Convection excitation in a system of a binary solution layer and an inhomogeneous porous medium layer in the field of high-frequency vibrations

We investigate convection excitation in a two-layer system of a horizontal binary solution layer and an inhomogeneous porous medium layer saturated with the solution in the gravity field and in the field of transverse high-frequency vibrations. It is believed that porosity of medium linearly depends on the vertical coordinate. Permeability is estimated by the Сarman-Kozeny relation for various values of a non-dimensional porosity gradient mz. The averaging method is applied for a description of convection in the gravity field and the field of high-frequency vibrations. The linear stability problem for a mechanical equilibrium of fluid is solved numerically by the shooting method. The critical parameters corresponding to a threshold of convection excitation in the system heated either from below or above are found. When the system is heated from below, there is an abrupt change in the character of instability with the variation of porosity gradient or vibration intensity. It is shown that when porosity increases with depth at mz = -0.2, the instability is due to the development of long-wave perturbations covering both fluid and porous layers. When porosity decreases with depth at mz = 0.2, short-wave perturbations localized in the fluid layer are the most dangerous. For intermediate porosity gradients the critical Rayleigh-Darcy numbers determining the stability threshold of equilibrium with respect to long-wave and short-wave perturbations are of close values. Neutral curves are bimodal. When the system is heated from below, vertical vibrations effectively suppress convection in the fluid layer, so a transition from the most dangerous short-wave to long-wave perturbations occurs as vibration intensity grows. The most significant increase in the stability threshold is observed when porosity decreases with depth. When the system is heated from above, vibrations destabilize equilibrium in layers and lead to wavelength shortening for critical perturbations. Wavelength reduces monotonically. Its greatest change is fixed for the layers, whose porosity increases with depth.