Three-dimensional Navier-Stokes simulations of miscible fingering with nonmonotonic viscosity profiles

We investigate the influence of nonmonotonic viscosity-concentration correlations on the growth of viscous fingers in a Hele-Shaw cell by solving the variable viscosity Navier-Stokes equations coupled to a convection-diffusion equation for a scalar field that captures the concentration of the displaced fluid. We examine shear displacement flows across the Hele-Shaw plates. Then, by imposing a small amplitude perturbation of the most unstable wavelength, the nonlinear algorithm reproduces linear growth rate results obtained using the three-dimensional Stokes equations (Schafroth et al., Eur. J. Mech. B Fluids, 2007). Finally, we present results from the three-dimensional nonlinear simulations and compare fingers growing under the nonmonotonic correlation with those following the traditional exponential relationship.