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Miscible viscous fingering with linear adsorption on the porous matrix

par Mishra, Manoranjan ;Martin, M;De Wit, Anne
Référence Physics of fluids, 19, page (073101)
Publication Publié, 2007

Article révisé par les pairs

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Résumé :

Viscous fingering between miscible fluids of different viscosities can affect the dispersion of finite samples in porous media. In some applications, as typically in chromatographic separations or pollutant dispersion in underground aquifers, adsorption onto the porous matrix of solutes (the concentration of which rules the viscosity of the solution) can affect the fingering dynamics. Here, we investigate theoretically the influence of such an adsorption on the stability and nonlinear properties of viscous samples displaced in a two-dimensional system by a less viscous and miscible carrying fluid. The model is based on Darcy's law for the evolution of the fluid velocity coupled to a diffusion-convection equation for the concentration of a solute in the mobile phase inside the porous medium. The adsorption-desorption dynamics of the solute onto the stationary phase is assumed to be at equilibrium, to follow a linear isotherm and is characterized by a retention parameter κ′ equal to the adsorption-desorption equilibrium constant Κ multiplied by the phase ratio F. In practice, retention on the porous matrix renormalizes the log-mobility ratio by a factor (1 + κ′). Correspondingly, a linear stability analysis and nonlinear simulations of the model show that an increase of κ′ leads to a stabilization of viscous fingering with fingers appearing on a dimensional time scale multiplied by (1 + κ′) 3 and with a dimensional wavelength multiplied by (1 + κ′). © 2007 American Institute of Physics.