Kapitsa theory wavy flow

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. 

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. 

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... 

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. 

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 ... 

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). 

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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