Abstract:
We examine the transport in a homogeneous porous medium of a finite slice of a
solute which adsorbs on the porous matrix following a Langmuir adsorption isotherm
and can influence the dynamic viscosity of the solution. In the absence of any viscosity
variation, the Langmuir adsorption induces the formation of a shock layer wave at the
frontal interface and of a rarefaction wave at the rear interface of the sample. For a finite
width sample, these waves interact after a given time that varies nonlinearly with the
adsorption properties to give a triangle-like concentration profile in which the mixing
efficiency of the solute is larger in comparison to the linear or no-adsorption cases. In
the presence of a viscosity contrast such that a less viscous carrier fluid displaces the more
viscous finite slice, viscous fingers are formed at the rear rarefaction interface. The fingers
propagate through the finite sample to preempt the shock layer at the viscously stable
front. In the reverse case, i.e., when the shock layer front features viscous fingering, the
fingers are unable to intrude through the rarefaction zone and the qualitative properties
of the expanding rear wave are preserved. A nonmonotonic dependence with respect to
the Langmuir adsorption parameter b is observed in the onset time of interaction between
the nonlinear waves and viscous fingering. The coupled effect of viscous fingering at the
rear interface and of Langmuir adsorption provides a powerful mechanism to enhance the
mixing efficiency of the adsorbed solute.
