Nanoparticles impact on miscible viscous fingering with absorbing boundary condition at inlet

Abstract

We examine the flow configuration in a Hele-Shaw cell, where, initially, the cell is filled with a viscous fluid and then displaces it with other viscous fluid-carrying nanoparticles through the inlet boundary. How such nanoparticles modulate viscosity and impact the miscible viscous fingering dynamics is analyzed, showing the nonmonotonic nature of the onset of nanoparticle diffusion instability. The results provide a basis for controlling the viscous fingering instability using nanofluid displacement processes by delivering fluid-carrying nanoparticles to $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ contaminated areas. Examples are nanoparticle-based drug delivery and soil and groundwater remediation.