Instabilities of nanofluid flow displacements in porous media

Thanks to a number of advantageous characteristics, nanofluids are widely used in a variety of fluid flow systems. In porous media flows, the presence of nanoparticles can have dramatic effects on the flow dynamics and in particular on viscous fingering instabilities that develop when a less viscous fluid displaces a more viscous one. In the present study, these effects have been investigated both analytically and numerically using linear stability analysis (LSA) and non-linear simulations. The LSA problem was solved analytically using step function approximation, and general conclusions about the effects of nanofluids on the instability were derived from long wave expansion and cutoff wave number analyses. Furthermore, the quasi-steady-state approximation was used to expand the results of the LSA to diffusing initial concentration profiles, and simulations of the full non-linear problem have been carried out using a Hartley-transform based pseudo-spectral method. Results revealed that nanoparticles cannot make an otherwise stable flow unstable but can enhance or attenuate the instability of an originally unstable flow. In particular it was found that increases in the nanoparticles deposition rate or their rate of diffusion have both destabilizing effects. Furthermore, nanoparticles deposition can change the initial monotonically decreasing viscosity distribution to a non-monotonic one and results in the development of vortex dipoles. Analyses of vortex structures along with the viscosity distributions allowed to explain the observed trends and the resulting finger configurations. Published by AIP Publishing.