Influence of nanoparticles on the dynamics of miscible Hele-Shaw flows

In this study, we have made an attempt to address how the nanoparticle flows may affect the hydrodynamic instability around a miscible front. In order to explore the role of nanoparticles in such flows, a linear stability analysis was performed to examine the impact of nanoparticle addition for an already unstable miscible displacement. The growth rates of the temporal modes of the instability are determined for different profiles or physical properties of nanoparticles. The results reveal that the diffusion of either the carrier fluids or nanoparticles initially has destabilizing effects, but demonstrates stabilizing effects at longer times, as the cutoff spectrum is initially shifted to larger wavenumbers, but shifted back later. It was found that deposition of nanoparticles into the medium stabilizes the miscible front, such that the maximum growth rates and cutoff wavenumbers increase continuously. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3592228]