Double-Diffusive Convection in a Porous Layer in the Presence of Vibration

Abstract

The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal layer of a binary fluid mixture saturating a porous medium. A constant temperature and concentration distribution are assigned on the rigid boundaries, so that there exist vertical temperature and concentration gradients. The mathematical model is described by equations of filtration convection in the Darcy–Oberbeck–Boussinesq approximation. The linear stability analysis for the quasi-equilibrium solution is performed using Floquet theory. Employing the method of continued fractions allows derivation of the dispersion equation for the Floquet exponent in an explicit form. The neutral curves of the Rayleigh number versus horizontal wave number are constructed for the three types of instability modes: synchronous, subharmonic, and complex conjugate. Asymptotic formulas for these curves are derived for large values of vibration frequency using the method of averaging. It is shown that, at some finite frequencies of vibration, there exist regions of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility to convection. In addition, even in the presence of vibration, the onset of convection in the system is affected by variations in the concentration of the solute in the mixture.