may be in other regions. In some

embodiments, ring-like structures shape the spreading droplet into a bowl (e.g., a waterbowl).

As described herein, a smaller contact area between a droplet and a surface (e.g., a non-wetting surface) is possible using patterned surfaces. Specifically, if during the spreading stage, the shape of the droplet is modified to that of a bowl (e.g., a waterbowl), the resulting contact area will be smaller. As described below, in certain embodiments, a bowl (e.g., a waterbowl) shape is introduced by ring-like structures (e.g., macro-scale features) on the surface.

In certain embodiments, the surface comprises a plurality of macro-scale features (e.g., ring-like structures). For example, FIG. 2A shows a portion of surface 210 with macro-scale feature 220, while the top three photos on the right side of FIG. 9C and FIG. 4 show a portion of a surface that has a plurality of macro-scale features. The macro scale features may have, for example, a dimension (e.g., diameter and/or height) greater than or equal to 0.001 mm, greater than or equal to 0.01 mm, greater than or equal to 0.1 mm, greater than or equal to 1 mm, or greater than or equal to 5 mm. The macro-scale features may have, for example, a dimension (e.g., diameter and/or height) less than or equal to 10 mm, less than or equal to 5 mm, less than or equal to 1 mm, less than or equal to 0.1 mm, or less than or equal to 0.01 mm. Combinations of these ranges are also possible (e.g., 0.1 to 10 mm, inclusive).

In some embodiments, the average diameter (d) of the macro-scale features (e.g., ring-like structures) is larger than the average diameter (D) of the droplet(s). In some embodiments, the ratio (d/D) of the average diameter (d) of the macro-scale features (e.g., ring-like structures) to the average diameter (D) of the droplet(s) is greater than or equal to 1, greater than or equal to 1.5, greater than or equal to 2, greater than or equal to 3, greater than or equal to 4, greater than or equal to 5, greater than or equal to 10, greater than or equal to 25, greater than or equal to 50, or greater than or equal to 75. In some embodiments, the ratio (d/D) of the average diameter (d) of the macro-scale features ( e.g ., ring-like structures) to the average diameter (D) of the droplet(s) is less than or equal to 100, less than or equal to 75, less than or equal to 50, less than or equal to 25, less than or equal to 10, less than or equal to 5, less than or equal to 4, less than or equal to 3, less than or equal to 2, or less than or equal to 1.5. Combinations of these ranges are also possible (e.g., in some embodiments, the macro-scale features (e.g., ring like structures) have an average diameter (d) between 1 and 100, inclusive; 1 and 10, inclusive; 1 and 5, inclusive; 1 and 2, inclusive; or 1 and 1.5, inclusive; times the average diameter (D) of the droplet(s)). The diameter is calculated by measuring the smallest cross-sectional dimension. For example, in FIG. 2B, diameter 230 is the smallest cross- sectional dimension of macro-scale feature 220.

In some embodiments, a relatively large percentage of the macro-scale features have cross-sectional diameters that are at least as large as (e.g., between 1 and 1.5 times) the average size of incoming liquid droplets. For example, in some embodiments, at least 30%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 90%, at least 95%, or more of the macro-scale features have cross-sectional diameters that are at least as large as (e.g., between 1 and 1.5, or between 1 and 1.4, or between 1 and 1.3, or between 1 and 1.2 times) the average size of incoming liquid droplets.

In certain cases, the ratio (h/D) of the average height (h) of the macro-scale features to the average diameter of the droplets (D) is greater than or equal to 0.001, greater than or equal to 0.005, greater than or equal to 0.01, greater than or equal to 0.05, greater than or equal to 0.1, or greater than or equal to 0.5. In some embodiments, the average height (h) of the macro-scale features is less than or equal to 1, less than or equal to 0.5, less than or equal to 0.1, less than or equal to 0.05, less than or equal to 0.01, or less than or equal to 0.005. Combinations of these ranges are also possible (e.g., 0.001- 1, inclusive; or 0.01-0.1, inclusive).

As used herein, unless specified otherwise,“average” refers to a numerical average.

In certain embodiments, at least a portion of the macro-scale features (e.g., ring like structures) are arranged in a periodic pattern. As a non-limiting example, FIG. 9B and the top three photos on the right side of FIG. 9C show ring-like macro-scale features arranged in periodic patterns. In some embodiments, greater than or equal to 30%, greater than or equal to 50%, greater than or equal to 70%, or greater than or equal to 90% of the macro-scale features are arranged in a periodic pattern.

In some embodiments, the macro-scale features form a collection of ring like structures in contact with each other to form an aggregated array. Examples of such aggregated arrays are shown, for example, in FIGS. 9B and the top three photos on the right of 9C.

Additionally, the macro-scale features ( e.g ., ring-like structures) may have, for example, a ratio of the average spacing between each of the macro-scale features (e.g., ring-like structures) to the average droplet diameter (D) greater than or equal to 1, greater than or equal to 2, greater than or equal to 3, greater than or equal to 4, greater than or equal to 5, greater than or equal to 10, or greater than or equal to 15. In some

embodiments, the ratio of the average spacing between each of the macro-scale features (e.g., ring-like structures) to the average droplet diameter (D) is less than or equal to 20, less than or equal to 15, less than or equal to 10, less than or equal to 5, less than or equal to 4, or less than or equal to 2. Combinations of these ranges are also possible (e.g., 1- 20, inclusive; or 1-4, inclusive). The“average spacing” between a plurality of macro scale features refers to the average of the nearest neighbor distances of those features, where, for each feature, the nearest neighbor distance is the shortest distance between the geometric center of that feature and the geometric center of another feature within the plurality of features. For example, in FIG. 4, surface 410 comprises macro-scale features 420, and spacing 480 is the shortest distance between the geometric centers of macro scale features 420.

In some embodiments, the surface is constructed and arranged to induce redirection of liquid droplets impinging onto it. In certain embodiments, the plurality of macro-scale features is configured to induce redirection of a droplet impinging onto the surface, and/or redirection of the momentum of a droplet impinging onto the surface. In certain cases, this redirection reduces the contact area between the droplet and the surface. In some embodiments, the method comprises exposing a non-wetting surface to an impinging droplet, redirecting the momentum of the impinging droplet, and reducing the area of contact between the impinging droplet and the non-wetting surface.

In some embodiments, the surface comprises a plurality of ring-like structures.

In certain embodiments, at least a portion of the macro-scale features are ring-like. For example, in some embodiments, greater than or equal to 30%, greater than or equal to 50%, greater than or equal to 70%, or greater than or equal to 90% of the macro-scale features are ring-like. Examples of ring-like structures include a perfect or imperfect circle, a perfect or imperfect oval, a perfect or imperfect hexagon, a perfect or imperfect pentagon, a perfect or imperfect heptagon, a perfect or imperfect octagon, a perfect or imperfect nonagon, a perfect or imperfect polygon with 10 or more sides, and/or combinations thereof. As a non-limiting example, FIG. 9B and the top three photos on the right side of FIG. 9C show macro-scale features/ring-like structures that are circles.

In some embodiments, all or a portion of the macro-scale features (e.g., greater than or equal to 30%, greater than or equal to 50%, greater than or equal to 70%, or greater than or equal to 90% of the macro-scale features) are substantially circular. A shape is considered to be“substantially circular” when the radius of the shape does not deviate, along the perimeter of the shape, by more than 25% of the average radius of the shape (where the radius is the distance from the geometric center of the shape to the perimeter of the shape).

In some embodiments, the macro-scale features have relatively low aspect ratios. For example, in some cases, at least 30%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, at least 90%, at least 95%, or more of the macro-scale features have aspect ratios of less than 3:1, less than 2.5:1, less than 2:1, less than 1.5:1, less than 1.3:1, less than 1.2:1, or less than 1.1:1. The aspect ratio of a macro-scale feature refers to the ratio of its longest cross-sectional dimension to its shortest cross-sectional dimension when viewed from above. For example, referring to FIG. 2A, when viewed from above, the aspect ratio of macro-scale feature 220 is the ratio of diameter 230 (dimension Y), which is the shortest cross-section, to largest cross-section 280

(dimension Z).

In some embodiments, at least a portion of the macro-scale features (e.g., ring like structures) each comprise a continuous or discontinuous perimeter (e.g. , ridge) extending, from the remainder of the surface absent the ridge, a distance. In certain cases, the distance is no more than 0.5 times, no more than 0.4 times, no more than 0.3 times, no more than 0.2 times, or no more than 0.1 times the diameter of the macro-scale feature (e.g., ring-like structure). In some cases, the distance is greater than or equal to 0.1 times, greater than or equal to 0.2 times, greater than or equal to 0.3 times, or greater than or equal 0.4 times the diameter of the macro-scale feature (e.g., ring-like structure). Combinations of these ranges are also possible (e.g., 0.1-0.5 times). For example, in FIG. 2B, macro-scale feature 220 comprises a continuous or discontinuous perimeter ( e.g ., ridge) extending, from surface 210, height 240, wherein height 240 is no more than 0.5 times, for example, diameter 230 of macro-scale feature 220.

In some embodiments, at least a portion of the macro-scale features (e.g., ring like structures) each comprises a continuous or discontinuous perimeter (e.g., ridge) extending, from the remainder of the surface absent the ridge, a distance. In certain cases, this distance is greater than or equal to 0.5%, greater than or equal to 1%, greater than or equal to 5%, greater than or equal to 10%, greater than or equal to 30%, greater than or equal to 50%, or greater than or equal to 100% of the average thickness of the lamella,

L_t. In some instances, this distance is less than or equal to 500%, less than or equal to 250%, less than or equal to 100%, less than or equal to 50%, less than or equal to 30%, less than or equal to 10%, or less than or equal to 5% of the average thickness of the lamella, L_t. Combinations of these ranges are also possible (e.g., 30-100%). For example, in FIG. 2B, macro-scale feature 220 comprises a continuous or discontinuous perimeter (e.g., ridge) extending, from surface 210, height 240, wherein height 240 is greater than or equal to 30%, for example, lamella thickness 10 defined in FIG 1C.

In some embodiments, the height of the lamella is dictated by the merging of the viscous boundary layer with the free surface of the liquid such that

oc D Re^~2^⁵.

In some embodiments, at least a portion of the macro-scale features (e.g., ring like structures) each comprise a discontinuous perimeter (e.g., ridge). For example, FIG. 3 shows surface 310 comprising macro-scale feature 320 comprising perimeter 325, wherein perimeter 325 is discontinuous. In some embodiments, at least a portion of the macro-scale features (e.g., ring-like structures) each comprise a continuous perimeter (e.g., ridge). For example, FIG. 2A shows surface 210 comprising macro-scale feature 220 comprising perimeter 225, wherein perimeter 225 is continuous. In some

embodiments, at least a portion of the macro-scale features (e.g., ring-like structures) each comprise a substantially continuous perimeter (e.g., ridge). For example, FIG. 3 shows surface 310 comprising macro-scale feature 320 comprising perimeter 325, wherein perimeter 325 is substantially continuous. In some embodiments, greater than or equal to 30%, greater than or equal to 50%, greater than or equal to 70%, or greater than or equal to 90% of the macro-scale features comprise a substantially continuous perimeter. In some embodiments, the substantially continuous perimeter comprises discontinuity or discontinuities defining less than or equal to 90%, less than or equal to 80%, less than or equal to 70%, less than or equal to 60%, less than or equal to 50%, less than or equal to 40%, less than or equal to 30%, less than or equal to 20%, less than or equal to 10%, less than or equal to 1%, or 0% of the shape of the macro-scale features ( e.g ., ring-like structure). The percent discontinuity is calculated by extending the implied shape to make a continuous perimeter, and then calculating the percentage of the perimeter that needed to be extended versus the total perimeter of the shape once extended. For example, in FIG. 3, there are four points of discontinuity in perimeter 325 and the implied shape of macro-scale feature 320 is a circle. The percent discontinuity of macro-scale feature 320 is calculated as follows: (the total perimeter that would need to be added over the four points of discontinuity to make a continuous circle) / (the perimeter of the continuous circle) * 100.

In certain embodiments, a ratio of the height of the average height, h, of the macro-scale features (e.g., height 240 of FIG. 2B) to the average thickness of the lamella, L_t (e.g., lamella thickness 10 of FIG. 1C) (i.e., h / L_t) is greater than or equal to 0.005, greater than or equal to 0.01, greater than or equal to 0.1, greater than or equal to 1, greater than or equal to 2.5, or greater than or equal to 5. In some embodiments, the ratio of the height of the macro-scale feature, h, to the lamella thickness, L_t, is less than or equal to 10, less than or equal to 5, less than or equal to 2.5, less than or equal to 1, or less than or equal to 0.1. Combinations of these ranges are also possible (e.g., 0.01-10, inclusive).

As used herein, the term“lamella” refers to a thin layer of liquid spreading on the surface (e.g., a pancake-shaped volume of liquid on the surface during the spreading stage of a droplet). For example, liquid 16 in FIG. 1C is a lamella.

In certain embodiments, to achieve or maintain superhydrophobicity, the surface includes non-wetting features having a length scale L_n. As mentioned above, the non wetting features are chosen so that O_d is greater than 90 degrees and CAH is less than 30 degrees, less than 20 degrees, or less than 10 degrees.

In some embodiments, the methods, articles, and systems described herein lead to a major reduction (e.g., over 30%) in the contact area compared to the contact area the surface would exhibit in the absence of the macro-scale features but under otherwise identical conditions. In some embodiments, the reduction in contact area is greater than or equal to 30%, greater than or equal to 40%, greater than or equal to 50%, greater than or equal to 60%, greater than or equal to 70%, greater than or equal to 80%, or greater than or equal to 90%, and/or up to 95%, up to 99%, or more.

In certain embodiments, the methods, articles, and systems described herein may be used in a wide variety of industries and applications where droplet repellency is desirable. For example, textile companies that manufacture rainproof fabrics, such as rainwear, umbrellas, automobile covers, etc., could significantly improve fabric waterproof performance, in some embodiments. Likewise, energy companies that manufacture steam turbines could reduce moisture-induced efficiency losses caused by water droplets entrained in steam, which impinge on turbine blades and form films, thereby reducing power output, in some embodiments. Condensers in power and desalination plants may utilize some embodiments of the articles, systems, and methods described herein to promote dropwise shedding condensation heat transfer. Further, in aircraft and wind turbine applications, a reduced contact time of supercooled water droplets impinging upon aircraft surfaces is desirable to prevent the droplets from freezing and thereby degrading aerodynamic performance. In atomizer applications, the ability of surfaces to break up droplets can be used to create new atomizers for applications in engines, agriculture, and pharmaceutical industries. In gas turbine compressors, the articles, systems, and methods described herein may be used to prevent oil-film formation and reduce fouling.

In some embodiments, the methods, articles, and systems described herein have a wide range of applications, including in rainproof products, wind turbine blades, steam turbine blades, aircraft wings, engine blades, atomizers, condensers, and/or gas turbine blades. In some embodiments, the article comprises (or is part of) a rainproof product, wind turbine blade, steam turbine blade, exterior aircraft part ( e.g ., aircraft wing), engine blade, atomizer, condenser, garment, condenser, drip shield for storage of radioactive material, self-cleaning solar panel, roofing, external building surfaces, power cables, siding, construction materials, fabric, and/or gas turbine blade. Table 1 presents typical droplet radius values for several of these applications. As indicated, for rainproof products and wind turbine applications, droplet radius values may be from 0.1 mm to 5 mm. Similarly, for steam turbine blades, aircraft icing, and gas turbine blade

applications, droplet radius values may be from 0.01 mm to 5 mm. In one embodiment, for rainproof products and wind turbine applications, lamella thickness values are from 0.01 mm to 1 mm,

values are from 5 to 100. In another embodiment, for steam turbine blades, aircraft icing, and gas turbine blade applications, lamella thickness values are from 0.001 mm to 1 mm, and x_{w c} values are from 5 to 100.

In certain embodiments, Table 1 is used to identify appropriate dimensions for the macro-scale features (e.g., ring-like structures) described above for reducing the contact area between an impinging droplet and a surface. For example, referring to Table 1, if the intended application is rainproof products and the feature type is a periodic ring-like structure, then appropriate feature dimensions are a diameter of 0.15-7 mm and a height of 0.01-0.5 mm, with enhanced results for a d/D of 1.3 and a h/D of 0.05-0.1. Likewise, if the intended application is steam turbine blades and the feature type is a periodic ring-like structure, then appropriate feature dimensions are a diameter of 0.15-7 mm and a height of 0.002-0.5 mm, with enhanced results for a d/D of 1.3 and a h/D of 0.05-1.

As indicated in Table 1, d may be 0.15-7 mm, in certain embodiments. In certain embodiments, h may be 0.01-0.5 or 0.002-0.5 mm. In some cases, d/D may be 1.3. In certain instances, h/D may be 0.05-0.1.

TABLE 1

Ranges for droplet radius and macro-scale feature dimensions.

In alternative embodiments, the methods, articles, systems, and uses described herein apply to droplets of oil-based liquids impinging on an oleophobic surface or a superoleophobic surface. In this case, the macro-scale features may produce oil droplet impingement dynamics that are similar to those shown and described for water droplets impinging a hydrophobic or superhydrophobic surface.

In certain embodiments, when a water droplet impinges a surface that is hot enough to vaporize the liquid quickly and generate sufficient pressure, the droplet can spread and rebound without ever touching the surface, mimicking a situation seen in superhydrophobic surfaces. This so-called Leidenfrost phenomenon is an example of a non-wetting situation without the surface being superhydrophobic. In one embodiment, the macro-scale features applied to this type of surface are effective in reducing the contact area of an impinging droplet. Specifically, the droplet dynamics are similar to those described above for the superhydrophobic surfaces, and the contact area reduction is of similar magnitude (about 50% of the theoretical limit). In one embodiment, to achieve the desired non- wetting behavior, the surface is heated to a temperature greater than the Leidenfrost temperature.

Blades of steam and gas turbines are sometimes fouled by metallic fragments that are produced due to erosion/corrosion of intermediary equipment in the power cycle. These fragments are carried along with the working fluid (steam or combustion gases, as the case may be) and melt when they reach regions of high temperatures. The melted liquid impinges upon turbine blades and gets stuck thereby deteriorating aerodynamic performance and hence turbine power output. In some embodiments, the methods, articles, and systems disclosed herein can solve this problem by rapidly repelling the impinging molten liquid before it can freeze on blade surfaces.

The following examples are intended to illustrate certain embodiments of the present invention, but do not exemplify the full scope of the invention.

EXAMPLE 1

This example describes methods of redirecting droplets and related systems and uses thereof.

In this example, surfaces were designed to redirect the momentum of spreading lamella causing them to lift-off into 3-dimensional shapes thereby dramatically reducing the contact area with the surface. Superhydrophobic surfaces with an in-plane discontinuity leading to an accumulation of vertical momentum resulting in an out-of- plane ejection of the lamella into water bowls were designed. In this example, the amount of energy or mass exchanged was equal to the flux through the contact area over the contact time. A two-fold reduction in the heat transfer between a cold rain and a warm surface was demonstrated. In some embodiments, this technique can be broadly applied to other transport phenomena involving mass and energy exchange to limit heat loss under precipitation, icing of surfaces, reduce salt deposition on a surface exposed to ocean spray, or inhibit the formation of a water film on wings or wind turbine blades. Drops impacting a surface are found in a variety of both natural and industrial phenomena such as rain, inkjet printing, thermal or agricultural sprays. During the impact, energy and mass transport can occur between the liquid and solid. It is often desirable to control the exchanges happening at the interface such as to limit the heat loss through a roof or restrict the salt deposition from ocean spray. Depending on the impact conditions and the substrate, the outcome of a drop impact can vary from a puddle of liquid to splashing and rebounding, providing a first level of control over the liquid- solid interaction.

FIG. 5A shows, in accordance with certain embodiments, a chronophotography of an impacting droplet on a flat superhydrophobic surface (top) and on a surface with a ring placed at d/D = 1.3 (bottom). Pictures at time t = 0, 0.8, 2.2, and 4ms after impact, respectively. FIG. 5B shows, in accordance with certain embodiments, wet area, A, normalized by the maximum spreading area in the control case, Ao. Schematics of impacting droplet in two configurations: without a wall (left) and with a wall (right).

In FIG. 5A, top row, the droplet spread horizontally along the surface to form an elongated pancake. The maximum spreading diameter of this pancake, Dmax, resulted from the balance of inertia and capillary forces and was shown to scale as D_max oc D M/e¹/⁴, where D is the diameter of the impinging droplet and the Weber number (We = pV²D /s) is the ratio of inertial to capillary forces. The total solid area exposed to the liquid was shown to scale as A_{0 <}x D²We¹^². On a superhydrophobic surface, the real contact area is actually a fraction of the apparent contact area scaled by the solid fraction of the rough substrate, f. Since the roughness of all the substrates in this study was identical, the scaling factor was omitted f for clarity.

To quantify the interaction between an impinging liquid droplet and a solid substrate, it was shown that flux-based transport phenomena occur through the contact area, A(t), during the contact time, T_c. Interaction parameter, /, which controls transport, was defined as the integral of the liquid-solid contact area over time:

It was demonstrated that both the contact time and area participate in the interaction between the liquid and solid. In this example, surfaces were designed that can restrict the liquid- solid contact area during the impact, thereby reducing the interaction parameter. These surfaces comprised macroscopic rings a few hundred microns tall that were decorated with a hierarchical micro/nano texture (see methods). When a drop impacted these surfaces, the spreading momentum was redirected vertically and the lamella was ejected upwards to form a 3-dimensional structure in the shape of a water bowl as shown in FIG. 5A, bottom row. The retraction phase was similar to that following an impact on a superhydrophobic surface, except that it happened away from the surface until it reached the rim of the texture. Notably, the substrate area beyond the ring remained dry during the entire impact.

FIG. 5B shows the interaction parameter as the area under the curve for a drop impact on a plain superhydrophobic surface and with an ejecting ring, of height h and diameter d. The overall contact time was not significantly affected by the presence of the ring as the droplet spread to a similar diameter in both cases. However, in the presence of the ring, most of the spreading happened in air, away from the surface. Therefore, the affected contact area was capped by that of the ring leading to an interaction parameter,

7, typically an order of magnitude smaller than that on the control substrate, 7₀. The circular ring facilitated the conversion of part of the horizontal momentum of the lamella in vertical momentum, such that the entire lamella was ejected away from the surface in FIG. 5B, right.

To further investigate the effect of the ring on the transport, interaction parameter, 7, was measured normalized by that obtained in the reference case of a regular superhydrophobic surface, 7₀, as a function of the ring diameter, d, for We = 144. FIGS. 6A-6B show, in accordance with certain embodiments, the interaction parameter of an impacting droplet on a surface with a macroscopic ring texture of diameter d and height h, normalized by that obtained in the reference case of a regular superhydrophobic surface as a function of ring diameter (FIG. 6A) and Weber number of the impinging drop (FIG. 6B). The error bars represent the measurement uncertainty in the interaction parameter (y-axis) and the standard deviation of the drop diameter (x-axis).

When the diameter of the ring was too large, it never intersected the spreading lamella (7/7₀ = 1). In contrast, when the ring was smaller than the diameter of the impinging droplet ( d / D < 1) the drop overran the wall leading to no reduction in interaction (7/7₀ = 1). It was demonstrated that between these limiting cases, there is a range of diameters that result in a reduced interaction parameter. In this regime, the interaction parameter was experimentally observed to increase quadratically (black solid line) with the ring diameter.

Indeed, in the control case of a droplet impacting a superhydrophobic surface, the affected area scaled a

and the contact time, t₀, was independent of the Weber number and scaled with the inertial-capillary timescale such that t₀ oc (pD³)/o , were p is the density of the liquid. Therefore, the interaction parameter in the control case scaled as /₀ oc

By contrast, in the case of an impact on a microtextured ring, the spreading of the droplet on the substrate was restricted to the diameter of the ring, d. In addition, FIG. 5A suggests that the lamella spread a similar distance in both cases albeit the spreading happened in air for the impact in the ring, which could explain why the overall contact time of the droplet was not significantly affected by the presence of the ring (FIG. 5B). The interaction parameter in this case scaled as / oc d² (pD ³) /o . Finally, it was demonstrated that in the range where the spreading lamella is ejected by the ring, the normalized interaction parameter can be expressed as

where the quadratic dependence on the ring diameter is apparent.

However, FIG. 6B shows that, as the ring diameter approached the impacting drop diameter, the lamella overran the ridge before d/D = 1 was reached and the interaction parameter reverted to the case of a plain superhydrophobic surface. It was determined that, in some embodiments, there is an enhanced ring diameter of slightly larger than the diameter of the impinging drop. Indeed, in the initial stages of spreading, the lamella still had downward momentum that needed to be overcome by the upward momentum created by the wall for the lamella to takeoff. In some embodiments, this can be achieved by placing the wall further away from the impact point as the spreading lamella converts its downward momentum in horizontal momentum or by increasing the height of the wall to redirect more momentum upward. In some embodiments, the enhanced diameter depends on the wall height and, because of the absence of analytical models for the momentum distribution in the drop during the early stages of the spreading phase, was experimentally found to be d/D = 1.2 for a wall 200 pm high and d/D = 1.35 for a height of 100 pm.

To investigate the role of the inertia of the impacting droplet, the freefall height was varied from 10 to 200 cm and the drop diameter was varied from 2 to 4 mm on macrotextures with a ring diameter close to the enhanced, d/D = 1.3. This facilitated probing of a wide range of Weber number, from 40 to 3,000. FIG. 6B shows that the normalized interaction parameter, ///₀, decreased with increasing Weber number as I /I_Q OC 14/ e ^{1/ 2} (broken black line in FIG. 6B), consistent with the scaling provided in Equation 2. It was determined that this approach becomes more effective compared to a plain surface as the Weber number increases. This can be especially important for applications where millimetric drops impact at terminal velocity (e.g. rain) where We ~ 3,000.

The wall parameters (diameter d and height h) dictated whether the lamella was ejected and the shape of the bowl (e.g., the waterbowl) formed. The regime map in FIG. 7A shows the ejection (all points to the right of the curve, labeled 2) or overrun (all points to the left of the curve, labeled 1) of the lamella as a function of the wall parameters for two different Weber numbers (We = 144, circles and We = 500, triangles). The figure reveals a sharp drop of the necessary height to eject as the ring diameter increased past d/D » 1.5. Indeed, past this point the spreading lamella converted all of its downward momentum into horizontal momentum and a very small wall (ca. twice the roughness of the substrate) was sufficient to create enough upward momentum for the lamella to takeoff. The other limiting case was for a wall height on the order of the size of the droplet where the ring diameter was arbitrarily close to the drop diameter. Between these limits (1.2 < d/D < 1.5), the lamella wasn’t at equilibrium and its ejection was governed by a balance between the remaining downward momentum from the impact and the upward momentum generated by the presence of the wall. At this early stage, the spreading of the droplet was self- similar such that the proportion of remaining downward momentum did not depend on the droplet velocity and the regime map was independent of We as shown by the overlap of the regime boundary for We = 144 and We = 500.

In some embodiments, when the diameter of the ring is large enough for the lamella to have purely horizontal momentum (d/D > 1.5), the angle of ejection, Q, of a lamella of height h_t and the shape of the bowl created can be predicted. FIG. 7E shows, in accordance with certain embodiments, schematics of the ejection of the lamella at different angles based on the wall height changing. The ejected lamella’s momentum resulted from a combination of a proportion h/h_t redirected vertically by the wall (lighter shading on the bottom, a, in FIG. 7E) and 1— h/h_t not encountering the wall (darker shading on the top, b, in FIG. 7E). The ejection angle was expressed by combining these terms as sin 0 = h/hi. In addition, in the range of Reynolds numbers considered (3,000 < Re < 13,000), the height of the lamella arose from the merging of the viscous boundary layer with the free surface such that

angle of the lamella can therefore be scaled as

sinG oc h Re²/⁵//)

FIG. 7D shows, in accordance with certain embodiments, sine of the ejection angle as a function of the scaled height of the wall for a ring diameter such that d/D =

2.3. The cross shows the standard deviation of the ejection angle measurement and the uncertainty of the scaling factor. FIG. 7D shows that experimentally measured ejection angles for different impacting droplet speeds and diameters follow this scaling up to saturation, when the ejection angle becomes effectively vertical. The pictures show three different ejection angles obtained by varying the height of the wall while keeping all the other parameters constant. This facilitated fine tuning of the shape of the created bowl.

In some embodiments, the droplet impacts off-center. FIG. 8 shows the contact time (top) and interaction parameter (bottom) of a droplet impacting a surface patterned with a single ring of diameter d at a distance e, the offset, from the center of the ring (see schematic in inset). The drop diameter, D, is 2.13mm, the ring diameter, d, is 5mm, and the ring height, h, is 200pm. The dashed lines are guides for the eye. The pictures in FIG. 8 reveal four different regimes as the offset increased. For small offsets, 2e < d - D (first quadrant, left to right), the entire drop was contained in the ring and the process was similar to a centered impact: the lamella was ejected by the vertical wall and did not contact the substrate beyond the wall. As the drop started to straddle the wall, for d - D < 2e < d + D (second quadrant, left to right), it was split in two parts. For larger offset distances, up to 2e < d + Dmax (third quadrant, left to right), the droplet impacted outside of the ring but was still influenced by it because part of the spreading lamella contacted the border of the ring and was ejected. Finally, for 2e > d + Dmax (fourth quadrant, left to right), the droplet was far enough that it did not interact with the ring.

The contact time and interaction parameter plots in FIG. 8 show the evolution of the performance of the surface. When the drop impacted entirely inside the ring, the mechanism studied earlier was recovered: while the contact time was not significantly affected by the presence of the texture, the restriction of the solid-liquid contact area led to a drastic reduction in interaction parameter. Note that the interaction parameter was independent of the impact position as long as the entire projected area of the drop was within the ring. This property provided robustness to off-center impacts. When a significant portion of the drop impacted over the wall of the ring, however, the lamella was no longer ejected but spread on both sides of the macrotexture. This led to a step change in solid-liquid contact area between cases where the droplet was split and cases where at least a part of the lamella was ejected. On the other hand, a reduction in contact time was observed when the drop was split by the ring, consistent with the prior studies of drops impacting a macroscopic ridge. Note that the minimum in contact time corresponded to the drop being split in two equal parts (2e/d = 1). The combination of these two effects resulted in the discontinuities in interaction parameter that can be observed in FIG. 8 (bottom). However, even at the minimum in contact time, the interaction parameter was still significantly larger than in the case of an impact inside the ring. For impacts outside the ring, the interaction parameter increased with the offset as a smaller portion of the extended lamella was ejected while the contact time remained constant, ultimately reaching the base case where the drop did not interact with the ring at all. Without wishing to be bound by theory, these results suggest that, while impacts inside the ring are enhanced, off-center impacts still exhibit a reduction in interaction parameter compared to a standard superhydrophobic surface.

The actual restriction of a flux-based transport phenomena was analyzed. As a proof of concept, the heat transfer between a cold rain and a warm surface was measured in the experiment schematized in FIG. 9A. FIG. 9A shows, in accordance with certain embodiments, a schematic of the experimental setup facilitating the simulation of rain on a periodic substrate and the measure of the substrate temperature. FIG. 9B shows, in accordance with certain embodiments, a picture of impacting rain droplets on the substrate with enhanced ring diameter. FIG. 9C, left, shows, in accordance with certain embodiments, surface temperature drop, AT, normalized by the equilibrium temperature drop on a control superhydrophobic surface, ATo, on substrates with different textures, where the shaded areas represent the standard deviation between samples. FIG. 9C, right, shows, in accordance with certain embodiments, photographs of the different textures used in FIG. 9C, left, (the scale bar represents 5mm).

Water cooled to 3°C was atomized with a standard spray nozzle in a millimetric rain ( D = 3.25 mm, v = 2.42 m/s, We ~ 300) over a patterned surface. The temperature of the surface was monitored during the experiment as it dropped from room temperature (20°C) to an equilibrium temperature arising from the balance between convection to the air and heat transfer with the cold rain. Steady state was deemed to be achieved when the temperature fluctuation was less than 1°C over 10 or more seconds. The substrate was inclined by 30° to facilitate rapid clearing of the drops once they bounced. Note that while the tilt angle modified the shape of the bowl ( e.g ., the waterbowl), it did not affect the mechanism of lamella ejection. FIG. 9C shows the reduction of temperature on each substrate, AT(t), scaled by the equilibrium temperature drop obtained on a control superhydrophobic surface, |DG₀| » 8°C. The macrotextured substrate with a ring diameter close to the mean diameter of the impacting droplets experienced a temperature drop 40% smaller than the control superhydrophobic sample. This ring diameter corresponds to the enhanced found in FIGS. 6A-6B confirming that the ejection of the lamella plays a major role in reducing the liquid-solid interaction. Furthermore, the splitting of droplets impacting off-center by inducing non-axisymmetric recoil facilitates reduction in interaction parameter regardless of the impact position. In contrast, patterned surfaces with a non-enhanced diameter showed lower effectiveness.

In conclusion, this example demonstrated an approach to enable momentum redirection and ejection of a spreading lamella off a surface by introducing a

macroscopic texture affecting the flow. The resulting bowl (e.g., waterbowl) minimized solid-liquid contact area and therefore the interaction between the drop and the substrate. The enhanced design parameters were determined as a function of the impact conditions and the effectiveness of this method to reduce heat transfer between a cold rain and a warm surface was demonstrated. Remarkably, in contrast to previous approaches, the contact area available for transport to occur was determined to be independent of the Weber number, the ratio of inertial to capillary forces acting on the droplet that dictates the maximum spreading diameter of a drop on a flat substrate for impacts where the drop deforms (We > 2). In some embodiments, the approach can be extended to the impact of low surface tension fluids by making the substrate amphiphobic and other cases of spreading lamella such as the application of a surface coating. In some embodiments, the reduction in interaction can be generalized to any form of flux-based transport phenomena such as icing of rain droplets impacting a cold surface, vapor diffusion from rain through the pores of hydrophobic clothing, chemical abrasion from oxidizing agents, or particulate fouling. This example further provided a model to predict the shape of the bowl (e.g., the waterbowl) created, in some embodiments. Combined with a way to rapidly cure the droplet material, this model could facilitate single-step manufacturing of tailored 3 -dimensional concave shapes, in some embodiments.

Methods

Laser ablation used for texturing - A 150W continuous output Nd:YAG laser beam pulsed at 20kHz with a 200ns pulse duration was directed at the surfaces in an array with a pitch of 25pm, smaller than the spot size of 40pm in diameter. This procedure was repeated a number of times (between 10 and 60 times) while

electronically masking the area occupied by the ring to produce a macroscopic ring of controlled height, width and diameter. Specifically, the laser was commanded to hit each black point of a binary raster image. In the masked regions, the laser simply did not hit the surface. To ensure consistent underlying micro-nano structure, the laser was commanded to hit the entire surface with the same pulse properties and DPI before starting the macro-texturing process. The resulting samples displayed a hierarchic micro/nano texture resulting from the laser irradiation.

Hydrophobic functionalization - The silicon samples were functionalized with octadecyltrichlorosilane (Sigma Aldrich) in the presence of a stoichiometric quantity of water emulsified in the toluene solvent. The combination of this hydrophobic modifier and hierarchic texture led to high contact angles of water (advancing 161+1°, receding 154+1°) and low roll-off angle (4+1°) .

Experimental procedure - The deionized water droplets were generated from a 30-gauge needle held at a controlled height above the samples. A high-speed camera (Photron SA 1.1) was used to image the impacts at 10,000 fps either in the horizontal plane (to measure the ejection angle) or at a 45° angle (to measure the interaction parameter). The droplet velocity, ejection angle, and interaction parameter were measured using the image analysis software ImageJ. Indeed, the portion of the drop in contact with the substrate led to a magnifying effect and bright reflections of the light which facilitated the measure of the solid-liquid contact area and the contact time.

Similarly, the ejection angle of the lamella was measured from side view videos (at the moment of maximum extension of the lamella).

Temperature measurements - A square silicon substrate of size 3 x 3 inches and thickness 750pm was patterned using laser ablation with close-packed rings of different diameters and treated to be rendered hydrophobic. The temperature of the plate was 750mth*500\n/th^zK

assumed to be uniform ( Bi = 148 W/mK 3 10 ³ « 1) and was measured with a thermocouple attached to the underside of the sample. The sample was affixed to a stage with thermal insulating tape to limit the heat transfer to the stage. The rain was generated using a standard showerhead (AATCC 0150) that replicates characteristics of rain with an identical volume and flow rate for each experiment.

While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and/or methods, if such features, systems, articles, materials, and/or methods are not mutually inconsistent, is included within the scope of the present invention.

The indefinite articles“a” and“an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean“at least one.”

The phrase“and/or,” as used herein in the specification and in the claims, should be understood to mean“either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and/or B,” when used in conjunction with open-ended language such as“comprising” can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

As used herein in the specification and in the claims,“or” should be understood to have the same meaning as“and/or” as defined above. For example, when separating items in a list,“or” or“and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as“only one of’ or“exactly one of,” or, when used in the claims,“consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term“or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e.“one or the other but not both”) when preceded by terms of exclusivity, such as “either,”“one of,”“only one of,” or“exactly one of.”“Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase“at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase“at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example,“at least one of A and B” (or, equivalently,“at least one of A or B,” or, equivalently“at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. Some embodiments may be embodied as a method, of which various examples have been described. The acts performed as part of the methods may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include different (e.g., more or less) acts than those that are described, and/or that may involve performing some acts simultaneously, even though the acts are shown as being performed sequentially in the embodiments specifically described above.

In the claims, as well as in the specification above, all transitional phrases such as “comprising,”“including,”“carrying,”“having,”“containing,”“involving,”“holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases“consisting of’ and“consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

CLAIMS What is claimed is:

1. An article, comprising:

a non- wetting surface having a dynamic contact angle of at least 90 degrees, the non-wetting surface comprising a plurality of macro-scale features configured to induce momentum redirection of a droplet impinging onto the non- wetting surface, thereby reducing an area of contact between the droplet and the non-wetting surface.

2. The article of claim 1, wherein at least a portion of the macro-scale features each comprise a substantially continuous perimeter.

3. The article of any one of claims 1-2, wherein at least a portion of the macro-scale features each comprise a substantially continuous perimeter comprising discontinuity or discontinuities defining less than or equal to 90% of the perimeter.

4. The article of any one of claims 1-3, wherein at least a portion of the macro-scale features each comprise a substantially continuous perimeter comprising discontinuity or discontinuities defining less than or equal to 50% of the perimeter.

5. The article of any one of claims 1-4, wherein at least a portion of the macro-scale features are arranged in a periodic pattern.

6. The article of any one of claims 1-5, wherein at least a portion of the macro-scale features are ring-like.

7. The article of any one of claims 1-6, wherein the average diameter (d) of the macro-scale features is larger than the average diameter (D) of the droplet.

8. The article of any one of claims 1-7, wherein a ratio (d/D) of the average diameter (d) of the macro-scale features to the average diameter (D) of the droplet is between 1 and 100, inclusive.

9. The article of claim 8, wherein the ratio (d/D) is between 1 and 5, inclusive.

10. The article of any one of claims 1-9, wherein a ratio (h/D) of the average height

(h) of the macro-scale features to the average diameter (D) of the droplet is between 0.001 and 1, inclusive.

11. The article of claim 10, wherein the ratio (h/D) is between 0.01 and 0.1, inclusive.

12. The article of any one of claims 1-11, wherein a ratio (h/L_t) of the average height (h) of the macro-scale features to the average thickness of the droplet when a spreading lamella is between 0.005 and 5.

13. The article of claim 12, wherein the ratio (h/L_t) is between 0.1 and 1, inclusive.

14. The article of any one of claims 1-13, wherein a ratio of the average spacing between each of the macro-scale features to the average droplet diameter (D) is between 1 and 20, inclusive.

15. The article of claim 14, wherein the ratio of the average spacing between each of the macro-scale features to the average droplet diameter (D) is between 1 and 4, inclusive.

16. The article of any one of claims 1-15, wherein the article comprises roofing, external building surfaces, siding, construction materials, aircraft wings, turbine blades, power cables, fabric, and/or a garment.

17. An article, comprising:

a surface constructed and arranged to induce redirection of liquid droplets impinging onto it, comprising a plurality of ring-like structures having average diameters between 1 and 10 times the average diameter of the droplets, the ring-like structures comprising a continuous or discontinuous ridge extending, from the remainder of the surface absent the ridge, a distance of greater than or equal to 0.5% of the average thickness of the droplets when a spreading lamella, and where discontinuous, the discontinuity or discontinuities defining no more than 30% of the shape of the ring-like structure.

18. The article of claim 17, wherein the distance is greater than or equal to 30% of the average thickness of the droplets when a spreading lamella.

19. The article of any one of claims 17-18, wherein a ratio (h/D) of the average height (h) of the ring-like structures to the average diameter (D) of the droplets is between 0.001 and 1, inclusive.

20. An article, comprising:

a surface constructed and arranged to induce redirection of a spreading liquid lamella, comprising a plurality of structures comprising a continuous or discontinuous ridge extending, from the remainder of the surface absent the ridge, a distance of greater than or equal to 0.5% of the thickness of the average spreading liquid lamella, the discontinuity or discontinuities defining no more than 30% of the shape of the structure.

21. The article of claim 20, wherein the plurality of structures comprises a plurality of ring-like structures.

22. The article of any one of claims 20-21, wherein the spreading liquid lamella comprises droplets.

23. The article of any one of claims 20-22, wherein a ratio (h/D) of the average height (h) of the structures to the average diameter (D) of the droplets is between 0.001 and 1, inclusive.

24. An article, comprising:

a surface constructed and arranged to induce redirection of liquid droplets impinging onto it, comprising a plurality of ring-like structures having average diameters between 1 and 10 times the average diameter (D) of the droplets and a ratio (h/D) of the average height (h) of the ring-like structures to the average diameter (D) of the droplets between 0.001 and 1, inclusive, the ring-like structures comprising a continuous or discontinuous ridge, and where discontinuous, the discontinuity or discontinuities defining no more than 30% of the shape of the ring-like structure.

25. The article of any one of claims 17-24, wherein at least a portion of the continuous or discontinuous ridge is a continuous ridge.

26. The article of any one of claims 17-25, wherein at least a portion of the continuous or discontinuous ridge is a discontinuous ridge.

27. The article of any one of claims 17-26, wherein the discontinuity or

discontinuities of the discontinuous ridge defines no more than 90% of the shape of the ring-like structure.

28. The article of any one of claims 17-27, wherein the discontinuity or

discontinuities of the discontinuous ridge defines no more than 50% of the shape of the ring-like structure.

29. The article of any one of claims 17-28, wherein at least a portion of the ring-like structures are arranged in a periodic pattern.

30. The article of any one of claims 17-29, wherein the ring-like structures have average diameters between 1 and 2 times the average diameter of the droplets.

31. The article of any one of claims 19 and 23-30, wherein the ratio (h/D) is between 0.01 and 0.1, inclusive.

32. The article of any one of claims 17-31, wherein a ratio of the average spacing between each of the ring-like structures to the average droplet diameter (D) is between 1 and 20, inclusive.

33. The article of claim 32, wherein the ratio of the average spacing between each of the ring-like structures to the average droplet diameter (D) is between is between 1 and 4, inclusive.

34. The article of any one of claims 17-33, wherein a ratio (h/L_t) of the average height (h) of the ring-like structures to the average thickness of the droplets when a spreading lamella is between 0.005 and 5.

35. The article of claim 34, wherein the ratio (h/L_t) is between 0.1 and 1, inclusive.

36. The article of any one of claims 17-35, wherein the article comprises roofing, external building surfaces, siding, construction materials, aircraft wings, turbine blades, power cables, fabric, and/or a garment.

37. A method, comprising:

exposing a non- wetting surface to an impinging droplet;

redirecting the momentum of the impinging droplet; and

reducing an area of contact between the impinging droplet and the non-wetting surface;

wherein the non-wetting surface comprises a plurality of macro-scale features and a dynamic contact angle of at least 90 degrees.

38. The method of claim 37, wherein at least a portion of the macro-scale features each comprise a substantially continuous perimeter.

39. The method of any one of claims 37-38, wherein at least a portion of the macro scale features each comprise a substantially continuous perimeter comprising

discontinuity or discontinuities defining less than or equal to 90% of the perimeter.

40. The method of any one of claims 37-39, wherein at least a portion of the macro scale features each comprise a substantially continuous perimeter comprising

discontinuity or discontinuities defining less than or equal to 50% of the perimeter.

41. The method of any one of claims 37-40, wherein at least a portion of the plurality of macro-scale features are arranged in a periodic pattern.

42. The method of any one of claims 37-41, wherein at least a portion of the macro scale features are ring-like.

43. The method of any one of claims 37-42, wherein the average diameter (d) of the macro-scale features is larger than the average diameter (D) of the impinging droplet.

44. The method of any one of claims 37-43, wherein a ratio (d/D) of the average diameter (d) of the macro-scale features to the average diameter (D) of the impinging droplet is between 1 and 100, inclusive.

45. The method of claim 44, wherein the ratio (d/D) is between 1 and 5, inclusive.

46. The method of any one of claims 37-45, wherein a ratio (h/D) of the average height (h) of the ring-like structures to the average diameter (D) of the droplet is between 0.001 and 1, inclusive.

47. The method of claim 46, wherein the ratio (h/D) is between 0.01 and 0.1, inclusive.

48. The method of any one of claims 37-47, wherein a ratio of the average spacing between each of the macro-scale features to the average droplet diameter (D) is between 1 and 20, inclusive.

49. The method of claim 48, wherein the ratio of the average spacing between each of the macro-scale features to the average droplet diameter (D) is between 1 and 4, inclusive.

50. The method of any one of claims 37-49, wherein a ratio (h/L_t) of the average height (h) of the macro-scale features to the average thickness of the impinging droplet when a spreading lamella is between 0.005 and 5.

51. The method of claim 50, wherein the ratio (h/L_t) is between 0.1 and 1, inclusive.

52. The method of any one of claims 37-51, wherein the non- wetting surface comprises roofing, external building surfaces, siding, construction materials, aircraft wings, turbine blades, power cables, fabric, and/or a garment.

53. The method of any one of claims 37-52, wherein the method is used to reduce heat transfer, reduce salt deposition, restrict vapor diffusion, and/or collect rain.