The influence of a non-monotonic viscosity–concentration relationship on miscible
displacements in porous media is studied for radial source flows and the quarter five-spot configuration. Based on linear stability results, a parametric study is presented
that demonstrates the dependence of the dispersion relations on both the Péclet
number and the parameters of the viscosity profile. The stability analysis suggests
that any displacement can become unstable provided only that the Péclet number
is sufficiently high. In contrast to rectilinear flows, for a given end-point viscosity
ratio an increase of the maximum viscosity generally has a destabilizing effect on the
flow. The physical mechanisms behind this behaviour are examined by inspecting the
eigensolutions to the linear stability problem. Nonlinear simulations of quarter five-spot displacements, which for small times correspond to radial source flows, confirm
the linear stability results. Surprisingly, displacements characterized by the largest
instability growth rates, and consequently by vigorous viscous fingering, lead to the
highest breakthrough recoveries, which can even exceed that of a unit mobility ratio
flow. It can be concluded that, for non-monotonic viscosity profiles, the interaction
of viscous fingers with the base-flow vorticity can result in improved recovery rates.