Abstract:
A method and apparatus is disclosed wherein the flow resistance of a droplet disposed on a nanostructured or microstructured surface is controlled. A closed-cell feature is used in a way such that, when the pressure of at least a first fluid within one or more of the cells of said surface is decreased to or below a desired level, a droplet disposed on that surface is caused to at least partially penetrate the surface. In another illustrative embodiment, the pressure within one or more of the cells is increased to or above a desired level in a way such that the droplet of liquid is returned at least partially to its original, unpenetrated position. In yet another embodiment, a closed-cell structure feature pattern is used to prevent penetration of the nanostructured or microstructured surface, even when the pressure of the fluid disposed on the surface is relatively high.

Description:
CROSS REFERENCE TO A RELATED APPLICATION 
     This Application is a Divisional of U.S. application Ser. No. 10/674,448 filed on Sep. 30, 2003, to Marc Hodes, et al., entitled “METHOD AND APPARATUS FOR CONTROLLING THE FLOW RESISTANCE OF A FLUID ON NANOSTRUCTURED OR MICROSTURCUTRED SURFACES,” currently Allowed; commonly assigned with the present invention and incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to the motion of liquids disposed on a surface with extremely small, predetermined surface features and, more particularly, to controlling flow resistance experienced by a liquid disposed on a surface with predetermined nanostructure or microstructure features. 
     BACKGROUND OF THE INVENTION 
     Many beneficial devices or structures in myriad applications are characterized at least in part by having a liquid that is in contact with at least one solid surface. Recent applications have focused on the movement of small droplets of liquid disposed on nanostructured or microstructured surfaces which can be manufactured by various methods, such as various means of lithography or etching. Such surfaces result in surfaces that are useful for significantly reducing flow resistance experienced by droplets of liquid disposed on the surfaces. 
     One such application is described in “Nanostructured Surfaces for Dramatic Reduction of Flow Resistance in Droplet-based Microfluidics”, J. Kim and C. J. Kim, IEEE Conf. MEMS, Las Vegas, Nev., January 2002, pp. 479-482, which is hereby incorporated by reference herein in its entirety. That reference generally describes how, by using surfaces with predetermined nanostructure features, the flow resistance to the liquid in contact with the surface can be greatly reduced. The Kim reference teaches that, by finely patterning the surface in contact with the liquid, and using the aforementioned principle of liquid surface tension, it is possible to greatly reduce the area of contact between the surface and the liquid. It follows that the flow resistance to the liquid on the surface is correspondingly reduced. However, as exemplarily taught by the Kim reference, the flow resistance to the liquid is reduced to such a level that it was difficult or impossible to control the movement of the liquid. Thus, it was necessary to dispose the droplets in a narrow channel or other enclosure to control the freedom movement of the droplet to within a prescribed area. 
     In order to better control the movement of liquid droplets disposed on surfaces patterned with nanostructures or microstructures, more recent attempts have relied on characteristics of the droplet or, alternatively, intra-pattern characteristics of the nanostructures or the microstructures to control the lateral movement of liquid droplets. Such control is the subject of copending U.S. patent application Ser. No. 10/403,159, filed Mar. 31, 2003, entitled “Method And Apparatus For Variably Controlling The Movement Of A Liquid On A Nanostructured Surface” which is hereby incorporated by reference herein in its entirety. In one embodiment described in that application, the lateral movement of a liquid droplet is achieved by designing, illustratively, the size, shape, density, or electrical properties of the nanostructure or microstructure such that the contact angle of the leading edge of a droplet is made to be lower than the contact angle of the trailing edge of the droplet. The resulting force imbalance causes the droplet to move in the direction of the leading edge. In another embodiment, the droplet is caused to penetrate the feature pattern at a desired area such that it becomes substantially immobile. This penetration can be affected, for example, by changing the surface tension of the droplet, the temperature of either the droplet or the pattern or the voltage differential between the droplet and the feature pattern. 
     As described in the &#39;159 application, one or both of the above embodiments may be useful in a variety of applications, such as, illustratively, a biological or micro-chemical detector, a chemical reactor, a patterning application, a tunable diffraction grating, a total internal reflection mirror, a microfluidic mixer, a microfluidic pump or a heat dissipation device. 
     Thus, the above-described prior efforts focused on either reducing flow resistance experienced by a droplet or controlling the movement of a droplet of water across a surface. In another recent attempt, nanostructures or microstructures are used to reduce the flow resistance experienced by a body moving through a fluid. That attempt is described in copending U.S. patent application Ser. No. 10/649,285, entitled “Method And Apparatus For Reducing Friction Between A Fluid And A Body,” filed Aug. 27, 2003 and is hereby incorporated by reference herein in its entirety. According to the embodiments of the invention disclosed in the &#39;285 application, at least a portion of the surface of a vehicle moving through a fluid is patterned with nanostructures or microstructures. Thus, according to the principles discussed above, the flow resistance across the patterned surface is reduced. Also as discussed above, by causing the fluid to penetrate the patterned surface, flow resistance across the patterned surface can be increased. 
     SUMMARY OF THE INVENTION 
     While prior attempts to reduce the flow resistance of a fluid in contact with a surface are advantageous in many regards, we have realized that it would be extremely advantageous to be able to control the degree of penetration of a fluid disposed on a nanostructured or microstructured surface. Therefore, we have invented a method and apparatus wherein, in a first illustrative embodiment, a closed-cell nanostructured or microstructured surface is used in a way such that, when the pressure of at least a first fluid within one or more of the cells of said surface is decreased to or below a desired level, a droplet disposed on that surface is caused to at least partially penetrate the surface. In another illustrative embodiment, the pressure within one or more of the cells is increased to or above a desired level in a way such that the droplet of liquid is returned at least partially to its original, unpenetrated position. In this way, the penetration of the droplet into the surface can be varied to achieve a desired level of flow resistance experienced by the droplet of liquid. 
     In yet another embodiment, a closed-cell structure feature pattern is used to prevent penetration of the nanostructured or microstructured surface, even when the pressure of the fluid disposed on the surface is relatively high. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIGS. 1A ,  1 B,  1 C,  1 D and  1 E show various prior art nanostructure feature patterns of predefined nanostructures that are suitable for use in the present invention; 
         FIG. 2  shows an illustrative prior art device wherein a liquid droplet is disposed on a nanostructured or microstructured feature pattern 
         FIG. 3A  shows the droplet of liquid of  FIG. 2A  suspended on the nanostructured feature pattern of  FIG. 3 ; 
         FIG. 3B  shows the droplet of liquid of  FIG. 4A  when it is caused to penetrate the nanostructured feature pattern of  FIG. 3 ; 
         FIGS. 4A and 4B  show an illustrative prior art device whereby the electrowetting principles are used to cause a liquid droplet to penetrate a nanostructure feature pattern; 
         FIGS. 5A ,  5 B and  5 C show a device in accordance with the principles of the present invention wherein a droplet is disposed in an initial position suspended on top of a nanostructured feature pattern ( FIG. 5A ), is caused to penetrate the feature pattern ( FIG. 5B ), and is then caused to return to a position suspended on top of the feature pattern ( FIG. 5C ); 
         FIGS. 6A and 6B  show an illustrative closed-cell structure in accordance with the principles of the present invention; 
         FIGS. 7A and 7B  show the detail of one cell in the illustrative structure of  FIGS. 6A and 6B ; 
         FIGS. 8A ,  8 B and  8 C show a device in accordance with the principles of the present invention wherein a droplet is disposed in an initial position suspended on top of a nanostructured feature pattern ( FIG. 8A ), is caused to penetrate the feature pattern ( FIG. 8B ), and is then caused to return to a position suspended on top of the feature pattern ( FIG. 8C ); 
         FIG. 9  shows a graph of the temperature of the fluid in a closed cell necessary to achieve a transition from the device in  FIG. 5A  to the device in  FIG. 5B  as a function of the initial temperature in that cell and the size d of the cell; 
         FIG. 10  shows a graph of the temperature of the fluid in a closed cell necessary to achieve a transition from the device in  FIG. 5B  to the device in  FIG. 5C  as a function of the initial temperature in that cell and the size d of the cell; 
         FIGS. 11A and 11B  show another embodiment of a closed-cell structure in accordance with the principles of the present invention; 
         FIG. 12  shows a graph of pressure versus cell dimensions for the embodiment of  FIGS. 11A and 11B ; 
         FIGS. 13A and 13B  show another embodiment of a closed-cell structure in accordance with the principles of the present invention; 
         FIG. 14  shows a graph of pressure versus cell dimensions for the embodiment of  FIGS. 11A and 11B . 
     
    
    
     DETAILED DESCRIPTION 
     As described above, microstructures and nanostructures have been used recently to reduce the flow resistance of experienced by a liquid as it moves across a surface. Such prior micro- or nanostructures can take many forms. For example,  FIGS. 1A-1E  show different illustrative prior art arrangements of nanoposts produced using various methods and further show that such various diameter nanoposts can be fashioned with different degrees of regularity. These figures show that it is possible to produce nanoposts having various diameters separated by various distances. An illustrative method of producing nanoposts, found in U.S. Pat. No. 6,185,961, titled “Nanopost arrays and process for making same,” issued Feb. 13, 2001 to Tonucci, et al, is hereby incorporated by reference herein in its entirety. Nanoposts have been manufactured by various methods, such as by using a template to form the posts, by various means of lithography, and by various methods of etching. As used herein, unless otherwise specified, the terms nanostructures/nanoposts and microstructures/microposts are used interchangeably. Throughout the description herein, one skilled in the art will recognize that the same principles applied to the use of nanoposts or nanostructures can be equally applied to microposts or other larger features in a feature pattern. 
     As is noted by the Kim reference described hereinabove, prior attempts at placing a droplet on surfaces having nanostructures or microstructures were problematic, as the extremely low flow resistance experienced by the droplet made it almost impossible to keep the water droplets stationary on the respective surface. As shown in  FIG. 2 , the reason for this low flow resistance is that the surface tension of droplet  201  of an appropriate liquid (depending upon the surface structure) will enable the droplet  201  to be suspended on the tops of the nanostructure feature pattern  202  with no contact between the droplet and the underlying solid surface  203 . While nanostructures  202  are illustratively cylindrical posts in  FIG. 2 , one skilled in the art will realize that many suitable geometric shapes, such as conical posts, may be equally advantageous. As illustratively shown in  FIG. 2 , suspending the droplet on top of the nanostructures results in an extremely low area of contact between the droplet and the nanostructured surface  204  (i.e., the droplet only is in contact with the top of each post  202 ) and, hence low flow resistance. 
       FIG. 3A  shows a macro view of the droplet  201  of  FIG. 2  when it is suspended on top of the nanostructure feature pattern  202 . As in  FIG. 2 , the droplet in  FIG. 3A  does not penetrate the feature pattern  202  and, accordingly, experiences a low flow resistance.  FIG. 3B , however, shows illustrative droplet  201  in a configuration in which it does penetrate feature pattern  202 . When the droplet  201  penetrates the feature pattern  202 , the droplet becomes relatively immobile, i.e., it experiences a relatively high degree of flow resistance. In general, a liquid droplet will penetrate a feature pattern, for example, when the surface tension of the liquid droplet is sufficiently low. Therefore, depending upon the characteristics of the feature pattern  202 , one skilled in the art will be able to select a liquid for droplet  201  with an appropriate surface tension to facilitate such penetration of the pattern  202 . Alternatively, as described in copending U.S. patent application Ser. No. 10/403,159, discussed and incorporated by reference hereinabove, various methods can be used to reduce the surface tension of the droplet  201  that is suspended on top of the feature pattern, as is illustrated in  FIG. 3A . 
       FIGS. 4A and 4B  show such a prior art embodiment of one method useful to cause the droplet  201  to penetrate a nanostructure feature pattern.  FIG. 4A  illustrates, for example, the area  301  in  FIG. 3  of droplet  201  in contact with feature pattern  202 . Referring to  FIG. 4A , droplet  201  is illustratively a conducting liquid and is disposed on nanostructure feature pattern  202  of conical nanoposts. As described above and illustrated in  FIG. 3A , the surface tension of the droplet  201  is such that the droplet  201  is suspended on the upper portion of the feature pattern  202 . In this arrangement, the droplet  201  only covers surface area f 1  of each nanopost. The nanoposts of feature pattern  202  are supported by the surface of a conducting substrate  203 . Droplet  201  is held illustratively at an electrical potential difference with respect to substrate  203 , applied by voltage source  401  through lead  402 . 
       FIG. 4B  shows that, by applying a low voltage (e.g., 10-20 volts) to the conducting droplet of liquid  201 , a voltage difference results between the liquid  201  and the nanoposts of feature pattern  202 . As a result, the contact angle of droplet  201  decreases and droplet  201  moves down in the y-direction along the surface of the nanoposts and penetrates the nanostructure feature pattern  202  until it completely surrounds each of the nanoposts and comes into contact with the upper surface of substrate  203 . In this configuration, the droplet covers surface area f 2  of each nanopost. Since f 2 &gt;&gt;f 1  the overall contact area between the droplet  201  and the nanoposts of feature pattern  202  is relatively high and, accordingly, the flow resistance experienced by the droplet  201  is greater than in the embodiment of  FIG. 4A . Thus, as shown in  FIG. 4B , the droplet  201  effectively becomes stationary relative to the nanostructure feature pattern in the absence of another force sufficient to dislodge the droplet  201  from the feature pattern  202 . 
     The present inventors have recognized that it would be desirable to be able to selectively cause a droplet of liquid to penetrate a feature pattern and, then, to be able to selectively reverse this penetration.  FIGS. 5A ,  5 B and  5 C illustrate such a selective/reversible penetration of droplet  501  into pattern  504 .  FIG. 5A  shows an illustrative droplet  501  disposed on a nanostructure or microstructure feature pattern  504  that is supported by substrate  505 . The angle of contact between the droplet and the feature pattern is shown as θ 1 . Next, as shown in  FIG. 5B  and discussed above, droplet  501  is caused to penetrate the feature pattern  504 . The angle of contact between the droplet and the feature pattern increases in this case to θ 2  as the droplet moves down along the individual elements (e.g., nanoposts) toward substrate  505 . Finally, as shown in  FIG. 5C , it is desirable to reverse the penetration of droplet  502  into the pattern  504 . In this case the contact angle between the droplet and the feature pattern is as low or lower than θ 1 . Here, illustratively, the contact angle between the droplet  501  and the feature pattern  504  is shown as θ 3 , which is illustratively a smaller angle than θ 1 . 
       FIGS. 6A and 6B  show, respectively, a three-dimensional view and a top cross-sectional view of an illustrative feature pattern in accordance with the principles of the present invention that is capable of accomplishing the reversible penetration shown in  FIGS. 5A-5C . Specifically, in the present illustrative embodiment represented by  FIGS. 6A and 6B , the feature pattern does not comprise a number of posts spaced a distance away from each other. Instead, a number of closed cells, here illustrative cells of a hexagonal cross section, are used. As used herein, the term closed cell is defined as a cell that is enclosed on all sides except for the side upon which a liquid is or could be disposed. One skilled in the art will recognize that other, equally advantageous cell configurations and geometries are possible to achieve equally effective closed-cell arrangements.  FIGS. 7A and 7B  show a top cross-sectional view and a side view of an illustrative individual cell of the feature pattern of  FIGS. 6A and 6B . Specifically, referring to  FIG. 7A , each individual cell  701  is characterized by a maximum width  702  of width d, an individual side length  703  of length d/2 and a wall thickness  704  of thickness t. Referring to  FIG. 7B , the height  705  of cell  701  is height h. 
       FIGS. 8A ,  8 B and  8 C show how an illustrative closed-cell feature pattern similar to the feature pattern of  FIGS. 6A and 6B , here shown in cross-section, may be used illustratively to cause a droplet  801  of liquid to reversibly penetrate the feature pattern. Specifically, each cell within feature pattern  804 , such as cell  701  having a hexagonal cross-section, is a completely closed cell once the droplet of liquid covers the opening of that cell. Thus, referring to  FIG. 8A , each such closed cell over which the droplet is disposed contains a fluid having an initial temperature T=T 0  and an initial pressure P=P 0 . As used herein, the term fluid is intended to encompass both gases (such as, illustratively, air) and liquids that could be disposed within the cells of the feature pattern. The present inventors have recognized that, by changing the pressure within the individual cells, such as cell  701 , the liquid droplet  801  can be either drawn into the cells or, alternatively, repelled out of the cell. Specifically, referring to  FIG. 8B , if the pressure within the cell  701  is caused to be below the initial pressure (i.e., P&lt;P 0 ), then the contact angle of the droplet with the feature pattern will increase from θ 1  to θ 2  and the droplet above that cell will be drawn into the cell a distance related to the magnitude in reduction of the pressure P. Such a reduction in pressure may be achieved, illustratively, by reducing the temperature of the fluid within the cells such that T&lt;T 0 . Such a temperature reduction may be achieved, illustratively, by reducing the temperature of the substrate  805  and/or the feature pattern  804 . In this illustrative example, the temperature of the fluid may be reduced by well-known conduction/convection principles and, accordingly, the pressure within the cell will drop. One skilled in the art will recognize that any method of reducing the pressure within the cells, including any other method of reducing the temperature of the fluid within the cells, will have similar results. 
       FIG. 8C  shows how, by increasing the pressure to or above the initial pressure P 0 , it is possible to reverse the penetration of the droplet  801 . Once again, such a pressure increase may be achieved by changing the temperature of the fluid within the cells, illustratively in  FIG. 8C  to a temperature greater than the initial temperature T 0 . The increased temperature will increase the pressure within the cells above the initial pressure P 0 . The contact angle between the droplet and the elements of the feature pattern will thus change to θ 3 , which is smaller than θ 1  and the liquid will move out of the cells, thus returning droplet  801  to a very low flow resistance contact with feature pattern  804 . Once again, one skilled in the art will recognize that any method of increasing the pressure within the cells to reverse the penetration of the droplet  801 , including any other method of increasing the temperature of the fluid within the cells, will have similar results. 
       FIG. 9  shows a graph  904  of the temperature (T trans ) necessary to achieve a 120 degree contact angle of advancement (θ 2  in  FIG. 8B ) in order to achieve penetration of the droplet into a feature pattern.  FIG. 9  assumes a cell height h of 160 microns and a droplet interfacial tension of 62 mN/m. With these conditions,  FIG. 9  shows that, for an initial temperature T 0  of the fluid within the cells and for a representative width d (represented by plots  901 ,  902  and  903  and shown in  FIGS. 7A and 7B  as dimension  702 ), there is a given temperature (T trans ) at or below which a droplet will penetrate the feature pattern. For example, If the width of the cell is 15 microns, illustrated by plot  902  on graph  904 , and the initial temperature T 0  of the fluid in the cells is 60 degrees Celsius, then the pressure will drop sufficiently to cause the droplet to penetrate the feature pattern at or below a transition temperature T trans  of approximately 15 degrees Celsius, represented by point  905  on plot  902 . 
       FIG. 10  shows a graph  1004  having plots  1001 ,  1002  and  1003  representing different cell widths d, discussed above. Once again, the interfacial tension of the droplet is assumed to be 62 mN/m and the cell height h is assumed to be 160 microns.  FIG. 10  shows the temperature change necessary to achieve a 0 degree contact angle (θ 2  in  FIG. 8B ) which is the smallest contact angle theoretically achievable to reverse the penetration of the droplet after it has penetrated the feature pattern. For example, once again for a cell width of 15 microns, represented by plot  1002 , for an initial temperature T 0  (prior to any penetration of the feature pattern) of 40 degrees Celsius, point  1005  on plot  1002  shows that a transition temperature T trans  of approximately 110 degrees Celsius is necessary to increase the pressure within the cells and reverse the contact angle of the droplet to 0 degrees and achieve full reversal of the penetration. One skilled in the art will recognize that different contact angles may be achieved and, in the case of reversing the penetration, lower transition temperatures will generally result in greater contact angles, all else remaining equal. Thus, many different temperatures (lower than T 0 ) may be used to penetrate the liquid into the feature pattern and, similarly, many different temperatures (higher than T 0 ) may be used to reverse that penetration. 
     Thus, the foregoing discussion illustrates how penetration of a feature pattern may be achieved and how that penetration can be selectively reversed. However, in addition to facilitating penetration reversal, the present inventors have recognized that closed cell feature patterns such as that described above, are useful for other purposes. For example, such feature patterns may function to substantially prevent any penetration of the feature pattern even in the presence of increasing pressure exerted by the droplet onto that feature pattern. Such a function may be desirable on, for example, a submersible vehicle. The use of above-described open-celled nanostructured feature patterns on submersible vehicles is the subject of copending U.S. patent application Ser. No. 10/649,285, entitled “Method And Apparatus For Reducing Friction Between A Fluid And A Body,” filed Aug. 27, 2003, which is hereby incorporated by reference herein in its entirety. 
     The &#39;285 application discloses how open-celled nanostructure feature patterns, when used on a submersible vehicle such as a submarine or a torpedo, will dramatically reduce the friction (drag) caused by flow resistance of, illustratively, water passing across the surface of the underwater vehicle. However, while such reduced friction is advantageous in many situations, the present inventors have recognized that, when the pressure of the water exceeds a certain threshold (depending upon the characteristics of the feature pattern), the water will penetrate the feature pattern, possibly dramatically increasing the drag on the submersible vehicle. Therefore, the present inventors have further recognized that it is desirable to prevent the water from penetrating the feature pattern even in the presence of relatively high pressure. 
       FIGS. 11A and 11B  show one illustrative embodiment in accordance with the principles of the present invention whereby liquid is prevented from penetrating a feature pattern even when that liquid is at a relatively high pressure. Referring to  FIG. 11A , a top view of a nanostructured or microstructured feature pattern is shown wherein each cell has a rectangular cross section. Each cell has a length l, a wall thickness t and a width r. Referring to  FIG. 11B , each cell also has a height h. Illustratively, l=10 micrometers, t=0.3 micrometers, r=4 micrometers and h=0.25 micrometers. Initially, the pressure within each of the cells in  FIG. 11A  is at an ambient pressure P 0 . Thus, for example, in the case where the feature pattern of  FIGS. 11A and 11B  is disposed on the surface of a submarine, when the submarine is traveling on the surface of water at least a portion of the cells will have an initial pressure of the air surrounding the submarine. When the submarine submerges, however, as is illustratively represented by  FIG. 11B , the water begins to exert a pressure P 2  onto the feature pattern, thus resulting in a contact angle θ between the liquid and the pattern. The resulting increased contact angle will correspondingly increase the pressure of the fluid (e.g., air) within the cell from P 0  to P 1 . As the depth of the submarine increases and the pressure P 2  increases, the contact angle θ will increase and, as a result, the pressure P 1  within the cell will similarly increase. At a threshold determined by the characteristics of the feature pattern  1103  (e.g., the length, height and width of the cells), the pressure P 2  and hence the contact angle θ will become too great and the water  1102  will penetrate the feature pattern  1103  until it contacts substrate  1101 . For the feature pattern of  FIGS. 11A and 11B , therefore, up to a certain pressure limit there will be a range of pressures (that correspond to depths in water for the illustrative example of a submarine) for which the water will not penetrate the feature pattern. Thus, in the case of the submarine, the submersible vehicle can submerge to a depth much greater without penetration of the feature pattern than would be the case where an open-celled feature pattern of, for example, nanoposts, were used. As a result, low flow resistance can be maintained to a much greater depth that using such an open pattern. 
       FIG. 12  shows a graph  1204  with plots  1201 ,  1202  and  1203  that illustrate how different pressures within the cells of the feature pattern of  FIGS. 11A and 11B  will result in a specific contact angle when the cells are defined by a particular height to width ratio (h/r). For example, plot  1201  shows that, for cells having h/r=0.18, a pressure P 1  that is two times the initial pressure P 0  will result in a contact angle of 120 degrees. Plots  1202  and  1203  show how changes in the pressure P 1  will result in different contact angles for given cell dimensions. One skilled in the art will readily be able to develop different plots for different contact angles other than those shown in  FIG. 12 . 
       FIG. 12  also shows that, for pressures and cell dimension combinations that fall within area  1205  of graph  1204 , there are no solutions that would lead to an unpenetrated surface of the feature pattern. Thus, for example, for any cell dimensions, a pressure P 1  that is 5 times the initial ambient pressure P 0 , will lead to penetration of the feature pattern. However, since such pressures are routinely experienced by underwater vehicles such as submarines, it is highly desirable to be able to prevent penetration of the feature pattern for significantly greater pressures. 
       FIGS. 13A and 13B  show an illustrative cell configuration that will prevent the penetration of water into the feature pattern at significantly greater pressures. As shown in  FIG. 13A  the top cross section view of the feature pattern capable of withstanding greater pressures appears to be the same as that in  FIG. 11A  and, indeed, can have the same length (l=10 micrometers), wall thickness (t=0.3 micrometers) and width (r=4 micrometers) as the embodiment in that figure. Similarly, referring to  FIG. 13B , the height of the individual cells is, illustratively, the same as the height h (0.25 microns) of the cells of  FIG. 11B .  FIG. 13B  shows, however, that instead of being rectangular in side cross section, as were the cells in  FIG. 11B , the cells of  13 B are rounded at the bottom and, thus, each cell is capable of holding less fluid (e.g., air). As a result, when the pressure P 2  rises and compresses the fluid within the cell, the pressure P 1  rises more quickly than was the case in the embodiment of  FIGS. 11A and 11B . Thus, the cell can withstand a much higher pressure of water before the liquid will penetrate the cells of the feature pattern. 
       FIG. 14  shows a graph  1404  with plots  1401 ,  1402  and  1403  that illustrate how different pressures within the cells of the feature pattern of  FIGS. 13A and 13B  will result in a specific contact angle when the cells are defined by a particular height to width ratio (h/r). As can be seen at point  1405 , for a height to width ratio of approximately 0.12, a contact angle of approximately 110 degrees will result from a pressure P 1  of 5 times the initial ambient pressure P 0 . Similarly, point  1406  shows that, for a slightly higher cell height to width ratio of 0.18, a contact angle of 120 degrees will result from a pressure P 1  of 6 times the initial ambient pressure P 0 . In fact, a contact angle of 120 degrees is practically limitless with regard to the pressure P 1  that can be withstood without penetration of the feature pattern. Accordingly, the low-flow properties of the surface remain intact and, in the case of a submarine, a low friction (drag) will continue to be experienced even at great water pressures/depths. 
     The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are within its spirit and scope. Additionally, one skilled in the art, in light of the descriptions of the various embodiments herein, will recognize that the principles of the present invention may be utilized in widely disparate fields and applications. For example, one skilled in the art will recognize that, although not explicitly described hereinabove, other well known methods of producing nanostructures or microstructures, such embossing, stamping, printing, etc., could be used. 
     All statements herein reciting aspects and embodiments of the invention, as well as specific examples thereof, are intended to encompass functional equivalents thereof. Moreover, all examples and conditional language recited herein are intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited examples and conditions. For example, while the description of the above embodiments is limited to discussing a droplet disposed on a nanostructured or microstructured surface, one skilled in the art will readily recognize that the above embodiments are intended to encompass any flow of a liquid across a surface or the movement of a surface through a liquid. Additionally, while pressure variations are discussed as being used to cause a liquid to penetrate a feature pattern, one skilled in the art will recognize that prior methods of causing such penetration, such as causing the surface tension of the droplet to drop, will be equally advantageous. Also, in light of the principles set forth above, one skilled in the art will be able to devise many different applications could benefit from the ability to prevent penetration of a feature pattern or from reversing such a penetration. Finally, penetration of a liquid into a feature pattern and the reversing of that penetration may be accomplished by other means other than increasing or decreasing the temperature of the fluid within closed cells. For example, air may be blown/withdrawn into/from the cells, thus increasing/decreasing, respectively, the pressure within those cells.