Stability Marangoni instability

In the last two sections, we considered mass transfer from the film toward the droplets and the reverse, from droplets toward the film. In both cases, the diffusion fluxes lead to stabilization of the film. Here we consider the third possible case corresponding to mass transfer from the first droplet toward the second one across the film between them. In contrast with the former two cases, in the last case the mass transfer is found to destabilize the films. Experimentally, the diffusion transfer of alcohols, acetic acid, and acetone was studied. - The observed destabilization of the films can be attributed to the appearance of Marangoni instability, which manifests itself through the growth of capillary waves at the interfaces, which eventually can lead to film rupture. 

The governing equations for the linear stability theory are the same as for the Rayleigh-Benard problem, namely (12-215), except that it is customary to drop the buoyancy terms because these are of secondary importance for very thin fluid layers where Marangoni instabilities are present but Ra <neutral state. Assuming that... 

Problem 12-11. Marangoni Instability (The Principle of Exchange of Stabilities). Following the procedure that was outlined in Section F for the Rayleigh-Benard problem, prove that the principle of exchange of stabilities is valid for the Marangoni instability problem (Section H). 

Interfacial phenomraia involving heat and mass transfer are described and analyzed in Chapter 6. Much of the chapter again deals with stability, in this case the Marangoni instability produced by interfacial trasion gradients associated with temperature and eoneentration gradients along the interface. Time-dependent variation of interfadal tension resulting from diffusion, adsorption, and desorption of various species is also diseussed. 

Figure 1. Schematic diagram showing the possible mechanisms of thin film stabilization, (a) The Marangoni mechanism in surfactant films (b) The viscoelastic mechanism in protein-stabilized films (c) Instability in mixed component films. The thin films are shown in cross section and the aqueous interlamellar phase is shaded.

In the case where foam instability is desirable, it is essential to choose surfactants that weaken the Gibbs-Marangoni effect. A more surface-active material such as a poly(alkyl) siloxane is added to destabilize the foam. The siloxane surfactant adsorbs preferentially at the air/liquid interface, thus displacing the original surfactant that stabilizes the foam. In many cases, the siloxane surfactant is produced as an emulsion which also contains hydrophobic silica particles. This combination produces a synergetic effect for foam breaking. 

Problem 12-15. Stability of a Fluid Layer in the Presence of Both Marangoni and Buoyancy Effects. A fluid layer is heated from below. It has a rigid, isothermal boundary at the bottom, but its upper surface is a nondeforming fluid interface. There are now two potential mechanisms for instability when the fluid is heated from below buoyancy-driven and surface-tension-gradient-driven convection. Determine the eigenvalue problem (i.e., the ODE or equations and boundary conditions) that you would need to solve to predict the linear instability conditions. Is the principle of exchange of stabilities valid Discuss how you would approach the solution of this eigenvalue problem. 

Now, it is important to note that in the case of the Benard-Marangoni convection in a liquid layer with a deformable interface, as was previously shown by Takashima (1981a) through a linear stability analysis (see the 7), there exist two monotonous modes of surface tension driven instability. 

The first term on the right part of last equation (33) is the desorption or evaporation of the surfactant from the liquid phase into the gas phase, kg — gas phase masstransfer coefficient of surface active solute, m — the ratio of the concentration in the liquid phase to the concentration in the gas phase at equilibrium. These equations have been employed by Palmer and Berg (1972), Hennenberg et al. (1992) for the stability of a horizontal liquid layer with solutal Marangoni effect. In Ji and Setterwall (1994) the instability of falling film for the partial case of T = const is investigated. The coefficient... 

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