Electric field mediated von Kármán vortices in stratified microflows: transition from linear instabilities to coherent mixing

Abstract

Application of an electric field across the pressure-driven stratified flow of a pair of miscible fluids inside a microchannel manifests interesting electrohydrodynamic (EHD) instabilities. Experiments uncover distinctive instability regimes with an increase in electric field Rayleigh number ($Ra^{\unicode[STIX]{x1D713}}$) – a linear-onset regime, a time-periodic nonlinear regime analogous to the von Kármán vortex street in the downstream and a regime with coherent flow patterns. The experiments also reveal that such linear and nonlinear instabilities can be stimulated non-invasively in a microchannel to mix or de-mix fluids simply by turning the electric field on or off, indicating the suitability of the process for on-demand micromixing. The characteristics of these instabilities have been theoretically investigated with the help of an Orr–Sommerfeld framework, which discloses the possibility of five distinctive finite-wavenumber modes for the instability. The EHD stresses originating due to the application of electric field stimulate a pair of shorter-wavelength electric field modes beyond a critical value of $Ra^{\unicode[STIX]{x1D713}}$. Increase in the levels of charge injection and EHD stresses lower the critical $Ra^{\unicode[STIX]{x1D713}}$ of these modes. The relatively longer-wavelength viscous mode is found to appear when the viscosity stratification between the fluid layers is high. Beyond a threshold Schmidt number ($Sc$), a diffusive mode is also found to appear near the mixed interfacial region. A thinner interface between the fluids at a higher $Sc$ helps this mode to behave as the interfacial mode of immiscible fluids. Contrast of ionic mobility in the fluids leads to the appearance of the K-mode of instability at much shorter wavelengths. The reported phenomena can be of significance in the domains of microscale mixing, pumping, heat exchange, mass transfer and reaction engineering.