Falling films waves

FIGURE 15.142 Flow patterns in falling film waves for wave height to substrate height ratios of 2, 4, and 6 (from Jayanti and Hewitt [359], with permission of Elsevier Science). Note axial distance foreshortened by a factor of about 400 for presentational purposes. 

Grimley (G10, Gil) used an ultramicroscope technique to determine the velocities of colloidal particles suspended in a falling film of tap water. It was assumed that the particles moved with the local liquid velocity, so that, by observing the velocities of particles at different distances from the wall, a complete velocity profile could be obtained. These results indicated that the velocity did not follow the semiparabolic pattern predicted by Eq. (11) instead, the maximum velocity occurred a short distance below the free surface, while nearer the wall the experimental results were lower than those given by Eq. (11). It was found, however, that the velocity profile approached the theoretical shape when surface-active material was added and the waves were damped out, and, in the light of later results, it seems probable that the discrepancies in the presence of wavy flow are due to the inclusion of the fluctuating wavy velocities near the free surface. 

Work done by Brauer (10) pointed out that the waves arising in a falling film at low viscosity are about 2.6 times higher than the mean film thickness defined by Equation 1. In Figure 2, the mean thickness of the film according to Equation 1 is expressed as a function of the peripheral load for different product viscosities (curve 1 water 1 CST, curve 2, 3 higher viscosities. 

The heat transfer in the lower part of the sphere is highly nonlinear, and no correlation was reported for this region. Karapantsios and Karabelas [184] experimentally examined the influence of flow intermittency on direct contact condensation of a quasistagnant vapor-gas mixture on falling liquid waves. Flow intermittency was found to increase the heat transfer rate by as much as an order of magnitude. Mikielewicz et al. [218] recently included turbulent diffusion effects in studying direct-contact condensation of steam on a horizontal water film. 

In turbulent falling films, there is a complex combined effect on heat transfer of the turbulence and interfacial waves. An empirical correlation for this region is that of Chun and Seban [357], which is as follows ... 

F. K. Wasden and A. E. Dukler, Numerical Investigation of Large Wave Interaction on Free Falling Film, Int. J. Multiphase Flow (15) 357-370,1989. 

Repeat the analysis of wave motion on a falling film for the case where... 

Chang H.-Ch., Demekhin E.A. and Kopelevich D.I. (1993). Nonlinear evolution of waves on a vertically falling film. J. Fluid Mech., 250,433-480. 

Chang H.-Ch. (1994). Wave evolution on a falling film. Ann. Rev. Fluid Mech., 26,103-136. 

Chang H.-Ch. and Demekhin E.A. (1996). Solitary Wave Formation and Dynamics on Falling Films. Advances in Appl. Mech. 32,1-58. 

The investigations of waves in falling films have been stimulated by well-known experiments of P.Kapitsa and S.Kapitsa (1949). The capillary film flows demonstrate many types of instabilities and formed wave structures. The interest of investigators is attracted by possibilities of visualization of waves and measurements of their parameters that may be unrealizable in other flows. 

This set of parameter values fits well a liquid metal with 7 = 29.2, Ca = 0.2. The calculations of eigenvalues are completed for various values Ma, T, a. In Figure 10 typical curves for = Cr oi) and aci = aci a) are plotted. As amplification factor aci a) of various instability modes could differ to several orders, a normalized amplification factor f = maCi where m is appropriate scale is used in figures. One of these growing modes is easily identified as the hydrodynamic mode of the falling film with small wavenumber and is indeed the same when Ma = 0. The phase velocity Cr of this wave mode diminishes from Cr = 3 as a grows form a = 0, takes a minimum value, and then increases. Amplification factor aCi is positive in the interval 0 < o < a and has maximum value aci)m inside of this interval. Other growing modes, which are referred to as diffusion modes appear only at Ma 7 0. The term diffusion could be applied for any mode which disappears at... 

Veriable surface excess concentration. In general case F const of a falling film of weak volatile surfactant solution in which the surfactant mass transfer is governed by the diffusion, evaporation and adsorption-desorption processes in the near-surface layer the development of instability depends on nine dimensionless external parameters. We can take 7, 6, Cq, Pe, G, Bi, T, Di, and Ma as these independent parameters. If the parameters are given, the problem reduces to the numerical solution of the dispersion relation for various of the wave number a and the spectral analysis of cj = u a). 

For a given thickness of the falling film the number and type of instability modes in it substantially depend on the surfactant transfer model adopted. For the systems described by the insoluble surfactant model solutions of the explosive-growth wave type exist. In the systems in which the complete model of the adsorption-desorption processes is taken into account the instability is described only by solutions with finite amplification coefficients. 

The wavenumber interval on which new diffusion instability modes exist is bounded from below and not bounded from above. Consequently, these perturbations are mainly shortwave. At the same time, the formation of regular nonlinear wave structures in falling film of a pure liquid is associated with the fact that only perturbations on the bounded interval 0 < a < are unstable. 

Chang, H.-C., and Demekhin, E. A. (1996). Solitary wave formatiom and dynamics on falling film. Adv. Appl. Mech 32 1-58. 

Sisoev, G. M., and Shkadov, V. Y. (1999). On two-parametric manifold of the waves solutions of equation for falling film of viscous liquid. Physics-Doklady 44(7) 454-459. 

Hikita et al. [Chemical Engr. Sci., 45, 437-442 (1990)] report Sherwood numbers for a laminar wave-free falling film entering a wetted wall column. Their result is... 

The Leveque-type correlation, Eq. (26), has been used for mass-transfer from a liquid film falling under gravity (110, W13b), where it holds for Reynolds numbers in the laminar range, in spite of the presence of surface waves on the film. The latter caused small local oscillations of the mass-... 

Irradiation of films of proteins with ultra-violet light produces very complex changes in pressure and potential 1 light of different wave-lengths produces different effects. The first effect is usually an increase of both pressure and potential later the protein molecule appears to be broken down so far that some solution of the film takes place, so that pressure and potential fall. A remarkable fact is that very small traces of metallic ions in solution may cause some of these reactions to take place in visible light. 

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