Stable and unstable miscible displacement of a shear-thinning fluid at low Reynolds number

Abstract

We present the results of experiments performed for the displacement of an aqueous low-concentration polymer solution that initially fills a capillary tube (diameter < 1 mm), using water. Aqueous carboxymethyl-cellulose polymer solutions were prepared at initial concentration 0.5 < c0 < 0.75 (w/w). Polymer concentrations are low such that the displaced fluids may be considered shear-thinning. We measured the shear viscosity of the aqueous polymer solutions and obtained values for Carreau shear-thinning fluid model parameters at each polymer concentration. Separately, we measured the average bulk diffusivity for each solution. The estimates of the residual film using penetrating fluid tip and mean velocities were measured as a function of the Peclet (Pe), Reynolds (Re), Carreau (Cu0), and viscous Atwood number based on zero shear-rate viscosity (At0) where the latter two were computed using c0. For Cu0 > 1, we observe a corkscrew type instability where the wavelength increases as diffusion is diminished but requires a finite amount of diffusion to appear.