Suppressing the interfacial instability during fluid displacement, namely, viscous fingering, has been a long-lasting challenge in many applications. Numerous strategies have been proposed to control this phenomenon. Despite the recent advancements in utilizing electric fields to regulate viscous fingering, the absence of a rigorous characterization of this interfacial instability under an electric field hinders its further application. Therefore, in this work, we conduct numerical and theoretical investigations into the impact of an external electric field on viscous fingering in microfluidic channels for perfect dielectric fluids. It is shown that the development of viscous fingering can be delayed in the presence of an electric field and completely suppressed when the electric field strength $E$ exceeds a certain value. Based on the force balance, a nondimensional parameter $\varphi$ is defined to reflect the relative importance of stabilizing and destabilizing stress by taking into account the electrical, capillary, and viscous stress on the fluid interface. Extensive simulations show that $\varphi$ can effectively characterize the transition from an unstable viscous fingering to stable displacement under different fluid properties and flow conditions. The findings of this study are of fundamental importance in elucidating the influence of an external electric field on interfacial instability, thereby contributing to the development of improved strategies for controlling and optimizing displacement efficiency in diverse fluid systems and complex geometries.

• Received 9 October 2023
• Accepted 19 January 2024

DOI:https://doi.org/10.1103/PhysRevFluids.9.033701