Numerical simulation of electrokinetic control of miscible viscous fingering

Abstract

Active control of viscous fingering (VF) is of critical importance for many industrial and experimental systems. Here, we numerically study the electrokinetic control of miscible VF using an externally applied electric field. Simulations for three intrinsically hydrodynamically unstable mobility ratios are carried out using two different configurations for each: case I where the high-viscosity resident fluid has higher electroosmotic mobility than the invading low-viscosity fluid and case II where the resident fluid has a lower electroosmotic mobility than the invading fluid. For both cases, the theoretical critical electric field value required to (de)-stabilize the interface is computed and electric fields around this value are applied in simulations. Qualitative results show that VF can be fully suppressed if an electric field is applied with an absolute value above the critical field strength. For case I, this means an electric field in the direction of the pressure-driven flow, while for case II, a field in opposite direction is required. Our quantitative analysis using interfacial and mixing lengths was used to support the qualitative findings. Even though any field strength applied in the right direction will reduce the instability, full suppression is only achieved if the absolute field strength is higher than the required critical field strength. The results from this work provide useful insights that can be applied to electrokinetically enhanced oil recovery, spreading of pollution zones in aquifers, band broadening in liquid chromatography, and electrokinetic soil remediation.