STABILITY OF PLANE COUETTE FLOW OF POWERLAW FLUID PAST A NEO-HOOKEAN DEFORMABLE SOLID

Abstract

The stability of Couette flow of power-law fluid of thickness R past Neo-Hookean deformable solid of thickness HR subjected to shear flow is considered in this work. Powerlaw fluid is chosen as it is the simplest model of fluid which can show the effects of shear thickening and shear thinning behavior. Whereas Neo Hookean solid, which is a nonlinear constitutive model accurately captures the behavior of flow as it leads to values of critical shear rate which are smaller than those obtained by using the linear viscoelastic solid model. Four key dimensionless parameters, i.e. γ (Imposed shear rate), n (power-law index), T (interfacial tension) & H (thickness ratio) characterizes the problem. Linear stability analysis is performed to find the stability of the system. Shear flow of the fluid due to Couette flow tends to destabilize the surface fluctuations. Various diagrams have been plotted between growth rates as a function of wavenumber showing the study of parameters how they affect the flow. For large values of H, i.e. solid to fluid thickness ratio, critical shear rate goes on decreasing and shear thickening fluids has more stabilizing effect in comparison with shear thinning fluids keeping all other governing parameters constant. The results obtained are potentially of great interest for enhancing mixing in microfluidic devices.