Abstract:
The curvature of the unstable part of the miscible interface between a circular blob and the ambient fluid
in two-dimensional homogeneous porous media depends on the viscosity of the fluids. The influence of the
interface curvature on the fingering instability and mixing of a miscible blob within a rectilinear displacement
is investigated numerically. The fluid velocity in porous media is governed by Darcy’s law, coupled with a
convection-diffusion equation that determines the evolution of the solute concentration controlling the viscosity
of the fluids. Numerical simulations are performed using a Fourier pseudospectral method to determine the
dynamics of a miscible blob (circular or square). It is shown that for a less viscous circular blob, there exist three
different instability regions without any finite
R
-window for viscous fingering, unlike the case of a more viscous
circular blob. Critical blob radius for the onset of instability is smaller for a less viscous blob as compared to its
more viscous counterpart. Fingering enhances spreading and mixing of miscible fluids. Hence a less viscous blob
mixes with the ambient fluid quicker than the more viscous one. Furthermore, we show that mixing increases with
the viscosity contrast for a less viscous blob, while for a more viscous one mixing depends nonmonotonically on
the viscosity contrast. For a more viscous blob mixing depends nonmonotonically on the dispersion anisotropy,
while it decreases monotonically with the anisotropic dispersion coefficient for a less viscous blob. We also
show that the dynamics of a more viscous square blob is qualitatively similar to that of a circular one, except
the existence of the lump-shaped instability region in the
R
-Pe plane. We have shown that the Rayleigh-Taylor
instability in a circular blob (heavier or lighter than the ambient fluid) is independent of the interface curvature.
