Abstract
Linear stability analysis within the solute analogy of Horton–Rogers–Lapwood (HRL) problem has been investigated. Solute immobilization (solute sorption) of nanoparicles by the porous medium is taken into account within the fractal model of MIM approach. The solute concentration difference between the layer boundaries and the horizontal external filtration flux are assumed as constant. The system of equations that determine the frequency of neutral oscillations and the critical value of the Rayleigh-Darcy number is derived. Neutral curves of the critical parameters on the governing parameters are plotted. Stability maps are obtained numerically in a wide range of parameters of the system. It was found that taking immobilization into account leads to an increase in the critical value of the Rayleigh-Darcy number with an increase in the intensity of the external filtration flux. The case of weak time-dependent external flux is investigated analytically. It was shown that the modulated external flux leads to an increase in the critical value of the Rayleigh–Darcy number and a decrease in the critical wavenumber.
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