CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Application Serial No. 13/776,459, filed by Enright, on February 25, 2013, entitled "SLOPED HIERARCHICALLY-STRUCTURED SURFACE DESIGNS FOR ENHANCED CONDENSATION HEAT TRANSFER," commonly assigned with this application and incorporated herein by reference.

TECHNICAL FIELD

The invention relates to in general, heat transfer apparatuses, and methods for manufacturing the same.

BACKGROUND

This section introduces aspects that may help facilitate a better understanding of the inventions. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is prior art or what is not prior art.

Condensation is an important process in a number of two-phase heat transfer apparatuses implemented for thermal management. Improving the efficiency of such condensation heat transfer processes has the potential to enable size reductions of heat transfer apparatuses while still achieving the same overall heat transfer performance.

SUMMARY

One embodiment is an apparatus. The apparatus comprises a distribution of microstructures on an area of a surface, each of the microstructures having one or more sloping sides. The apparatus comprises a distribution of nanostructures being located on the one or more sloping sides. The distribution of microstructures on the area of the surface is configured to nucleate and grow droplets of liquid from a gas. The distribution of nanostructures forms a superhydrophobic surface for the liquid.

In any of the above embodiments of the apparatus, the microstructures are configured to nucleate the droplets between the nanostructures. In some embodiments, the microstructures are ridges. In some embodiments, the microstructures are pointed structures. Any of the above embodiments of the apparatus can further include a heat pipe or a vapor chamber, the distribution of microstructures being located in a condenser portion of the heat pipe or the vapor chamber. In some embodiments, the one or more sloping sides intersects with at least one side of the microstructure to form an apex shaped as a peak. In some embodiments, the separation distance between apexes of adjacent ones of the microstructures is equal to or less than about 10 microns. In some embodiments, at least one of the sloping sides intersects with at another side of an adjacent one of the microstructures at a base layer to form a valley. In some embodiments, at least one of the sloping sides and another side of the one microstructure separately intersect with a third side of the one microstructure to form an apex shaped as a mesa. In some embodiments, at least one of the sloping sides and another side of an adjacent one of the microstructures separately intersect with a horizontally oriented layer that is covered with the nanostructures and is adjacent to a base layer. In some embodiments, at least one of the sloping sides intersects with another side which forms a right angle with respect to a base layer. In some embodiments, at least one of the sloping sides intersects with another side of the one microstructure, and, the other side forms a different acute angle with respect to the line perpendicular to a base layer. In some embodiments, for at least one of the sloping sides, there are sloped portions that have the acute angle interspersed horizontal portions that are parallel with a base layer. In some embodiments, a distance between adjacent ones of the nanostructures is greater than a critical condensation radius for a nucleating one of the liquid droplet.

One embodiment is a system. The system comprises heat generating equipment and a heat transfer apparatus configured to remove heat generated by the electronic equipment. The apparatus includes a distribution of microstructures on an area of a surface, each of the microstructures having one or more sloping sides. The apparatus comprises a distribution of nanostructures being located on the one or more sloping sides. The distribution of microstructures on the area of the surface is configured to nucleate and grow droplets of liquid from a gas. The distribution of nanostructures forms a superhydrophobic surface for the liquid.

In some embodiments of the system, the distribution of microstructures is located on the surface of a condenser of the apparatus. In some embodiments, the condenser is part of a heat pipe. In some embodiments, the condenser is part of a vapor chamber.

One embodiment is a method. The method comprises forming a distribution of microstructures on an area of a surface, each of the microstructures having one or more sloping sides, wherein the distribution of microstructures on the area of the surface is configured to nucleate and grow droplets of liquid from a gas. The method comprises forming a distribution of nanostructures being located on the one or more sloping sides, wherein the distribution of nanostructures forms a superhydrophobic surface for the liquid.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the disclosure are best understood from the following detailed description, when read with the accompanying FIGURES. Some features in the figures may be described as, for example, "top," "bottom," "vertical" or "lateral" for convenience in referring to those features. Such descriptions do not limit the orientation of such features with respect to the natural horizon or gravity. Various features may not be drawn to scale and may be arbitrarily increased or reduced in size for clarity of discussion. Reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

FIG. 1 A presents a perspective view of an embodiment heat transfer apparatus;

FIG. 1 B presents a perspective view of an alternative embodiment of a heat transfer apparatus;

FIG. 1 C presents a perspective view of another alternative embodiment of a heat transfer apparatus;

FIG. 2A presents a cross-sectional view of the apparatus shown in

FIG. 1 B along view line 2-2;

FIG. 2B presents a cross-sectional view of an alternative embodiment of a heat transfer apparatus, analogous to the view along line 2-2 in FIG. 1 B; FIG. 2C presents a cross-sectional view of an alternative embodiment of the heat transfer apparatus, analogous to the view along line 2-2 in FIG. 1 B;

FIG. 2D presents a cross-sectional view of an alternative embodiment of a heat transfer apparatus, analogous to the view along line 2-2 in FIG. 1 B;

FIG. 2E presents a cross-sectional view of an alternative embodiment of a heat transfer apparatus, analogous to the view along line 2-2 in FIG. 1 B;

FIG. 3 presents a detailed cross-sectional view of a portion of the apparatus shown in FIG. 2A;

FIG. 4 presents a perspective view of the portion of apparatus presented in FIG. 3;

FIG. 5 presents a flow diagram of an example method of manufacturing a heat transfer apparatus, such as any of the example apparatuses described in the context of FIGs. 1 A-4;

FIG. 6 presents a flow diagram of a method; and

FIG 7 presents a block diagram of a system.

In the Figures and text, similar or like reference symbols indicate elements with similar or the same functions and/or structures.

In the Figures, the relative dimensions of some features may be exaggerated to more clearly illustrate one or more of the structures or features therein.

Herein, various embodiments are described more fully by the Figures and the Detailed Description. Nevertheless, the inventions may be embodied in various forms and are not limited to the embodiments described in the Figures and Detailed Description of Illustrative Embodiments.

DETAILED DESCRIPTION

The description and drawings merely illustrate the principles of the inventions. It will thus be appreciated that a person of ordinary skill in the relevant arts will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the inventions and are included within its scope. Furthermore, all examples recited herein are principally intended expressly to be for pedagogical purposes to aid the reader in understanding the principles of the inventions and concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the inventions, as well as specific examples thereof, are intended to encompass equivalents thereof. Additionally, the term, "or," as used herein, refers to a non-exclusive or, unless otherwise indicated. Also, the various embodiments described herein are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

Various heat transfer apparatuses of the disclosure have hierarchically structured condensation surfaces which enhance condensation heat transfer. The hierarchically structured surfaces may, e.g., have both micron-scaled structural features ("microstructures") and nanometer-scaled structural features ("nanostructures").

The use of non-wetting surfaces (synonymous with the term superhydrophobic surface as used herein) can enhance heat transfer coefficients, in comparison to the heat transfer via smooth surfaces. Surprisingly, when the non-wetting surface is a surface covered with nanostructures, similar enhancements to heat transfer coefficients have typically not been realized. As droplets form and grow on a surface covered with nanostructures, the droplet gets to a certain critical size, and heat conduction through the bulk of the droplet begins to limit the heat transfer rate. It is therefore desirable for the droplet to leave the surface (often referred to droplet jumping) before the droplet reaches its critical size. However, there is a characteristic droplet diameter, below which dissipation effects, e.g., viscous effects, form drag, surface adhesion, etc., can dominate or suppress droplet jumping. Furthermore, droplet jumping typically requires the coalescence of two or more droplets, which, in turn, is dictated by the number density of droplets nucleated on the surface. Thus, the minimum jumping droplet diameter may be also restricted by a small number of nucleated droplets (large droplet spacing).

Providing a hierarchically structured condensation surface, with separated microstructures having nanostructures thereon, may provide an efficient heat transfer surface. Providing microstructures having at least one sloped side may help to move larger droplets to the apexes of the microstructures, thereby freeing up surfaces for new droplet nucleation on condensation surfaces and promoting droplet jumping before a droplet reaches a critical size, which is heat-conduction limiting. Providing nanostructures on the microstructures can create a non-wetting surface that increases the apparent contact angle and reduces the contact angle hysteresis of droplets forming on the microstructures. Thus, such nanostructures may facilitate the movement of the droplets away from droplet nucleation sites and towards apexes of the nanostructures. A further benefit of using a hierarchically structured condensation surface with both microstructures and nanostructures thereon is that the effective heat transfer surface area is increased. Thus, there can be an increased number of nucleation sites on the condensing surface, leading to greater heat transfer rates compared to a condensing surface having only nanostructures.

FIGs. 1 A-1 C presents perspective views of different embodiments of heat transfer apparatuses 100. FIG. 2A presents a cross-sectional view of the apparatus shown in FIG. 1 B along view line 2A-2A. Figure 2A could also depict analogous cross-sectional views of the apparatuses shown in FIGs 1 A or 1 C. FIG. 3 presents a detailed view of a portion of the apparatus shown in FIG. 2A, although this figure could also depict analogous detailed views of the apparatuses shown in FIG. 1A or 1 C.

In some embodiments, the apparatus 100 comprises a condenser

105. The condenser 105 can be part of a variety of different two-phase heat transfer apparatuses such as, but not limited to, heat pipes, vapor chambers, looped heat pipes, two-phase forced convection flow loops or shell-and-tube surface condensers. For example, in some cases, the condenser 105 can be a portion of the heat transfer apparatus 100 configured as a heat pipe which further includes an evaporator portion 107. In still other embodiments the condenser 105 can be used in heat transfer apparatuses such as compact condensers for electronics thermal management, e.g., in telecommunications and data centers, industrial condensation heat exchangers, evaporator coils, dehumidifying coils, and/or water harvesting apparatuses.

The condenser 105 includes a base layer 1 10 and microstructures 1 15 (e.g., a distribution of microstructures) located on the base layer 1 10. Each microstructure 1 15 includes at least one sloped side 120 that forms an acute angle 125 with respect to a line 130 perpendicular to the base layer 1 10.

The at least one sloped side 120 connects to an apex 135 of the microstructure 1 15 located above the base layer 1 10. An outer surface 140 of the sloped side 120 has nanostructures 305 (e.g., a distribution of nanostructures) thereon, wherein the nanostructures 305 are spaced apart from each other and project out from the outer surfaces 140, e.g., as shown in FIG. 3.

As used herein, the term microstructure 1 15, as used herein, refers to a structure that has at least linear one-dimension 145 adjacent to the base layer 1 10 (e.g., a base width or depth) that extends a distance across the microstructure 1 15 in a range of 1 to 1000 microns.

As used herein, the term nanostructure 305, as used herein, refers to a structure that has at least one linear dimension (e.g. height, width, or depth) that extends a distance from one side to an opposing side (e.g., opposing lateral sides 310, 312, or, top and bottom sides 315, 317) of the nanostructure 305 in a range from 1 to 1000 nanometers. Additionally, the one linear dimension of the nanostructure 305 is at least 10 times smaller than the one dimension 145 of the microstructure 1 15. As a non-limiting example, when the one dimension 145 of the microstructure 1 15 equals 1 micron, then the one dimension of the nanostructure 305 can be up to 100 nanometers. Consequently, in this example, the at least one linear dimension of the nanostructure 305 (e.g., height, width, or depth), can be in a range of 1 to 100 nanometers. As another non-limiting example, when the one dimension 145 of the microstructure 1 15 equals 100 microns, then the one dimension of the nanostructure 305 (e.g., height, width, or depth), can be up to 1000 nanometers. Consequently, in this example, the one dimension of the nanostructure 305, can be in a range of 1 to 1000 nanometers. As used herein, the term acute angle refers to an angle that is greater than zero degrees and less than 90 degrees. In some embodiments, to increase the surface area of the condenser 105, the acute angle 125 is more preferably in a range from about 25 degrees to 65 degrees, and even more preferably, in a range from about 40 to 55 degrees.

In some embodiments of the apparatus 100, such as illustrated in Figure 1A, there is a single sloped side 120 that curves continuously around the entire microstructure 1 15, and each one of the microstructures 1 15 is a cone-shaped structure.

In other embodiments, such as illustrated in FIG. 1 B or 1 C, the at least one sloped side 120 joins with at least one other side 150 of the microstructure 1 15 at the apex 135, wherein an outer surface 155 of the at least other side 150 have the nanostructures 305 thereon.

For instance, as illustrated in FIG. 1 B, the at least one sloped side 120 can have a planar surface 140 and join with at least one other side 150 which also has a planar surface 155 to form ridge-shaped microstructures 1 15. Similar ridge-shaped microstructures could be formed where one or both of the surfaces 140, 155 of the sides 120, 150 are curved (e.g., curving inwards or curving outwards).

For instance, as illustrated in FIG. 1 C, the at least one sloped side

120 can join with two or more other sides 150, 160, 165 at the apex 135 to form pyramidal-shaped microstructures structures (e.g., structures with three or more planar or curved sides joining at the apex 135).

As further illustrated in FIG. 2A, in some cases, the at least one other side 150 that joins the sloped side 120 at the apex 135 is another sloped side that forms another acute angle 210 with respect to the line 130 perpendicular to the base layer 1 10. For instance, the other sloped side 150 can form an acute angle 210 that is about equal in magnitude but opposite in sign to the acute angle 125 of the sloped side 120. Similarly, in some embodiments, with more than two sides, such as illustrated in FIG. 1 C, each of the other sides 150, 160, 165 can be sloped sides and form about the same acute angles with respect to the line 130.

Referring to FIG. 2A, it is believed that the sloped side 120 (or other sloped sides 150, 160, 165 in some cases) helps to force a growing droplet 220 in a direction 222 away from droplet nucleation sites, e.g., sites in- between the nanostructures 305, towards the apexes 135 of the microstructures 1 15. E.g., the sloped side 120 may help such droplets 220 to move towards the apexes 135 of the microstructures 1 15. Although, in FIG. 2A, droplet nucleation is depicted as originating at a valley 225 between adjacent microstructures 1 15, a person of ordinary skill in the relevant arts would understand that droplet nucleation could originate at sites anywhere on the surfaces 140, 155, of the sides 120, 150.

Referring again to FIG. 2A, the apexes 135 of the microstructures 1 15 are separated from each other by a separation distance 230. The selection of the separation distance 230 between adjacent microstructures 1 15 is important to aiding the droplet 220 moving away the droplet nucleation sites, and to promote droplet jumping, before the droplet growth rate becomes heat conduction limited. As an example, water droplet growth become heat conduction limited at a droplet radius of about 5 microns or greater. Therefore, for certain embodiments of the apparatus 100, where heat transfer involves water condensation (e.g., occurs through a water condensation heat transfer processes), the separation distance 230 is preferably equal or less than about 10 microns. A person of ordinary skill in the relevant arts would understand how to determine a preferred maximal allowable droplet radius for different types of fluids, before the fluid's droplet growth rate becomes heat conduction limited. Accordingly, the separation distances 230 of a distribution of microstructures 1 15 could be set equal to or less than two times the preferred maximal allowable droplet radius. For instance, in some embodiments the separation distance 230 between the apexes 1 15 of adjacent ones of the microstructures 1 15 is in a range of 100 microns to 1 micron, and in some cases a range of 10 microns to 1 micron.

As further illustrated in FIG. 2A, in some embodiments of the apparatus 100, the sloped side 120 intersects with at least one other side 150 of the microstructure 1 15 to form the apex 135 shaped as a peak. It is believed that a peaked-shaped apex 135 can reduce a growing droplets 220 surface contact with the microstructures 1 15, and, thereby facilitate droplet jumping.

As further illustrated in FIG. 2A, in some embodiments of the apparatus 100, the sloped side 120 of the microstructure 1 15 intersects with at least one side (one of sides 120, 150) of an adjacent microstructure 1 15 at the base layer 1 10 to form a valley 225. Configuring the condenser 105 such that the sides of the adjacent microstructures 1 15 intersect at the base layer 1 10 helps to increase the total surface area of the condensation surface, and, can enhance condensation heat transfer by also providing a number of potential droplet nucleation sites.

In still other embodiments of the apparatus 100, however, the at least one sloped side 120 does not intersect with other sloping sides of the same microstructure 1 15 or of adjacent microstructures 1 15. For example, as illustrated in FIG. 2B, the sloped side 120 and another side 150 of the same microstructure 1 15 can separately intersect with a third side 235 (e.g., a planar horizontally oriented side) of the microstructure 1 15 to form the apex 135 shaped as a mesa. For example, as further illustrated in FIG. 2B, the sloped side 120 of one of the microstructures 1 15, and, another side 150 of an adjacent one of the microstructures 1 15 can separately intersect with a nanostructure 305 covered horizontally oriented layer 240 that is adjacent to the base layer 1 10.

The microstructures 1 15 can have various other shapes to increase the surface area upon which condensation can occur.

For instance, in other embodiments of the apparatus 100, as illustrated in FIG. 2C, the at least one sloped side 120 can intersect with another side 150 of the microstructure 1 15 which forms a right angle 250 with respect to the base layer 1 10, to form the apex 135, e.g., shaped as a peak. That is, the other side 150 has a surface 155 that is parallel with respect to a line 130 perpendicular to the base layer 1 10.

In other embodiments of the apparatus 100, as illustrated in FIG. 2D, the at least one sloped side 120 of one microstructure 1 15 can intersect with another side 150 of the same microstructure 1 15. The other sloped side forms a different magnitude acute angle 210 (e.g., at least about 10 percent different than the acute angle 125) with respect to the line 130 perpendicular to the base layer 1 10, to form the apex 135, e.g., shaped as a peak.

A person of ordinary skill in the relevant arts would appreciate how the sloped side 120 and the other sloped side 150, such as depicted in FIGs. 2C and 2D, could separately intersect with a third layer 235 or fourth layer 240 to form structures analogous to that shown in FIG. 2B.

In still other embodiments of the apparatus 100, as illustrated in FIG. 2E, the at least one sloped side 120, and in some cases, the other side 140, (or sides 140, 160, 165, FIG. 1 C) which are sloped, includes sloped portions 250 that have the acute angle 125 interspersed with horizontal portions 255 which are parallel with the base layer 1 10.

In some embodiments of the apparatus, such as depicted in FIGs. 1A-2E, the microstructures 1 15 of the condenser 105 can have the same shape and be about uniformly separated from each other. However, in other embodiments, microstructures 1 15 of the condenser 105 can have a variety of different shapes, such as, but not limited to, combinations of any of the shapes discussed in the context of FIGs. 1 A-2E, and/or, the microstructures 1 15 can have different separation distances 230, such as progressively increasing or decreasing distances 230 along one or more directions parallel to the base layer 1 10. For example, the separation distance 230 may monotonically increase or decrease with along one direction parallel to the base layer 1 10.

FIG. 4 presents a perspective view of the portion of example apparatus 100 presented in FIG. 3, depicting example nanostructures 305 of the apparatus 100. As illustrated, the nanostructures 305 can be ridged- shaped, and, the ridges are spaced apart from each other. In other embodiments, the nanostructures 305 can be pillar-shaped and the pillars are spaced apart from each other. The nanostructures 305 can cover the sloped side 120, and any of the other sides 150, 160, 165, peaked or mesa shaped apex 135, or horizontal layer 240 discussed in the context of FIGs. 1A-2E.

The use of nanostructures 305 to provide a non-wetting surface can be advantageous over conventional non-wetting condensing surfaces. Droplet adhesion to the condensation surface can be reduced with the appropriate nanostructure configuration. For instance, to reduce droplet adhesion, it is desirable for nanostructures to be configured to facilitate the droplet taking on a Cassie wetting state through contact line pinning at the base of the droplet. A person of ordinary skill in the relevant arts would understand that Cassie state refers to wetting state of the droplet where the droplet rests on the tops 315 of the nanostructures 305 in the vicinity of the droplet. For instance, in some cases, less than 10 percent of the nanostructure 305 nearest the top 315 is in contact with the droplet when the droplet is in a Cassie state. When in a Cassie state, most of the droplet is not in contact with the nanostructures 305, so that the droplet's adhesion to the nanostructures 305 is reduced. Additionally, because most of the droplet in a Cassie state rests on the tops 315 of the nanostructures 305, the sides 310, 312, and the surfaces 140, 155 that support the nanostructures 305, are available as sites for new droplet nucleation.

There are several structural attributes that the nanostructures 305 can have to facilitate a droplet in attaining a Cassie state.

For instance, in some preferred embodiments, it is desirable for the nanostructures 305 to provide the condensation surface with a certain amount of surface roughness to deter a droplet from taking on an undesirable Wenzel state. A Wenzel state refers to a wetting state where the droplet substantially contacts the entire surfaces of the nanostructures in the vicinity of the droplet. For example, in a Wenzel state, substantially the entire height of the droplet may contact the sides 310, 312 and tops 315 of the nanostructures 305 support surfaces 140, 155. In various embodiments, it is often undesirable that a droplet take Wenzel states, because the large contact area of the droplet in such a state can provide a large adhesion that pins the droplet in-between the nanostructures 305. Wenzel state formation therefore impedes the droplet from moving away from its nucleation site to the apexes 135 of the microstructures 1 15, which in turn may reduce the efficiency of condensation heat transfer.

To help avoid growing droplets taking such a Wenzel state, it is desirable for the surface 140, or surfaces 140, 155 that have the nanostructures 305 thereon, to satisfy the following condition when a liquid droplet rests on the surface:

-1/r ^* cos9a < 1

Here, the parameter r is the surface roughness factor of the surfaces of the nanostructure, and 9a is an intrinsic advancing contact angle of the liquid droplet. Herein, the surface roughness factor, r, is defined as the total surface area, including the areas of the sides 310, 312, and tops 315 and support surfaces 140, 150 in between the nanostructures divided by projected surface area of the surfaces 140, 150, e.g., the area support surfaces 140, 150 with no nanostructures 305 thereon. The intrinsic advancing contact angle, 9a, refers to the contact angle that the fluid droplet would have on a smooth surface, e.g., the support surfaces 140, 150 with no nanostructures 305 thereon.

For instance, in some preferred embodiments, it is desirable for the adjacent nanostructures 305 to be spaced apart by a minimum separation distance 320 (e.g., the distance from the side 310 of one nanostructure 305 to the side 312 of an adjacent nanostructure 305). The suitable minimum separation distance 320 is that which allows the droplets to form and grow in-between the nanostructures 305 while avoiding undesirable capillary evaporation effects.

Preferably, the distance 320 is greater than a critical condensation radius 410, r _c , for a nucleating fluid droplet. The critical condensation radius can be estimated by the formula:

r _c = 2Yu/(kTlnS),

Here, γ is the ratio of liquid to vapor surface tension, u is a molecular volume of the liquid phase , k is the Boltzmann constant, S is defined as the ratio of the vapor pressure pv to the saturation pressure at the condensing surface temperature T. For example, in some embodiments of the apparatus 100, for a water droplet, the distance 320 separating adjacent nanostructures is equal to of greater than about 10 nanometers. For example, in some embodiments of the device 100, the distance 320 is in a range of about 1 to 100 nanometers, and in some cases in a range of about 10 to 20 nanometers.

Preferably, the distance 320 between adjacent ones of the nanostructures 305 has a value that promotes a droplet to attain the Cassie state before the droplet radius 410, R, grows to size that is heat conduction limiting. For example, for water droplet this value of the radius 410 is about 5 microns or larger. The Cassie state, in turn, is promoted by spacing the nanostructures apart by a preferred distance 320 and by having a height 420 that facilitates the growing droplet to have a receding contact angle 430, 9r, of at least about 90 degrees.

For instance, in some preferred embodiments, the nanostructures satisfies the relationship:

cos0 _r < - (1 - h R)/(l + 2k w),

Here, 9r is a receding contact angle 430 of at least 90 degrees for a maximally desired size of droplet located on tops of the nanostructures, h is the uniform height 420 of the nanostructures 305, R is a radius 410 of the fluid droplet and w is a uniform separation distance 320 between adjacent ones of the nanostructures 305.

The term receding contact angle 430 as used herein is defined as the minimum stable angle that the droplet achieves while on the nanostructures 305. A person of ordinary skill in the relevant arts would be familiar with methods to measure the receding contact angle 430 of a droplet 220 (see e.g., "Condensation on Superhydrophobic Surfaces: The Role of Local Energy Barriers and Structure Length Scale" and Supporting Information, by Enright et al., Langmuir pub. Aug 29, 2012 ("Enright-1 "), incorporated by reference herein in its entirety).

Herein, the term receding contact angle 430 is defined as the minimum stable angle that the droplet achieves while on the nanostructures 305. A person of ordinary skill in the relevant arts would be familiar with methods to measure the receding contact angle 430 of a droplet 220 (see e.g., "Condensation on Superhydrophobic Surfaces: The Role of Local Energy Barriers and Structure Length Scale" and Supporting Information, by Enright et al., Langmuir pub. Aug 29, 2012 ("Enright-1 "), incorporated by reference herein in its entirety).

The receding contact angle 140 for a droplet to spontaneously achieve a Cassie state can be reduced by reducing the ratio h/R, and/or, increasing the ratio h/w.

For instance, consider a fluid whose critical size, where heat conduction through the bulk of the droplet begins to limit the heat transfer rate, and, that critical size corresponds to a droplet radius 410 of 5 microns or greater. Assuming a desired receding contact angle 430, Θ _Γ , equal to 120 degrees, to make the ratio of h, the uniform height 420 of the nanostructures 305 to R, a radius 410 of the fluid droplet less than or equal to 0.1 (i.e., h/R≤ 0.1 ) requires h≤ 0.5 μηι. For a h/R ratio equal to 0.1 and the height 420, h, equal to 0.5 μηι, the separation distance 320 between microstructures, w, is then equal to 833 nanometers and the h/w ratio equals 0.6. Continuing with the same example, where the h/R ratio equals 0.1 and h equals 0.5 μηι, for a receding contact angle 430, Θ _Γ , equal to 1 10 degrees, w, is then equal to 451 nanometers and the h/w ratio equals 1.1 , or, for a receding contact angle 430, Θ _Γ , equal to 100 degrees, w, is then equal to 187 nanometers, and the h/w ratio equals 2.7, or, for a receding contact angle 430, Θ _Γ , equal to 90 degrees, w, is then equal to 16 nanometers, and the h/w ratio equals 31 .3.

In some embodiments of the apparatus 100, reduce the adhesion of a de-wetted droplet (e.g., a droplet in a Cassie state) it is desirable to reduce the fraction of space occupied by the nanostructures 305 relative to the open space in-between adjacent ones of the nanostructures. For instance, in some embodiments, the solid fraction occupied by the nanostructures 305 is equal to or less than 0.1 . As used herein the term solid fraction herein is equal to d/(d+w), where d is the width 435 of the nanostructure and w is the separation distance 320 between adjacent ones of the nanostructures 305.

As a non-limiting example, in cases where the separation distance 320 is equal to 833 nanometers, then the width 435 is preferably equal or less than 93 nanometers. Or, when the separation distance 320 is equal to 451 nanometers, then the width 435 is preferably equal or less than 50 nanometers. Or, when the separation distance 320 is equal to 451 nanometers, then the width 435 is preferably equal or less than 50 nanometers. Or, when the separation distance 320 is equal to 187 nanometers, then the width 435 is preferably equal or less than 21 nanometers. Or, when the separation distance 320 is equal to 16 nanometers, then the width 435 is preferably equal or less than 1 .8 nanometers.

Referring to any of FIGs. 1 A-4, another apparatus 100 embodiment comprises a distribution of microstructures 1 15 on an area of a surface 180 (e.g., a condensation surface), each of the microstructures 1 15 having one or more sloping sides 120, 155, 160, 165. The apparatus 100 also comprises a distribution of nanostructures 310 being located on the one or more sloping sides 120, 155, 160, 165. The distribution of microstructures 1 15 on the area of the surface 180 is configured to nucleate and grow droplets 230 of liquid from a gas. The distribution of nanostructures 310 forms a superhydrophobic surface 325 for the liquid.

As used herein, a surface 325 is considered to be a superhydrophobic surface 325 (synonymous with the term non-wetting surface as used herein) when a fluid droplet 230 of the fluid laying on the surface 325 has a contact angle 325 of equal to or greater than about 90 degrees. This is in contrast to a hydrophillic surface (synonymous with the term wetting surface as used herein) where a fluid droplet 145 laying on the surface 325 has a contact angle 140 of less or equal to 90 degrees.

In some embodiments of the apparatus 100 the microstructures 1 15 are configured to nucleate the droplets between the nanostructures 310. In some embodiments, the microstructures 1 15 are ridges. In some embodiments, the microstructures 1 15 are pointed structures (e.g., the apexes 135 have a pointed shape). In some embodiments, the apparatus 100 further includes a heat pipe 170 or a vapor chamber 170, the distribution of microstructures being located in a condenser 105 portion of the heat pipe 170 or vapor chamber 170.

The distribution of microstructures 1 15 and the distribution of nanostructures 310 could include any combination of any or all of the microstructures 1 15 or nanostructures 310 configurations disclosed herein.

Still another embodiment is a method that comprises manufacturing a heat transfer apparatus. With continuing reference to FIGs. 1 A-4 throughout, FIG. 5 presents a flow diagram of an example method of manufacturing a heat transfer apparatus of the disclosure, such as any of the example apparatuses 100 described in the context of FIGs. 1A-4.

As illustrated in FIG. 5, the method includes a step 505 of manufacturing a condenser. Manufacturing the condenser (step 505) includes a step 510 providing a base layer 1 10 and step 515 of forming microstructures 1 15 on the base layer 1 10. Each microstructure 1 15 includes at least one sloped side 120 that forms an acute angle 125 with respect to a line 130 perpendicular to the base layer 1 10. The at least one sloped side 120 connects to an apex 135 of the microstructure 1 15 located above the base layer 1 10. The method also includes a step 520 of forming nanostructures 305 on a surface 140 of the at least one sloped side 120, wherein the nanostructures 305 are spaced apart from each other and project out from the surface 140.

In some cases, providing the base layer 1 10 in step 510 can simply include providing a material layer 170, e.g., of copper, aluminum, semiconductor material upon which the microstructures 1 15 are directly formed from in step 515. In some cases the use of a highly heat conductive material layer 170 such copper, aluminum is preferred. In other cases, the providing the base layer 1 10 in step 510 can include a step 525 of depositing a second material layer 175 on the first material layer 170, where the microstructures 1 15 is formed from the second material layer 175. For instance, a second material layer 175 of copper or aluminum could be deposited on a first material layer 170 of steel, via electrolytic, electroless or other deposition processes familiar to a person of ordinary skill in the relevant arts.

In some embodiments of the method, forming the microstructures 1 15 (step 515) includes a step 530 of mechanically modifying portions of the base layer 1 10. For instance, a base layer 1 10 of copper or aluminum, or, a second layer 175 of the base layer 1 10, can be mechanically indented, machined, stamped, embossed or otherwise mechanically modified to form any of the microstructure 1 15 shapes discussed in the context of FIGs. 1 A- 4.

In some embodiments of the method, forming microstructures 1 15 (step 515) includes a step 535 of etching portions of the base layer 1 10. For instance, a base layer 1 10 or a second layer 175, composed of a semiconductor material, such as a silicon layer, can be etched by wet or dry etching processes, or laser etching processes, familiar to a person of ordinary skill in the relevant arts to form the microstructures 1 15.

In some embodiments of the method, forming the nanostructures 305 (step 520) includes a step 540 of wherein forming the nanostructures includes exposing the surface 140 of the sloped side 120, (or surfaces 140, 155 of the sides 120, 150) of the microstructure 1 15 to an oxidation process. For instance a copper base layer 1 10 of second layer 175 can be exposed to chemical oxidation conditions such as in "Condensation on Superhydrophobic Copper Oxide Nanostructures," by Enright et al. Proceedings of the 3rd Micro/Nanoscale Heat and Mass Transfer International Conference, Atlanta, GA, March 3-6, 2012, MNHMT2012- 75277 ("Enright-2"), incorporated by reference herein in its entirety, to form the nanostructures 305 therefrom. For instance, an aluminum base layer 1 10 or second layer 175 can be exposed to well-known hydrothermal oxidation processes to form the nanostructures 305 therefrom.

In some embodiments of the method, forming the nanostructures 305 (step 520) includes exposing the surface 140 of the sloped side 120, (or surfaces 140, 155 of the sides 120, 150) of the microstructure 1 15 to an etch process in step 545. For instance, microstructures 1 15 composed of a semiconductor material, such as silicon, can be subjected to a reactive ion etching process to form the nanostructures 305, such as black silicon nanostructures. Other examples of etching process for forming nanostructures are presented in Enright-1.

In some embodiments of the method, part of forming the nanostructures 305 (step 520) includes functionalizing the nanostructures 305 in step 550 with a low surface energy material. The term low surface energy material, as used herein, refers to a material having a surface energy of about 22 dynes/cm (about 22 x 10-5 N/cm) or less as disclosed in U.S. Patent 7,695,550 to Krupenkin et al. ("Krupenkin"), incorporated by reference herein in its entirety.

Non-limiting examples of functionalizing nanostructures in accordance with step 550 includes coating nanostructures 305 with chlorosilanes, fluorosilanes or fluorinated polymers, such as disclosed in Krupenkin, Enright-1 or Enright-2.

With continuing reference to FIGs. 1A-4 throughout, FIG. 6 presents a flow diagram of another method embodiment of the disclosure. The method comprises a step 610 of forming a distribution of microstructures 1 15 on an area of a surface 180, each of the microstructures 1 15 having one or more sloping sides 120, 155, 160, 165. The distribution of microstructures 1 15 on the area of the surface 180 is configured to nucleate and grow droplets 230 of liquid from a gas. The method comprises a step 620 of forming a distribution of nanostructures 310 being located on the one or more sloping sides 120, 155, 160, 165. The distribution of 5 nanostructures forms a superhydrophobic surface 325 for the liquid.

The steps 610, 620 of forming the distribution of microstructures 1 15 and the distribution of nanostructures 310 could include any or all of the microstructures 1 15 or nanostructures 310 configurations disclosed herein and any combination of any or all of the method steps for of forming the l o microstructures 1 15 or nanostructures 310 disclosed herein.

FIG. 7 illustrates another embodiment of the disclosure, a system 700. In some embodiments the system 700 can be communication system such as a telecommunication system or a system component (e.g., electronic cabinet) of a communication system. The system 700 comprises

15 heat generating equipment 710, such electrical equipment, e.g., circuit boards having heat generating components thereon. The system 700 also comprises a heat transfer apparatus 720. The heat transfer apparatus 720 can be configured to remove heat generated by the equipment 710 of the system 700.

20 The heat transfer apparatus 720 can be or include any apparatuses described herein. In some cases, for instance, referring to FIGs. 1 A-4, the apparatus 720 can include a distribution of microstructures 1 15 on an area of a surface 180 (e.g., a condensation surface), each of the microstructures 1 15 having one or more sloping sides 120, 155, 160, 165. The apparatus

25 720 also comprises a distribution of nanostructures 310 being located on the one or more sloping sides 120, 155, 160, 165. The distribution of microstructures 1 15 on the area of the surface 180 is configured to nucleate and grow droplets 230 of liquid from a gas. The distribution of nanostructures 310 forms a superhydrophobic surface 325 for the liquid.

30 In some cases, for instance, with continuing reference to FIGs. 1A-4, in some embodiments of the system 700, the distribution of microstructures 1 15 is located on the surface 180 of a condenser 105 of the apparatus 710. In some embodiments, the condenser 105 is part of a heat pipe 170, while in other embodiments, the condenser 105 is part of a vapor chamber 170. Although the present disclosure has been described in detail, a person of ordinary skill in the relevant arts should understand that they can make various changes, substitutions and alterations herein without departing from the scope of the invention.