Control and suppression of viscous fingering displacing non-Newtonian fluid with time-dependent injection strategies

Abstract

We explore the stabilization mechanism of the fluid–fluid interface in the radial Hele–Shaw cell, displacing a non-Newtonian fluid. It is possible to stabilize the interface following a non-linear injection rate, Q∼t−(2−n)/(2+n), which is related to the displaced fluid rheology (n: power-law index). This suggests the absence of fingering at constant injection when n∼2. We propose a quantitative criterion to control the pattern formation and suppress fingering, through the dimensionless parameter J as a function of the physical and operating parameters, which is applicable for a generalized shear thinning fluid. The parameter J is related to the capillary number in the context of the power-law fluid, relating to the viscous and interfacial forces. The fingering morphology at higher order modes is affected by non-linear effects. The results are non-intuitive, and we have shown a feasible approach toward long term fingering stabilization.