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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 (
) – 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
. Increase in the levels of charge injection and EHD stresses lower the critical
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 (
), a diffusive mode is also found to appear near the mixed interfacial region. A thinner interface between the fluids at a higher
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.
Instabilities at the deformable free surface of a thin nematic liquid crystal film can develop interesting patterns when exposed to an external electrostatic field. A general linear stability analysis is performed involving the Ericksen–Leslie governing equations for the dynamics of the nematic film coupled with the anisotropic Maxwell stresses for the electric field to uncover the salient features of these instabilities. The study reveals the coexistence of twin instability modes: (i) long-wave interfacial mode – stimulated when the sole destabilizing influence of the electric field overcomes the Frank bulk elasticity and surface tension force, and (ii) finite-wavenumber mode – engendered by the combined destabilizing influence originating from the anisotropic electric field and Ericksen stress, for the films with positive dielectric anisotropy and weaker Frank bulk elasticity. The results reported here are in contrast with the same obtained from the more frequently employed long-wave approach. The air-to-liquid-crystal filling ratio between the electrodes as well as thermodynamic parameters such as the dielectric anisotropy, Frank elasticity, and director orientations across the film and boundaries are found to play crucial roles in the selection of modes, whereas kinetic parameters such as Leslie viscosity coefficients influence only the time scale of instability. Importantly, at higher field intensities a symmetry-breaking Fréedericksz-type transition of director orientations is found to happen, which also causes the transition of the dominant mode of instability from the long-wave to the finite-wavenumber mode for films with relatively lower values of Frank bulk elasticity and positive dielectric anisotropy.
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