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.
