  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 non-monotonic 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.
