Eur. Phys. J. E (2022) 45: 1
https://doi.org/10.1140/epje/s10189-021-00157-z

Regular Article - Flowing Matter

Electric-permittivity-based instability of two dielectric miscible liquids under DC field

¹ Institute of Mechanics and Engineering (I2M) CNRS, University of Bordeaux, 33400, Talence, France
² Department of Mathematics and Computer Science, Financial University, 350051, Krasnodar, Russian Federation
³ Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University, 350051, Krasnodar, Russian Federation
⁴ Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University, 119192, Moscow, Russian Federation

^a sakir.amiroudine@u-bordeaux.fr

Received: 7 October 2021
Accepted: 17 December 2021
Published online: 3 January 2022

Abstract

This paper considers the mixing of two dielectric miscible viscous liquids with different electric permittivities bounded by solid walls in an external electric field normal to the interface of the liquids. The mutual diffusion of these two liquids leads to the formation of an unsteady self-similar 1D diffusion layer. This layer is found to be unstable to the perturbations of the interface. A special sophisticated mathematical approach in self-similar variables is developed to estimate its stability. The results of a linear stability theory are verified by direct numerical simulations of the full nonlinear problem. A mixing efficiency based on the separation amplitude and an optimal electric field strength to achieve the fastest mixing are proposed in the present study.