Abstract:
Viscous fingering is a hydrodynamic instability that sets in when a low viscous fluid displaces a
high viscous fluid and creates complex patterns in porous media flows. Fundamental facets of the
displacement process, such as the solute concentration distribution, spreading length, and the solute
mixing, depend strongly on the type of pattern created by the unstable interface of the underlying
fluids. In the present study, the frontal interface of the sample shows viscous fingering and the strong
solvent causes the retention of the solute to depend on the solvent concentration. This work presents
a computational investigation to explore the effect of the underlying physico-chemical phenomena,
(i.e., the combined effects of solvent strength, retention, and viscous fingering) on the dynamics of
the adsorbed solute. A linear adsorption isotherm has been assumed between the mobile and stationary
phases of the solute. We carried out the numerical simulations by considering a rectangular
Hele-Shaw cell as an analog to 2D-porous media containing a three component system (displacing
fluid, sample solvent, solute) to map out the evolution of the solute concentration. We observed that
viscous fingering at the frontal interface of the strong sample solvent intensifies the band broadening
of the solute zone. Also notable increase in the spreading dynamics of the solute has been
observed for less viscous and strong sample solvent as compared to the high viscous sample slices
or in the pure dispersive case. On the contrary, the solute gets intensively mixed at early times for
more viscous sample in comparison to less viscous one. The results of the simulations are in qualitative
agreement with the behavior observed in the liquid chromatography column experiments.
