Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid

Abstract We study the dynamic behaviour of two viscous fluid films confined between concentric cylinders rotating at a small relative velocity. It is assumed that fluids are immiscible and volume outer film large compared to inner one. Moreover, while considered have constant viscosity, rheological thin determined by strain-dependent power-law. Starting from Navier–Stokes system, we formally derive evolution equations for interface separating fluids. Two competing effects drive dynamics interface, namely surface tension shear stresses induced rotation cylinders. When comparable, solutions behave, times, as in Newtonian regime. also regime which dominate In this case, prove local existence positive weak both shear-thinning shear-thickening latter show interfaces initially close circle converge finite time keep shape later times.