Development of Marangoni Instability

Determine the conditions for developmrait of instability when N u is very small, the initial tranpraature gradient (- ) is l°K/cm, and the liquid has the following properties  

FIGURE 6.5 Convection due to interfacial tension gradients during solute transfer 

The analysis is very similar to that of Section 3 except, of course, flow and transport in both phases must be considered. When a 1 (i.e., when both fluids are of great depth), and when solnte convection along the interface can be ignored, the marginal stability condition is that obtained by Stemling and Scriven (1959)  

/ ab is the distribution coefficient Cg/C for the solute at the interface, and Z B are the solute diffusivities in A and B, dy/dC is the rate of change of interfacial tension with respect to the interfadal concentration in phase A, and dC j/dz is the initial (uniform) concentration gradient in A. 

Equation 6.36 is closely related to the heat transfer result in Equation 6.35 in the limit of large a. Indeed, setting and D, as might be 

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A third mechanism of liquid-film breakage is observed when there is a transport of solute across the film (see Fig. 10c). This mechanism, investigated experimentally and theoretically by Ivanov and coworkers (109—111), was observed with emulsion systems (transfer of alcohols, acetic acid, and acetone across liquid films), but it could appear also in some asymmetric oil-water-air films. The diffusion transport of some solute across the film leads to the development of Marangoni instability, which manifests itself as... 

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