Abstract:
The present invention includes use of suitable inert, or non-reactive, gas, or gases, having suitably small molecules (such as helium or neon) in a heat pipe to enhance the surface tension (capillarity) of the heat pipe working fluid, thus improving the design and performance of almost any heat pipe. A region in the vapor space adjacent to the curved liquid surface contributes about 5-10% to the total surface tension, and is described as the Crutchfield Transition Region. The invention takes advantage of the kinetic theory of capillarity based on penetrations of the liquid surface by the overbearing gas and vapor molecules until a collision between liquid and gaseous molecules occurs. Smaller molecules such as helium penetrate further. A spread loss (or gain) of the particle flux frames a pressure change.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1 Field of the Invention  
           [0002]    The present invention generally relates to a thermodynamic system that takes advantage of the kinetic theory of capillarity, including a vapor-side component of capillarity. More specifically, the present invention is a thermal management system including a heat pipe having a helium atmosphere, the heat pipe utilizing a vapor-side component of capillarity.  
           [0003]    2. Description of the Related Art  
           [0004]    Conventional wisdom holds that the rise of water in a thin capillary tube is understood as a mismatch of intermolecular forces at the interface of the water surface and the overbearing atmosphere. The mismatch produces a state of tension at the surface such that for a hemispheric surface of the water in a capillary tube, the lifting force, σ in Newtons per meter (N/m), acting on the circumference of the hemisphere, will lift the water—ignoring air density above the surface in the tube—according to the following relationship:  
           2πσR=ΔρgHπR 2 ,   (1)  
           [0005]    where Δp is the difference in water density and the surrounding gas,  
           [0006]    H is height of rise of the column of water,  
           [0007]    g is the gravity constant, and  
           [0008]    σ is the surface tension in N/m.  
           [0009]    A review of units shows “Newtons”=“Newtons”, or “force”=“counter force”. Division by the capillary tube cross-sectional area, πR 2 , leaves the unit force per unit area, or pressure. The force of surface tension produces a step change in pressure across the meniscus surface equal to the drop in pressure produced by the rise of water in the tube.  
           [0010]    In the case of non-circular surfaces, the sum of orthogonal curvatures, 1/R 1 +1/R 2  must be used instead of 2/R as encountered in a circular tube. The wetting angle between the water surface and the tube surface must also be considered.  
           [0011]    Many have written about the capillary rise phenomena, including Newton, Gauss, Laplace, Gay-Lussac, Poisson and Maxwell. Further, the value of the surface tension of water has been thoroughly measured from the freezing temperature to the critical temperature, as partially shown in Table 1. Table 1 provides calculations of the three components of surface tension in 10° C. steps under atmospheric air. The temperature and density components in the vapor state are lumped by means of the Clausius-Clayperon factor.  
                                                                           TABLE                            SUFACE TENSION COMPONENTS, WATER IN AIR ATMOSPHERE, N/M 10 3                                      Steam Table       Temp   Liq. Density   Liq., T   Vapor       Eff. Molecular   Derived Radii,       (C°)   Component 1     Comp 2     Comp 3     σ TOTAL 4     Radii, Å 5     Å 6                      0   54.32   18.03   3.15   75.50   1.86   1.926       10   57.78   13.32   3.30   74.40   1.84   1.926       20   59.84   9.59   3.44   72.87   1.86   1.927       30   60.75   6.87   3.58   71.20   1.89   1.928       40   60.81   4.96   3.71   69.48   1.92   1.931       50   60.29   3.65   3.83   67.77   1.94   1.933       60   59.38   2.77   3.91   66.06   1.95   1.937       70   58.21   2.19   3.96   64.36   1.95   1.940       80   56.93   1.82   3.94   62.69   1.93   1.944       90   55.34   1.61   3.83   60.78   1.90   1.949       100   53.75   1.59   3,57   58.91   1.81   1.953                                                                  
 
           [0012]    Although the value of the surface tension of water has been measured, few have analytically quantified the values of surface tension over any range of temperatures. This is understandable, as those of the past had neither modern computers nor a suitable Equation of State for water, the equation itself a product of modern computers.  
           [0013]    It proves to be beneficial to provide a kinetic approach to surface tension, and to use such an approach to provide a new and non-obvious enlianced thermal management system. It is to the provision of such a system that the present invention is primarily directed.  
         BRIEF SUMMARY OF THE INVENTION  
         [0014]    The present invention is an application of a kinetic theory to explain the capillarity (surface tension) phenomenon, and will be discussed in examples using water as the working medium, although any element or mixture in its liquid state may be suitable, especially those exhibiting a relatively high surface tension, polarity, or a capability of hydrogen bonding. It is assumed the overbearing air and water vapor molecular penetrations into the water surface produce an expansion, or compression, of the liquid across a transition zone at a curved interface because of the focusing effect of the curved surface. A fallout of the theory is a discovery of a pressure change contribution across a vapor transition zone, usually about one order of magnitude less than the liquid transition contribution, this region hereby being defined as the “Crutchfield Transition Region.” 
           [0015]    In the vapor region remote from the liquid surface, constituent molecules develop a “mean free path” between collisions. This concept leads to pressure against a smooth container wall. Hitherto it stops short of consideration of a curved, partially penetrable liquid surface. Such curves and penetrations generally require no consideration in the case of a flat liquid surface. However, for a curved surface, molecules departing the surface experience either a compression or an expansion, hence either a rise or fall in temperature and pressure when joining their new surroundings. A Clausius-Clayperon relationship facilitates analysis of this situation.  
           [0016]    Accordingly, there are four components of the surface tension—a pressure one and a temperature one in the liquid transition zone, and a pressure one and a temperature one in the Crutchfield Transition Zone, the latter two amenable to coupling using the Clausius-Clayperon formula. Utilizing known data and an Equation of State, surface tension components of water from the freezing temperature to the critical temperature were calculated, with good results except near the critical temperature (where the basic assumptions are invalid). Results in Table 1 are shown for water under a standard atmosphere, 0° to 100° C.  
           [0017]    An experiment illustrates an increase in the capillary rise of water under a helium atmosphere (as opposed to air) attributable to the thicker transition zones effected by the relatively smaller helium atoms. 
       
    
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0018]    [0018]FIG. 1 is a cross section of a heat pipe according to the present invention.  
         [0019]    [0019]FIGS. 2 a - c  are examples of cycloids referenced herein. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0020]    A Kinetic Approach To Surface Tension  
         [0021]    A compressed gas exerts pressure on the walls of a container by means of the rebounds of myriad molecules of the contained gas against the walls. The same occurs against an underlying liquid surface, for example, water. However, some degree of penetration Δ PENETRATION  into the water should take place, depending upon the size and shape of the involved molecules of both the water and the gas. Though it is easier to measure a capillary rise, it is simpler to analyze effects on spherical droplets where the sphere&#39;s surface produces a focusing effect.  
         [0022]    Consider the normal direction from a differential area, ΔS, on the surface of a spherical drop of water in an air atmosphere. Unless the sphere is in motion with respect to its environment, non-radial molecular bombardments (and recoils) will cancel each other&#39;s non-radial forces. There will be a mean free distance that molecules will penetrate to, or emanate from, inside ΔS. The operative distance (similar to the development of viscosity theory), taking all directions into account, would be one-third a mean free path in the radial direction −δr. The focusing effect of the spherical surface drives the radial flux of water (and air) molecules according to the relationship:  
         Φ=Φ 0 ( R/r ) 2    (2)  
         [0023]    where Φ 0  is the flux at the surface, and  
         [0024]    where r=R.  
         [0025]    Vapor Component of Surface Tension  
         [0026]    A hitherto neglected phenomenon in the capillary arena is the region in the vapor area immediately surrounding the sphere which also extends to one-third a mean free path radially, Δr—orders of magnitude greater than that in the liquid.  
         [0027]    Since pressure of water may be defined by a function of density and temperature, the differential relationship follows:  
           dP=∂P/∂T dt+∂P/∂ρdρ   (3)  
         [0028]    Keenan, Keyes, Hill and Moore in their  STEAM TABLES, Thermodynamic Properties of Water Including Vapors Liquid, and Solid Phases,  Keenan, Keyes, Hill and Moore, John Wiley &amp; Sons, have provided an Equation of State for addressing Equation (3) above. The density is inversely proportional to r 2  in both the liquid and vapor regions, to wit:  
           d ρ=(−)(2 /R )ρ 0   dr    (4)  
         [0029]    where dr is one-third a mean free path in either region.  
         [0030]    Assuming the region extending to a distance ΔR in the vapor region is saturated, the Clausius-Clayperon relationship would apply, to wit:  
           dP =( h   fg   /v   fg ) dT/T    (5)  
         [0031]    where h fg  and v fg  are the enthalpy and volume differences between the saturated liquid and saturated vapor.  
         [0032]    Solving equations (3) and (5) provides a multiplying factor to apply to the partial derivative with respect to density, yielding the total derivative, dP/dρ, in the vapor region. The value of ΔR is calculated from known viscosities of saturated vapor. The change in temperature in the liquid region is obtained by multiplying the change in the vapor region by δr/ΔR, the respective one-third mean free paths.  
         [0033]    Referring back to Table 1, inasmuch as the radius of a helium molecule (atom) is about 40% that of nitrogen and oxygen, the one-third a mean free path in both regions should be considerably greater than those of water-under-air. In an experiment, the water rise in a capillary tube in air was marked. The air was then released, and commercial grade helium was substituted therefore. The water rose about 30% higher in the same capillary tube, as predicted.  
         [0034]    Effect of Helium Gas Coverage Versus Air  
         [0035]    The “dr” in the various differentials is linearly proportional to the relevant capillarity component. The governing characteristic is the penetration distance of the overbearing gas molecules before the first collision beyond the interfacial surface, or since the last collision in the Crutchfield Region. The sizes of the colliding molecules are a primary factor. (A similar relationship is encountered in nuclear reactor theory). In fact, the specific factor is the “collision diameter”—the sum of the radii of the colliding particles—the smaller the better. Helium is very attractive as one of the colliders. It is small, inert and, for many purposes, light.  
         [0036]    A proof-of-principle experiment in a helium atmosphere provided results indicating that the decreased collision diameter between the helium and water molecules versus that between air and water produced the desired results.  
         [0037]    As described above, this kinetic theory of capillarity proposes two transition zones at the interface between the liquid water and the overriding air/water vapor mixture. One zone is in the liquid of thickness δ the other is in the air/vapor mixture of thickness A. The thickness δ is established by the mean penetration of the air/vapor molecules into the liquid and is ⅓ the mean free path (MFP). The thickness Δ is, likewise, ⅓—MFP in the air/vapor mixture. Both are determined by the fluid densities and the “effective” liquid and gas molecule radii. (Molecular velocity considerations are subsumed in the term “effective”.) In the gas region, treating the mixture as homogeneous, the collision diameter would be the sum of the equal “effective” radii.  
         [0038]    Rohsenow and Choi in their  Heat, Mass and Momentum Transfer,  Prentice-Hall, 1961 (Table 20.1, p.493), provide molecular diameters in Å for several gases at 15° C. They list 3.72 Å as the diameter of the air molecule. Calculations by the applicant yielded 3.88 Å as the effective diameter of the liquid molecules at 15° C. This combination would yield a collision diameter of about 3.80 Å for saturated air molecules impinging on the water surface.  
         [0039]    Rohsenow and Choi set forth 2.18 Å as the molecular diameter of helium at 15°, and at atmospheric pressure, about 2.20 Å. It should be expected that the effective collision diameter for such molecules impinging on liquid water to be (3.88 Å+2.20Å)/2, or 3.04 Å. Since δ is inversely proportional to the square of the collision diameter, δ under the helium atmosphere should be greater than that in air by the square of the ratio 3.80/3.04, or about 1.56. The Δs should be related by the square of the ratio 3.80/2.20, or about 2.98.  
         [0040]    Because of this expansion of the transition zone in a helium atmosphere, one should expect a significant increase in the surface tension of water in such circumstances.  
         [0041]    An overbearing atmosphere of, for example, neon, another inert gas, with a molecular diameter of 2.59 Å according to Rohsenow and Choi, would also provide a greater capillary rise than an air atmosphere. A reduction in the collision diameter will provide an enhanced capillary rise, mutatis mutandis.  
         [0042]    High Altitude Effects  
         [0043]    In the rarer atmosphere at high altitudes where the pressure is considerably reduced, the one-third mean free path in the vapor region, ΔR, increases. For P halved, ΔR would be approximately doubled, at least to a first order effect. Since the pressure change across the transition zone is proportional to the product of P and ΔR, the pressure difference across ΔR should not change significantly, except for very small radii of curvature of the liquid surface.  
         [0044]    At 0° C. and sea level pressure, ΔR is approximately 3 centimicrons. At about an 18,000 feet altitude, 5.5 km, the pressure is halved. Assuming 0° C. at 5.5 km—a hot day at ground level—ΔR would double. A million-molecule spherical water droplet would have a radius of slightly less than 3 centimicrons. The focusing effect of the droplet would increase the particle density—both air and water vapor—nine-fold at the liquid surface, raising the droplet temperature to about 34° C.  
         [0045]    A million-molecule droplet in a 10° C. ambient environment would be at a temperature of about +23° C. Such droplets hitherto have been labeled “supersaturated”.  
         [0046]    These considerations point to the possible formation of clouds and fog particles in the form of collections of “Hot Air Balloons.” A cloud consisting of solid liquid balls would defy the law of gravity. However, surface tension phenomena afford the existence of such “hollow” constructs. The quenching of a volume of saturated air, creating a volume of super saturation, could effect such constructs, inter alia. The thickness of the liquid skin would depend primarily upon surface tension and the ambient atmospheric pressure, and weakly upon the balloon radius. An assumption is that the greater total force acting outward on the smaller inner liquid skin area equals the lesser total force acting inward on the outer surface of the liquid skin. Too large a balloon radius would deny enough heat to lighten the air-steam interior; too small, not enough lift to offset the liquid weight. Other factors to consider are the comparative molecular weights of water and air, and the energy balances, particularly between the heat of condensation going to liquid and the heating of the interior of the balloon.  
         [0047]    It is further interesting to note that the vapor contribution to surface tension suggests a possibility of “vapor wakes” behind ships or submarines. The theories regarding ocean waves have not addressed a Crutchfield Transition Zone, of course. Capillary phenomena generally are meaningful only at small, uninteresting dimensions. The prevailing theories have the parcels of water at the surface in deep ocean waters move essentially in circles, with the phase relationship producing various wave motions. One such curve is a cycloid, a curve described by a point on the circumference of a circle which rolls along a fixed straight line. At its lowest point the curvature of a cycloid is infinite, compressing the air above. A curtate cycloid is one described by a point just inside the circumference of the rolling circle. The curvature at the low point is not infinite, but can be large. There could be cumulative or resonant effects producing a wind shear. Winds make waves. It follows that waves can make winds. FIGS. 1 a - c  show various cycloids. FIG. 1 a  exhibits a curve described by a point on the circumference of a circle which rolls along a fixed straight line where x=a(Φ−b sin Φ) and y=a(1−cos Φ). The area of one arch=3πa 2 . The length of the arc of one arch=8a. FIGS. 1 b  and  1   c  exhibit proloate and curtate cycloids. Here, a curve is described by a point on a circle at a distance b from the center of the circle of radius a which rolls along a fixed straight line, where x=aΦ−b sin Φ and y=a−b cos Φ.  
         [0048]    Heat Pipes  
         [0049]    A system of thermal management utilizing the kinetic theory of capillarity is the heat pipe  10 , as shown in FIG. 2. A heat pipe  10  is a vapor-liquid phase-change device that transfers heat from a hot reservoir to a cold reservoir using capillary forces generated by a transfer device, preferably a wick  12  or porous material, and a working fluid  14 . A heat pipe typically comprises a container  16 , lined with the wick  12 , which provides the capillary driving force to return the condensate to the evaporator.  
         [0050]    The container isolates the working fluid from the ambient. It is leak-proof, maintains the pressure differential across its walls, and enables the transfer of heat from and into the working fluid.  
         [0051]    The container is filled with the working fluid near its saturation temperature. The working fluid has both a liquid phase and a vapor phase which is the desired range of operating temperatures. When one portion of the container is exposed to a relatively higher temperature, it functions as an evaporator section  18 . The working fluid is vaporized in the evaporator section and flows in the vapor phase to the relatively lower temperature section of the envelope which becomes a condenser section  22 . The working fluid is condensed in the condenser section and then returns in the liquid phase in a short time from the higher temperature section of the envelope to the lower temperature section as a consequence of the phase change of the working fluid.  
         [0052]    Because it operates on the principle of phase change rather than on the principles of conduction or convection, a heat pipe is capable of transferring heat at a much higher rate than conventional heat transfer systems.  
         [0053]    In heat pipes using a wick, the quantity of working fluid is selected so that no surplus liquid phase is provided at the desired operating temperature. As a result there is only modest interference between the liquid phase and the vapor phase.  
         [0054]    If a heat pipe container is generally tubular in shape and is disposed substantially horizontally, the liquid phase of the working fluid will return to the high temperature of the heat pipe in either direction under the action of gravity so that heat transfer is bidirectional and does not require a capillary wick to return the working fluid to the evaporative section, thus permitting a more inexpensive heat pipe to be used.  
         [0055]    In heat pipe design, a high value of surface tension is desirable in order to enable the heat pipe to operate against gravity and to generate a high capillary driving force. In addition to high surface tension, it is necessary for the working fluid to immerse the wick and the container material i.e. contact angle should be zero or very small. The vapor pressure over the operating temperature range must be sufficiently great to avoid high vapor velocities, which tend to setup large temperature gradient and cause flow instabilities.  
         [0056]    In one embodiment of the present invention, water is used as the working fluid in environments of between 0° and 100° C., while a gas  24 , such as helium, is supplied as an atmosphere in the heat pipe. Other atmospheres would be beneficial, including those with a particle diameter less than that of water, approximately 3.72-3.88 Å at 15° C. Other gasses, preferably inert, can be used other than helium.  
         [0057]    Other working fluids are more practical than water in different temperature ranges. In such environments, heat pipes have an effective thermal conductivity many thousands of times that of copper. The heat transfer or transport capacity of a heat pipe is specified by its “Axial Power Rating (APR)”. It is the energy moving axially along the pipe. The larger the heat pipe diameter, greater is the APR. Similarly, the longer the heat pipe, the smaller the APR. Heat pipes can be built in almost any size and shape.  
         [0058]    The present invention comprises the use of suitable inert, or non-reactive, gas, or gases, having suitably small molecules (such as helium or neon) in a heat pipe to enhance the surface tension (capillarity) of the heat pipe working fluid, thus improving the design and performance of almost any heat pipe.  
         [0059]    Although the present invention has been described with respect to particular embodiments, it will be apparent to those skilled in the art that modifications to the method of the present invention can be made which are within the scope and spirit of the present invention and its equivalents.