STABILITY OF TWO-LAYER NEWTONIAN PLANE COUETTE FLOW PAST A DEFORMABLE NEO-HOOKEAN SOLID: EFFECT OF WALL SLIP

Abstract

The linear stability of two-layer plane Couette flow of Newtonian fluids past a soft, deformable neo-Hookean solid with wall slip is studied using a combination of low wavenumber asymptotic analysis and a numerical method. Two qualitatively different interfacial modes, namely, the fluid-fluid interfacial mode due to viscosity stratification “mode 1” and the fluid–solid interfacial mode “mode 2” are observed. Detailed analysis of the respective effects of solid layer deformability, fluid viscosity stratification and effect of wall slip on these modes are analyzed in detail. Our low wavenumber asymptotic results show that the deformability of the solid layer and wall slip has a significant effect on the interfacial instability of mode 1. Our results assuming a no slip condition show that when the more viscous fluid is of smaller thickness, mode 1 becomes stable in presence of solid when the non dimensional elasticity parameter Γ = , increases beyond a critical value. However, in presence of slip at wall even for this critical value of Γ “mode 1” becomes unstable. Also we show that for a single layer flow past a solid the wall slip has a stabilizing effect. For short wave numbers, perturbations are localized near the fluid-fluid interface and therefore solid thickness and elasticity has no effect on the high k unstable modes, which can be stabilized only by a nonzero interfacial tension. Our results from Γ vs. k curves allow to choose values of elasticity parameters to stabilize a given system configuration.