Abstract:
The evolution of dissolved species in a porous medium is determined by its adsorption on the porous
matrix through the classical advection-diffusion processes. The extent to which the adsorption affects the
solute propagation in applications related to chromatography and contaminant transport is largely dependent
upon the adsorption isotherm. Here, we examine the influence of a nonlinear Langmuir adsorbed solute on
its propagation dynamics. Interfacial deformations can also be induced by classical viscous fingering (VF)
instability that develops when a less viscous fluid displaces a more viscous one. We present numerical simulations
of an initially step-up concentration profile of the solute that capture a rarefaction/diffusive wave solution
due to the nonlinearity introduced through Langmuir adsorption and variety of pattern-forming behaviors of
the solute dissolved in the displaced fluid. The fluid velocity is governed by Darcy’s law, coupled with the
advection-diffusion equation that determines the evolution of the solute concentration controlling the viscosity
of the fluids. Numerical simulations are performed using the Fourier pseudospectral method to investigate and
illustrate the role played by VF and Langmuir adsorption in the development of the patterns of the interface. We
show that the solute transport proceeds by the formation of a rarefaction wave results in the enhanced spreading
of the solute. Interestingly we obtained a nonmonotonic behavior in the onset of VF, which depends on the
adsorption parameters and existence of an optimal value of such adsorption constant is obtained near b = 1, for
which the most delayed VF is observed. Hence, it can be concluded that the rarefaction wave formation stands
out to be an effective tool for controlling the VF dynamics.
