WO2023039021A1

WO2023039021A1 - Methods, systems, and devices for cooling with minimal surfaces

Info

Publication number: WO2023039021A1
Application number: PCT/US2022/042836
Authority: WO
Inventors: Robert C. Ryan
Original assignee: Ryan Robert C
Priority date: 2021-09-08
Filing date: 2022-09-08
Publication date: 2023-03-16

Abstract

Method, systems, and devices are provided for cooling electronic devices through the use of minimal surfaces. Liquid may be input into a set of passageways comprising a minimal surface adjacent an electronic surface to be cooled, improving efficiency and responsiveness of the cooling system.

Description

METHODS, SYSTEMS, AND DEVICES FOR COOLING WITH MINIMAL SURFACES

BACKGROUND ART

[0001] Recent trends in electronics have continued to emphasize smaller and smaller components with increased energy density. Since these components create increasingly large amounts of heat within a small area, it has become a challenge to maintain electronic devices within a safe temperature range. Various cooling techniques are used in the art, such as liquid and air cooling. Due to the very limited physical space with microprocessors, one cooling technique uses forced air convection to spread heat over a much larger area. Another option is the use of liquid cooling. Due to the relatively high volumetric heat capacity of liquid, a significantly smaller amount of liquid is required to cool a typical electronic processor compared to an air cooled system. Liquid cooling techniques can include flow through channels and direct jet impingement on the heat generating device.

[0002] Efficiency and scaling problems hinder both air and liquid cooling systems. For example, the decreasing size of electronics presents problems for integrating cooling components as well as the pressure drop required by these devices. Therefore, more efficient and scalable methods for cooling electronic devices are needed.

SUMMARY OF THE DISCLOSURE

[0003] The present invention is useful in conjunction with various embodiments, methods, systems, and devices to provide cooling for electronic devices using minimal surfaces, including doubly periodic minimal surfaces. In certain embodiments, a method of cooling an electronic device may include steps comprising: injecting a fluid through an inlet into a first set of passages; passing the fluid from the first set of passages through a first portion of a minimal surface with a first set of holes formed therethrough; passing the fluid through the first set of holes onto a surface of the electronic device to be cooled; receiving the fluid through a second set of holes formed in a second portion of the minimal surface; passing the fluid from the second portion of the minimal surface into a second set of passages; and removing the fluid through an outlet in the second set of passages.

[0004] In some embodiments, the minimal surface forms a barrier between the first set of passages and the second set of passages. The minimal surface may be a doubly periodic minimal surface. The minimal surface may be Scherk’s First Surface. The minimal surface may be one of Karcher-Meeks-Rosenberg Surface, Wei’s Doubly Periodic Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface. The first and second portions of the minimal surface may be positioned in alternating rows, the minimal surface may have a thickness of about 100 nm. In a preferred embodiment, the fluid includes a liquid or is liquid.

[0005] A method of spreading heat from an electronic device is also provided, which may include steps of: circulating a first fluid through a first set of passages, the first set of passages comprising a minimal surface in thermal contact with the electronic device, the first set of passages further comprising one or more heat dissipation sections such that the fluid transports heat from the electronic device to the one or more heat dissipation sections; and circulating a second fluid through a second set of passages, the second set of passages comprising the minimal surface; the second set of passages further comprising one or more heat dissipation sections such that the fluid transports heat from the electronic device to the one or more heat dissipation sections.

[0006] In some embodiments, the minimal surface forms a barrier between the first set of passages and the second set of passages. The minimal surface may be a doubly periodic minimal surface. The minimal surface may be Scherk’s First Skeletal Graph. The minimal surface may be one of Karcher-Meeks-Rosenberg Surface, Wei’s Doubly Periodic Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface. In some embodiments, the first set of passages is connected to the second set of passages such that the first and second fluids circulate through both the first and second sets of passages. The minimal surface may have a thickness of about 100 nm.

[0007] A cooling apparatus for cooling an electronic device is also provided, comprising: an enclosure comprising one or more inlets for receiving a liquid, a doubly periodic minimal surface material disposed within the enclosure, wherein the minimal surface material is configured so that liquid passes through a first plurality of passageways through the minimal surface material to a surface of the electronic device positioned adjacent the minimal surface materials and back through a second plurality of passageways through the minimal surface material.

[0008] In some embodiments, the doubly periodic minimal surface material is Scherk’s First Surface. The doubly periodic minimal surface material may be a skeletal doubly periodic minimal surface material. The doubly periodic minimal surface material may be one of Karcher- Meeks -Rosenberg Surface, Wei’s Doubly Periodic Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface. The first and second pluralities of passageways through the minimal surface material may be positioned in alternating rows. In some embodiments, the minimal surface has material has a thickness of about 100 nm.

[0009] An advantage of this invention can provide improved cooling systems for electronic devices by maximizing available space, efficiency, and responsiveness of the cooling systems while maintaining such devices in an acceptable operating temperature range. To further understand the present invention and its applications, certain definitions of terms will prove helpful:

[00010] As used herein the term “Lagrange's equation” means (1).

(1 + h_v)h_uu - 2h_uh_vh_uv + (1 +h_u )/i_vv = 0 (1)

[00011] As used herein the term “Weierstrass Formula” (also known as the Weierstrass- Enneper parameterization) means a parameterization of a minimal surface in terms of two functions f z); g z , Equation 2:

where z = re¹ and R [z] is the real part of z.

[00012] As used herein the term “minimal surface” means that the mean curvature of the minimal surface is zero at each point on the surface.

[00013] As used herein, the term “principal curvatures” means the maximum and minimum of the normal curvature,

and k₂ at a given point on a surface.

[00014] As used herein the term “mean curvature” (H ) means the average of the two principal curvatures.

[00015] As used herein, the term “level set” means a real-valued function/of n variables of the form:

where c is a constant. That is, it is the set where the function takes on a given constant value and when the number of variables is three this is a level surface.

[00016] As used herein, the term “skeletal graph” means the end result of expanding or shrinking a surface along the direction of its normal vectors, while avoiding any pinching off that would change the topology of the surface, until all that remains is a connected graph of arcs and nodes.

[00017] As used herein, the term “doubly periodic minimal surface” means that the minimal surface is comprised of a unit that repeats in two dimensions, sometimes referred to as infinitely extending. Its topology is characterized by two interpenetrating networks - its “labyrinth graphs.”

[00018] As used herein the “level set approximation for the Scherk’s First minimal surface” is given by: e^z cosy — cos x = 0 (3)

[00019] As used herein, the term “pitch” means the center-to-center spacing of holes.

BRIEF DESCRIPTION OF THE DRAWINGS

[00020] The present disclosure is best understood from the following detailed description when read with the accompanying figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.

[00021] FIG. 1 is a view of Figs. 4 and 4A from (PRIOR ART) U.S. Patent No. 7,375,962;

[00022] FIG. 2 is a view of Fig. 8 from (PRIOR ART) U.S. Patent No. 8.413,712;

[00023] FIG. 3 is a view of Figs. 8-10 from (PRIOR ART) U.S . Patent No. 10,278,306;

[00024] FIG. 4A is a perspective view of Scherk’s First Surface;

[00025] FIG. 4B is a top view of Scherk’s First Surface;

[00026] FIG. 5 is a perspective view of Karcher-Meeks-Rosenberg Surface;

[00027] FIG. 6 is a perspective view of Wei’s Doubly Periodic Surface of Genus 2;

[00028] FIG. 7 is a perspective view of a Plane Surface with Catenoids;

[00029] FIG. 8 is a side view of a Doubly Periodic Catenoid Surface;

[00030] FIG. 9 is a top view of a Deformation of Scherk’s First Surface;

[00031] FIG. 10 is a top view of Scherk’s First Surface Jet Cooler;

[00032] FIG. 11 is a side view of Scherk’s First Surface Jet Cooler; [00033] FIG. 12 is a top view of Scherk’s First Skeletal Graph Jet Cooler with Integrated Return;

[00034] FIG. 13 is a bottom view of Scherk’s First Skeletal Graph Jet Cooler with Integrated Return;

[00035] FIG. 14 is a side view of Scherk’s First Skeletal Graph Jet Cooler with Integrated Return;

[00036] FIG. 15 is a top view of Scherk’s First Skeletal Graph Heat Spreader; and

[00037] FIG. 16 is an exploded view of Scherk’s First Surface Skeletal Graph Heat Spreader.

DETAILED DESCRIPTION

[0001] This description and the accompanying drawings that illustrate aspects, embodiments, implementations, or applications should not be taken as limiting — the claims define the protected invention. Various mechanical, compositional, structural, electrical, and operational changes may be made without departing from the spirit and scope of this description and the claims. In some instances, well-known structures, processes, or techniques have not been shown or described in detail as these are known to one of ordinary skill in the art.

[0002] In this description, specific details are set forth describing some embodiments consistent with the present disclosure. Numerous specific details are set forth in order to provide a thorough understanding of the embodiments. It will be apparent, however, to one of ordinary skill in the art that some embodiments may be practiced without some or all of these specific details. The specific embodiments disclosed herein are meant to be illustrative but not limiting. One of ordinary skill in the art may realize other elements that, although not specifically described here, are within the scope and the spirit of this disclosure. In addition, to avoid unnecessary repetition, one or more features shown and described in association with one embodiment may be incorporated into other embodiments unless specifically described otherwise or if the one or more features would make an embodiment non-functional.

[00038] This invention comprises, in general, a change in the basic design of electronics cooling devices. In one embodiment, the present invention represents an improvement over conventional cooling devices that use a flat array of holes for jet cooling such as that illustrated in Fig. 1 by incorporating a minimal surface design, preferably based on a doubly periodic minimal surface. In another embodiment, the present invention represents an improvement over conventional cooling devices using a flat array of holes for jet cooling where half of the holes are used for injection of cooling fluid and the other half are used for fluid removal such as that illustrated in Fig. 2 by incorporating a skeletal graph of a doubly periodic minimal surface. In another embodiment, the present invention represents an improvement over conventional heat spreader designs where the cooling fluid flows from one heat dissipation chamber through a heat absorption chamber to another heat dissipation chamber such as that illustrated in Fig. 3 by incorporating a doubly periodic minimal surface design in a heat spreader. These improvements enable cooling of electronic applications with higher efficiency. One measure of this effectiveness is represented by increased pressure drop, where lower values indicate a more efficient system.

[00039] A minimal surface is one that locally minimizes its area and this is equivalent to having a mean curvature of zero. A minimal surface parameterized as x = (M, V, h(u,v)) satisfies Lagrange's equation. To represent such a minimal surface, the Weierstrass Formula is typically used. As an example of a physical implementation, physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution and forming a soap film, the soap film forming a minimal surface whose boundary is the wire frame. Surface tension, which measures the energy needed to create a surface, acts as a physical surface minimizer: since energy is proportional to the soap film surface, the film deforms to minimize its surface and, thus its energy. This least area property of minimal surfaces has been useful in architecture, particularly for light roof construction. Within a set boundary, a minimal surface represents the surface of least area, which minimizes the amount of required material and associated weight while maintaining strength.

[00040] Additionally, mass transfer packing with a minimal surface area (and, in particular, a triply periodic minimal surface) enables significantly improved performance for separation and mixing applications, as discussed in U.S. Patent No. 9,440,216 to Ryan, the entire contents of which is incorporated herein by express reference thereto. Triply periodic minimal surfaces have also been used for facilitating heat exchange between two fluids, as discussed in U.S. Patent No. 4,915,164 to Harper and U.S. Patent No. 7,866,377 to Slaughter, the entire contents of which are incorporated herein by express reference thereto. However, minimal surfaces, and in particular, doubly periodic minimal surfaces, have not previously been used in the context of electronics cooling. As discussed above, the increasing need for smaller electronics devices has created a continuing need for very light and small cooling devices, and in particular devices that are flat or nearly flat, and it has been discovered and described herein how this need is met by using various minimal surfaces including doubly periodic minimal surfaces.

[00041] Some examples of doubly periodic minimal surfaces suitable for electronics cooling include but not limited to: Scherk’s First Surface as illustrated in Fig. 4, Karcher- Meeks- Rosenberg Surface illustrated in Fig. 5, Wei’s Doubly Periodic Surface of Genus 2 illustrated in Fig. 6, Plane Surface with Catenoids illustrated in Fig. 7, and Doubly Periodic Catenoid Surface illustrated in Fig. 8. In some embodiments, liquids or gases are passed through these surfaces to more efficiently dissipate heat from electronics, as shown in Figs. 11-16. The use of the minimal surfaces in cooling and heat dispersion may optimize the access to available surface area on electronics.

[00042] One aspect of the present invention is a method for jet cooling based on minimal surfaces, and preferably, doubly periodic minimal surfaces. A preferred embodiment of this method includes the application of Scherk’s First Surface as illustrated in Figs. 4A and 4B. Another aspect of the present invention is a method of jet cooling based on skeletal graphs of minimal surfaces, and preferably, doubly periodic minimal surfaces. A preferred embodiment of this method includes a skeletal graph of Scherk’s First Surface as illustrated in Figs. 12 and 13. Another aspect of the present invention is a method of heat spreading based on minimal surfaces, and preferably, doubly periodic minimal surfaces. A preferred embodiment of this method includes Scherk’s First Surface as illustrated in Figs. 4A and 4B. Yet another aspect of the present invention is a method of jet cooling based on a deformed minimal surface, preferably a deformed doubly periodic minimal surface. A preferred embodiment of this method includes a deformed Scherk’s First Surface as illustrated in Fig. 9 which may have the shape of the original Scherk’s First Surface (shown in Figs. 4A and 4B) twisted in one or more directions.

[00043] Fig. 1 shows a conventional jet impingement apparatus. For electronics cooling using this arrangement, efficiency is controlled by the size of the jet nozzles 400 as well as jet pitch. In particular, the cooling performance of a jet impingement cooler increases with decreasing jet pitch and jet nozzle size. However, relatively smaller nozzle dimensions result in increased pressure drop and this leads to a practical limit of small size and reasonable pumping costs with regard to the current jet impingement technology. In addition to the limitation of pitch and hole size due to pressure drop considerations, there is a practical limitation of the pitch distance due to strength considerations of the plate with holes.

[00044] Without being bound by theory, the use of a jet impingement cooling apparatus based on a doubly periodic surface overcomes these limitations. Due to the geometry of the minimal surface material, the thickness of the design can theoretically have a thickness equivalent to that of a typical soap bubble (about 100 nm). In some embodiments, the thickness of the minimal surface material is about 80-120 nm, and in other embodiments, the thickness of the minimal surface material is about 50-150 nm. As exemplified with the top view of a cooler device 1000 incorporating Scherk’s First Surface (as illustrated in Fig. 10), openings 1002 are actually composed of a checkerboard pattern of bridging arches 1004. This can advantageously permit more coolant, or larger electronics with a liquid coolant instead of gas coolant, etc., such that the cooling efficiency is increased compared to conventional electronic cooling systems.

[00045] One preferred embodiment of the cooler apparatus 1100 as illustrated in Fig. 11. This cooling apparatus 1100 may include an enclosure 1102 surrounding a material shaped with a minimal surface 1104 (in the example of Fig. 11, Scherk’s First Surface) with a fluid entrance 1106 and a heated surface 1108 to be cooled adjacent the minimal surface 1104. At an equivalent hole diameter to that of a conventional cooling system (referring to the holes 400 of Fig. 1), the doubly periodic minimal surface 1104 would produce a lower pressure drop that would contribute to a more efficient system. It is understood that further improvements in the overall design of the cooling apparatus 1100 are also contemplated, such as including multiple entrances 1106 at the top of the enclosure 1102 to improve the fluid distribution to the doubly periodic minimal surface material 1104. It is also expected that, depending on the temperature of the fluid and heated surface, both single and multiphase cooling can be applied. For example, different phases of cooling could occur within different sections of the same periodic surface material 1104. In other embodiments, more than one minimal surface material 1104 could be used within the cooler apparatus 1100. This can permit use of more or less heat-conductive materials to channel heat flow and provide increased cooling efficiency, as well.

[00046] Referring to Figs. 12-14, further improvements in jet cooling are also possible through the use of doubly periodic minimal surface skeletal graphs. One of the shortcomings with conventional planar jet cooling is that the removal of the cooling fluid from the heated surface results in an uneven distribution of the cooling fluid. One approach to solve this problem herein is to incorporate the fluid injection and removal in a single design. One preferred embodiment of a jet cooling system 1200 with a Scherk’s First Surface skeletal design is illustrated in Fig. 12, which may be configured to remove heat from a surface 1230 (illustrated in Fig. 14). In some embodiments, this surface 1230 is the top surface of an electronic component or assembly that produces heat, similar to the heated surface 1108 in Fig. 11. In some embodiments, a first set of passages 1202 is used for fluid injection while another set of passages 1204 is used for fluid removal. Inlets 1212 are used to inject fluid into the passages 1202 while outlets 1214 are used to remove fluid from the passages 1204. It is understood that the numbers of four inlets 1212 and four outlets 1214 are for illustrative purposes only, and that at a minimum, only one inlet 1212 and one outlet 1214 is required. In other implementations, more or fewer inlets 1212 and outlets 1214 may be included in the jet cooling system 1200. In some embodiments, equal numbers of inlets 1212 and outlets 1214 are included, while in others this can differ, particularly when different sizing is used.

[00047] As shown in Fig. 13, each set of fluid injection passages 1202 and fluid removal passages 1204 may include a set of holes 1220 that allow for the injection and removal of the cooling fluid from the surface 1230 to be cooled. It is understood that although the size of the holes 1220 is illustrated as being of the same, the holes 1220 can have different sizes to optimize the overall efficiency of the process. For example, in some embodiments, the holes 1220 of the fluid injection passages 1202 may be larger than the size of the holes 1220 in the fluid removal passages. 1204.

[00048] Referring to Fig. 14, a side view of the jet cooling system 1200 design is shown with the inlets 1212 and outlets 1214 along with the heated surface 1230. As shown in this view, fluid passes through the fluid injection passages 1202 through the holes 1220 and impinges on the heated surface 1230 to cool it. The fluid then passes through the holes 1220 to the fluid removal passages 1204 and may be removed from the system 1200. A small gap may be placed between the holes 1220 and heated surface 1230 to facilitate the flow of fluid directly to and from the surface 1230. An advantage of the use of the doubly periodic minimal surface within the system 1200 is that it easily allows for multiple inlets 1212 and outlets 1214 of cooling fluid, is relatively flat and thus conserves space, and has a relatively lower pressure drop due to the minimal surface design. [00049] Referring to Figs. 15-16, an exemplary heat spreading system 1500 is illustrated. Heat spreading is an important temperature controlling device for electronics. The system 1500 may be used to facilitate the transportation of a fluid from a heated surface to a remote location where heat is dissipated. With regard to Fig. 3, a conventional heat spreader is designed to spread heat in multiple directions but is limited because only a single fluid is contained within the fluid circuit. In contrast, the heat spreading system 1500 in Figs. 15-16 includes a doubly periodic skeletal graph design that may include a fluid circuit with one or more fluid sections.

[00050] The heat spreading system 1500 may include a minimal surface, such as the Scherk First Surface skeletal graph as illustrated in Fig. 15 with an exploded view in Fig. 16. A heated surface 1530 (which may be similar to the heated surface 1230 discussed with reference to Figs. 12-14) may be attached to a first spreader circuit 1502 and a second spreader circuit 1502 which include one or more fluids. In some implementations, a thermal contact is formed between the heated surface 1530 and spreader circuits 1502, 1504 such as thermal paste. In this case, fluid does not contact the heated surface 1530, but facilitates the spreading of heat away from the heated surface 1530. The first and second spreader circuits 1502, 1504 may include a number of heat dissipation sections 1506, 1508 (four sections 1506 for the first spreader circuit 1502 and four sections 1508 the second spreader circuit 1504 in the example of Fig. 15). Other numbers of dissipation sections 1506, 1508 may be included. In some embodiments, at least two dissipation sections 1506 1508 are included in the system 1500.

[00051] One advantage of the system 1500 based on the configurations shown in Fig. 15-16 is finer control of the heat spreading system 1500. In one embodiment, each circuit 1502, 1504 includes a fluid that can be used to optimize the cooling effect of the system 1500. For example, the pressure and volume of the fluid in each circuit 1502, 1504 may be varied independently. In another embodiment, the first and second spreader circuits 1502, 1504 are joined into a single loop circuit (e.g., a first dissipation section 1506 at 1 could be joined with a second heat dissipation section 1508 at 5, as well as joining 2 to 6, 3 to 7, and 4 to 8). In this embodiment, fluid would circulate continuously through the system 1500. As discussed above, any of the examples of minimal surfaces in Figs. 4A-10 may be used with the cooling systems 1100, 1200 and heat dissipation system 1500 shown in Figs. 11-16. Other minimal surfaces, and preferably doubly periodic minimal surfaces, may also be used in these cooling and heat dissipation systems. [00052] Since other modifications or changes will be apparent to those of ordinary skill in the art, there have been described above the principles of this invention in connection with specific apparatus, it is to be clearly understood that this description is made only by way of example and not as a limitation to the scope of the invention.

Claims

THE CLAIMS What is claimed is:

1. A method of cooling an electronic device which comprises: injecting a fluid through an inlet into a first set of passages; passing the fluid from the first set of passages through a first portion of a minimal surface with a first set of holes formed therethrough; passing the fluid through the first set of holes onto a surface of the electronic device to be cooled; receiving the fluid through a second set of holes formed in a second portion of the minimal surface; passing the fluid from the second portion of the minimal surface into a second set of passages; and removing the fluid through an outlet in the second set of passages.

2. The method of claim 1, further characterized in that the minimal surface forms a barrier between the first set of passages and the second set of passages.

3. The method of claim 1 or 2, further characterized in that the minimal surface is a doubly periodic minimal surface.

4. The method of claim 3, further characterized in that the minimal surface is Scherk’s First Surface or Scherk’s First Skeletal Graph.

5. The method of claim 3, further characterized in that the minimal surface is one of Karcher-Meeks-Rosenberg Surface, Wei’s Doubly Periodic Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface.

6. The method of any one of claims 1 to 5, further characterized in that the first and second portions of the minimal surface are positioned in alternating rows.

7. The method of any one of claims 1 to 6, further characterized in that the minimal surface has a thickness of about 100 nm.

8. The method of any one of claims 1 to 7, further characterized in that the fluid comprises a liquid.

9. The method of any one of claims 1 to 3, further characterized in that the minimal surface is one of Karcher- Meeks-Rosenberg Skeletal Graph, Wei’s Doubly Periodic Skeletal Graph of Genus 2, Plane Skeletal Graph with Catenoids, Doubly Periodic Catenoid Skeletal Graph, and a Deformation of Scherk’s First Skeletal Graph.

10. A method of spreading heat from an electronic device which comprises: circulating a first fluid through a first set of passages, the first set of passages comprising a minimal surface in thermal contact with the electronic device, the first set of passages further comprising one or more heat dissipation sections such that the fluid transports heat from the electronic device to the one or more heat dissipation sections; and circulating a second fluid through a second set of passages, the second set of passages comprising the minimal surface; the second set of passages further comprising one or more heat dissipation sections such that the fluid transports heat from the electronic device to the one or more heat dissipation sections.

11. The method of claim 10, further characterized in that the minimal surface forms a barrier between the first set of passages and the second set of passages.

12. The method of claim 10 or 11, further characterized in that the minimal surface is selected to be a doubly periodic minimal surface.

13. The method of any one of claims 10 to 12, further characterized in that the minimal surface is selected to include a Scherk’s First Skeletal Graph or Scherk’s First Surface.

14. The method of any one of claims 10 to 12, further characterized in that the minimal surface is selected to include one of Karcher-Meeks-Rosenberg Surface, Wei’s Doubly Periodic Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface.

15. The method of any one of claims 10 to 14, further characterized in that the first set of passages is connected to the second set of passages such that the first and second fluids circulate through both the first and second sets of passages.

16. The method of any one of claims 10 to 15, further characterized in that the minimal surface is selected to have a thickness of about 100 nm.

17. A cooling apparatus for cooling an electronic device, comprising: an enclosure comprising one or more inlets for receiving a liquid, a doubly periodic minimal surface material disposed within the enclosure, wherein the minimal surface material is configured so that liquid passes through a first plurality of passageways through the minimal surface material to a surface of the electronic device positioned adjacent the minimal surface materials and back through a second plurality of passageways through the minimal surface material.

18. The apparatus of claim 17, further characterized in that the doubly periodic minimal surface material is Scherk’s First Surface.

19. The apparatus of claim 17, further characterized in that the doubly periodic minimal surface material is a skeletal doubly periodic minimal surface material.

20. The apparatus of claim 17, further characterized in that the doubly periodic minimal surface material is one of Karcher-Meeks-Rosenberg Surface, Wei’s Doubly Periodic

14 Surface of Genus 2, Plane Surface with Catenoids, Doubly Periodic Catenoid Surface, and a Deformation of Scherk’s First Surface. The apparatus of any one of claims 17 to 20, further characterized in that the first and second pluralities of passageways through the minimal surface material are positioned in alternating rows. The apparatus of any one of claims 17 to 21, further characterized in that the minimal surface material is selected to have a thickness of about 100 nm.

15