Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

Abstract

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.