Effect of sinusoidal injection velocity on miscible viscous fingering of a finite sample: Nonlinear simulation.

The effect of a sinusoidal injection on the fingering instability in a miscible displacement in the application of liquid chromatography, pollutant contamination in aquifers, etc., is investigated. The injection velocity, is characterized by its amplitude of and time-period of . The solute transport, flow in porous media, and mass conservation in a two-dimensional porous media is modeled by the convection-diffusion equation, Darcy's equation, and the continuity equation, respectively. The numerical simulation is performed in COMSOL Multiphysics utilizing a finite-element based approach. The fingering dynamics for various time-period have been studied for two scenarios namely, injection-extraction and extraction-injection ( ). The onset of fingers and vigorous mixing is observed for , whereas for , the onset gets delayed. The viscosity contrast between the sample and the surrounding fluid is characterized by the log-mobility ratio . When the rare interface becomes unstable, while for the frontal interface deformed. In the case of the extraction-injection process attenuates the fingering dynamics, which is beneficial in chromatographic separations or pollutant dispersion in underground aquifers. The injection-extraction process is observed to have a longer mixing length, indicating early interaction between both interfaces. The degree of mixing is more pronounced for injection-extraction scenario and least for extraction-injection . The average convective forces are more dominant for till the deformed rare interface interact with diffusive frontal interface. The average diffusive forces are significant for which can be helpful in separation of chemicals in chromatography. This study therefore provided new insights into the role of alternate injection-extraction injections in altering the fingering dynamics of the miscible sample.