Effect of soluble surfactants on the stability of stratified flows through soft-gel-coated walls.

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The effect of a soluble surfactant on the linear stability of layered two-phase Poiseuille flows through soft-gel-coated parallel walls is studied in this paper. The focus is on determining the effect of the elastohydrodynamic coupling between the fluids and the soft-gel layers on the various flow instabilities. The fluids are assumed Newtonian and incompressible, while the soft gels are modeled as linear viscoelastic solids. The effect of a soluble surfactant on the different instabilities is specifically investigated. The soft-gel-coated plates are maintained at two different solute concentrations. The dynamics of the soluble surfactant in the fluids is captured using a species transport equation. A linear stability analysis is carried out to identify different instabilities in the system. The linearized governing equations are solved numerically using a Chebyshev spectral Collocation technique. The effect of deformability of the soft gels on three distinct instability modes, (a) a liquid-liquid long-wave mode, (b) a liquid-liquid short-wave mode, and (c) a liquid-liquid Marangoni short-wave mode, is analyzed. An analytical expression for the growth rate is obtained in the long-wave length limit using an asymptotic analysis. From the long-wave analysis a stability map is obtained, in which dominant effects in different regions are identified. The Marangoni stresses can either stabilize or destabilize the interfacial instability depending on the direction of mass transfer. They have a predominantly stabilizing effect on the interfacial instability when the mass transfer is from the more viscous broader fluid to the less viscous thinner fluid. Placing a gel closer to the more viscous fluid has a stabilizing effect on this instability. The Marangoni stresses and soft-gel layers can have opposing effects on the stability of the long-wave mode. The dominant of these two opposing effects is determined by the prevailing parameters. Insights into the dominant physical causes of different instabilities are presented.