Effect of Hele–Shaw cell gap on radial viscous fingering

Abstract

The flow through a Hele–Shaw cell is an experimental prototype to study the flow through a porous medium as well as the flow in microfluidic devices. In context with porous medium flows, it is used to visualize and understand hydrodynamic instabilities like viscous fingering (VF). The gap between the plates of the cell is an important parameter affecting the flow dynamics. However, the effect of the gap on the Hele–Shaw cell flows has been minimally explored. We perform experiments to understand the effect of the gap on VF dynamics. It is observed that a minimum gap is required to observe rigorous fingering instability. The onset time of instability, as well as the width of the fingers, increases with an increment in the gap due to a decrease in the convection. The instability increases with an increase in Péclet number, but the effect of gap width on fingering patterns is evident with broader fingers observed for larger b. The results are validated by performing numerical simulations. It is further shown that the gap-averaged three-dimensional simulations using the Stokes law approach and the two-dimensional Darcy’s law result in a small gap Hele–Shaw cell.

Interfacial instabilities in confined displacements involving non-Newtonian fluids

“…In contrast to Newtonian fluid displacement, the fully developed pattern took on a highly ramified structure, but became smoother with wider fingers at higher injection pressures. Unlike Newtonian displacement patterns [86], the characteristic finger width in granular fingering is independent of the HS cell gap [85]. The bulldozing effect and frictional fingers were absent in this study [85] due to the negligible threshold capillary pressure.…”