The influence of vibration on the onset of convection in a horizontal porous layer saturated with a ternary fluid

Abstract

This paper investigates the thermovibrational convection of a three-component hydrocarbon mixture in a horizontal layer of a porous medium with the Soret effect taken into account. The vibrations are assumed to be high-frequency and low-amplitude, with the vibration axis parallel to the temperature gradient. The analysis is based on the equations of thermovibrational convection in a porous medium, which take viscosity into account in the pulsation equations. The first part of the paper provides a linear stability analysis of the conductive state. Instability with respect to longwave perturbations is analyzed analytically using series expansion in terms of the wavenumber, while instability with respect to perturbations with nonzero wavenumbers is studied numerically using the shooting method. The study has found that vibrations do not affect the longwave instability of equilibrium. A stability map of mechanical equilibrium on the separation ratio – Rayleigh number plane was obtained for various values of the vibrational Rayleigh number. The effect of vibration on the system was found to increase the convection threshold, simultaneously narrowing the range of existence of cellular monotonic perturbations. As the separation ratio increases, the influence of vibrations on the wavenumber becomes progressively less significant. Vibrations have a qualitatively similar effect on the threshold of cellular oscillatory instability. The presence of vibrations reduces the oscillation frequency over the entire range of existence of disturbances. The influence of viscosity on the stability of mechanical equilibrium is investigated. In the second part of the paper, nonlinear convection regimes are numerically investigated using the finite difference method. The numerical data are in good agreement with the results of the linear stability analysis. The influence of convective motion of the liquid mixture on the distribution of impurity concentration over the layer is shown.