Kapitsa

P. L. Kapitsa (Moscow) basic inventions and discoveries in the area of low-temperature physics. 

Low-temperature research requires hard work and imagination, but successful advances are richly rewarded. Seven Nobel Prizes in physics and chemistry have been awarded for low-temperature research. The first, in 1913, went to the Dutch physicist Heike Kamerlingh Onnes, who discovered how to cool He gas to 4.2 K and convert it into a liquid. The American William Giauque received the 1949 prize in chemistry and the Russian Pyotr Kapitsa won the 1978 prize in physics. Each was honored for a variety of discoveries resulting from low-temperature research, and each developed a new technique for achieving low temperature. 

Kapitza, P. L., 1964, Wave Flow of Thin Layers of a Viscous Fluid, in Collected Papers of P. L. Kapitsa, vol. II, Macmillan, New York. (3)... 

The Kapitsa treatment of wavy film flow (K7), which is discussed in detail later, indicates that... 

Kapitsa was the first to attempt the solution of this system of equations (K7). In this original solution the term v du/dy in Eq. (47) was omitted, as also in the analysis by Portalski (P3) who resolved Kapitsa s equations to a higher degree of accuracy. By comparing the corrected solution by Bushmanov (B22, L9) with the original result, it appears that the errors caused by the omission of this term are not large. 

It is seen from (65) that the wave velocity is considerably smaller than the value given by the first approximation, (58). From (63), the ratio of the mean film thickness in wavy flow to the thickness of a smooth film at the same flow rate is given by 4>1/3 or, from above, 0.93. The corresponding value obtained by Portalski (P3) was 0.94. It is thus seen that for wavy flow of the type assumed here, the mean thickness of the wavy film is 6-7% smaller than the corresponding smooth film. It is pointed out by Kapitsa that it does not follow that there may not be some other type of film surface configuration which would lead to a greater reduction in thickness and, therefore, to greater stability of flow. 

It is claimed that this relationship is valid up to approximately Nne = 300. However, the Kapitsa treatment (K7) is shown to be valid only up to the condition that the wavelength is more than 13.7 times as great as the film thickness, which corresponds to A r6 = 50 for a vertical water film. 

Kapitsa and Kapitsa (K10) have shown that the relative change in wavelength for flow on a tube of radius R compared with that on a flat surface at the same flow rate is... 

Recently, Kasimov and Zigmund (K12) have published the first part of a new theoretical treatment of wavy film flow, extending their recent work on smooth laminar film flow (Section III, B, 5) to this case also. It is shown that, with appropriate assumptions, the new theory reduces to the Nusselt solution for smooth films, or to a result similar to the corrected Kapitsa solution. The most interesting conclusions to be drawn from the part of the theory so far published are ... 

Kapitsa (K8) extended his treatment of wavy free film flow to cover this case also. For the simplest case, in which the gas stream does not seriously affect the wavelength, it was found to a first approximation that the mean film thickness 5 could be given in terms of the flow rate per wetted perimeter Q and the mean gas velocity ugas by means of the equation... 

Konobeev el al. (K20, K21) have generalized the Semenov and Kapitsa results for the case of wavy film flow with an adjoining gas stream. In particular, the wavelength expression is obtained as... 

More recent film thickness measurements in the laminar wavy regime obtained by improved techniques (F2, F7, P3) have shown that there are appreciable reductions in the mean film thickness in the wavy regime for both vertical and sloped surfaces, as predicted by the Kapitsa theory. 

Feind (F2) measured the thickness of various films of kinematic viscosities 1 to 19.7 centistokes flowing in a vertical tube. An improved drainage technique was used. At the lowest values of Nr.,. (smooth laminar flow regime) the values of Nr fell along the line given by Eq. (97). Once wavy flow commenced, the values deviated towards the Kapitsa line,... 

Hence, the trend predicted by the Kapitsa theory is supported by the recent, more accurate, film thickness measurements. This does not indicate, however, that the Kapitsa theory will apply in detail over the whole wavy laminar regime of film flow, since Kapitsa (K7) pointed out that such a reduction in the mean thickness should result for other types of wavy flow besides the particular case considered in his theory. 

It is seen that in general the various theories are in reasonable agreement with each other, especially the Benjamin and the Ishihara theories. The simple condition Nvt = 1 shows a similar trend with channel slope, but the values lie slightly higher at all slopes. The Kapitsa theory predicts that the values of Nr<>, will change little with slope except at very small slopes. 

Tailby and Portalski (T4) have reported measurements of the wavelengths near the point of wave inception on vertical films of various liquids. Even in this case, it was found that the wavelengths were considerably greater than predicted by the Kapitsa theory, Eq. (67), even in the cases in which the conditions of the theory were satisfied. Similar results have been obtained for water films on walls of various slopes (F7). 

Although there are numerous published investigations in which records of the wavy surface profile have been obtained, e.g. (H9, D16, Sll), not many of these have been analyzed for information on wavelengths, most being concerned with wave-size (height) distributions. However, it may be noted that the experimental wavelengths of Kapitsa and Kapitsa (K10) show a trend in the direction of the data reported above, even at very small Reynolds numbers (lVa < 25). It seems, therefore, that the Kapitsa theory is applicable only at very small flow rates, as far as wave characteristics are concerned, in the case of the free flow of wavy films. Allen (A3) has reported a similar conclusion. 

Fig. 5. The lines c/u = 3 and c/u = 2.4 corresponding to the theories of Benjamin and Hanratty and Hershman and of Kapitsa are shown, together with the line given by Eq. (115), using 6 = 7 °. The remaining lines represent smoothed experimental wave velocity data (F7) for water films on wetted walls of slopes 7, 62, and 90°.

It can be seen immediately that the experimental values of c/U reach a value of 3 only at very small flow rates, near the flow rate for the onset of rippling, which is the zone for which Benjamin s theory is strictly applicable. The experimental values fall below the Kapitsa value of 2.4 at NRC = 30. The theoretical relationship by Ishihara et al. predicts that c/u will decrease as NRe increases, but less rapidly than observed experimentally. However, this theory is strictly applicable only at very small channel slopes and for waves of negligibly small amplitude, so that exact agreement cannot be expected. 

The experimental wave velocities of Kapitsa and Kapitsa (K10) for vertical water films are in agreement with the results given above, but these investigators only covered the range up to ARe = 25. The experimental wave velocities for water films given by Portalski (P3) (90°) and... 

Portalski (T2) has extended Kapitsa s treatment of wavy film flow to obtain an expression for the increase in interfacial area due to the waves [Eq. (68)]. For mobile liquids this relationship predicts that the increase in interfacial area will be very large, reaching 150% for 2-propanol at NRe = 175, for example, though the applicability of the Kapitsa theory at such large Reynolds numbers is in doubt. Experimental values of the... 

On the theoretical side, Dmitriev and Bonchkovskaya (D8) have shown that in principle turbulence should spread from waves. Kapitsa (K9) has calculated a general tensor quantity, termed the coefficient of wavy transfer, which is applicable to any flow with periodic disturbances, such as pulsations or surface waves. This treatment predicts an appreciable increase in the rates of heat and mass transfer in wavy films, though this increase does not appear to be as large as that observed experimentally under certain conditions. 

Kapitsa (K7, K8), 1948 Theoretical treatment of wavy flow of thin films of viscous liquids, including capillary effects. Only regular waves considered. Wavy flow shown to be more stable than smooth film, and about 7% thinner than smooth film at same flow rate. Also calculates wave amplitudes, wavelengths, etc., onset of wavy flow, effects of countercurrent gas stream, heat transfer. Theory applicable only if wavelength exceeds 14 film thicknesses. Error in treatment pointed out by Levich (L9). 

Kapitsa and Kapitsa (K10), 1949 Wavy flow of water and alcohol films on outside of tube of diameter 2 cm., NRe < 100, studied photographically and stroboscopically. Experimental data at low flow rates in agreement with Kapitsa theory waves become random at large flow rates. 

Semenov (S7), 1950 Extension of earlier work to wavy film flow. Kapitsa theory simplified by omitting inertia terms, and applied to wavy film flow with co- or counter-flow of gas to give thickness, velocity, wavelength, wave velocity, stability, onset of flooding, etc. 

Kapitsa (K9), 1951 Deals theoretically with heat and mass transfer to periodic flows, e.g., to wavy liquid films. 

Levich (L9), 1959 Final chapter deals with film flow theory (smooth, wavy laminar, turbulent) with and without gas flow. Also considers mass transfer to such films. Correction to theory of Kapitsa (K7). 

Tailby and Portalski (T2), 1960 Reports on extension of Kapitsa theory (K7) to give increase in interfacial area due to waves experimental measurements of Am, for wave inception, entry length, and increase in interfacial area. 

Allen (A3), 1962 Investigation of characteristics of liquid films on vertical surface, with emphasis on surface features. Kapitsa theory shown to be applicable only at low flow rates. Increase in interfacial area reported to be smaller than predicted by Portalski theory. 

Portalski (P4), 1963 Theories of film flow and methods of measuring film thickness are reviewed. Film thicknesses on vertical plate (zero gas flow) reported for glycerol solutions, methanol, isopropanol, water, and aqueous solutions of surfactants. Results compared with values calculated by Nusselt, Kapitsa, and corrected Dukler and Bergelin treatments. 

Portalski (P5), 1964 From Kapitsa s theory of wavy film flow, it is shown that regions of reversed flow exist under the wave troughs, leading to the generation of circulating eddies which may explain the increased rates of heat and mass transfer to wavy laminar films. 

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