Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability

In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number selection from the broadbanded initial noise is established.Comment: 13 pages, 8 figure

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

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

Instability of a salt jet emitted from a point source in an external electric field

The objective in the present work is to consider a simple example of instability of a conducting self-similar micro jet in the external electric field, which represents a prototype of some microfluidic instabilities. Salt from a point source is emitted into its own aquatic solution, which is subject to an external uniform velocity field together with an electrostatic field, and is convected downstream and diffused. The flow is considered in microscales so that, in contrast to the classical jets, the Reynolds numbers are practically zero, but the Péclet numbers are large. The parameters are found at which such a microjet is unstable. Along with the linear stability analysis, we have fulfilled the numerical simulations of the full nonlinear system of equations. The numerical simulation qualitatively confirmed the results of the linear stability and showed that this instability visually reminds classical instabilities of free jets and wakes

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

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