Interface stabilization in two-layer channel flow by surface heating or cooling

The linear stability of plane Poiseuille flow of two immiscible Newtonian liquids in a differentially heated channel is considered. The equations of motion and energy are fully coupled via temperature-dependent fluid-viscosity coefficients. A long-wave asymptotic formulation of the stability problem is presented together with numerical results for disturbances of arbitrary wavelength. Two combinations of immiscible liquids are analyzed: silicone/water and oil/water (water at the bottom layer in both cases). It is shown that an imposed wall temperature difference can be stabilizing or destabilizing depending on the disturbance wavenumber and layer thickness ratio. Interfacial tension has a stabilizing effect on the interface. Stabilizing influence of interfacial tension is observed at intermediate and large wavenumbers. Most importantly, for certain ranges of the controlling dimensionless parameters, stable interfaces at all disturbance wavelengths can be attained.