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We perform OpenFOAM simulations to compute miscible viscous fingering instability in three-dimensional displacement in a Hele-Shaw cell. For this purpose, Navier-Stokes equations (momentum conservation) are coupled with a convection-diffusion (for the species concentration). The dynamic viscosity of the fluid depends exponentially on the species concentration. The convective term of the species concentration equation is from the fluid velocity. Therefore, the two-way coupled system of equations is solved.
First movie: The first movie on the left-hand side shows the perspective view of the species concentration.
Second movie: The second movie on the left-hand side shows the z-plane cross-sectional view of the above three-dimensional simulation.
Third movie: The third movie on the left-hand side depicts miscible viscous fingering instability obtained from Navier-Stokes simulations for Re = 1. Here Re is the Reynolds number.
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