Viscous Fingering of Thixotropic Fluids: a Linear Stability Analysis

The displacement of a thixotropic fluid by an immiscible Newtonian fluid is investigated theoretically in a rectangular Hele-Shaw cell. Assuming that the thixotropic fluid of interest obeys the purely-viscous Moore model, use is made of the generalized Darcy's law for finding the basic-flow. Having imposed infinitesimally-small normal-mode perturbations to the basic-flow, an analytical solution is found for calculating the growth rate and wavenumber of unstable modes. The analytical solution enables us to easily investigate the effects of the Moore's model thixotropy parameters on the viscous fingering phenomenon in the Hele-Shaw cell. Based on the results obtained in the present work, it is concluded that thixotropy has a stabilizing effect on the Saffman-Taylor instability.