Viscous Fingering in a Hele-Shaw Cell With Finite Viscosity Ratio and Interfacial Tension

Abstract

A volume tracking method was developed to simulate time-dependent unstable viscous fingering in a Hele-Shaw cell. The effect of finite viscosity ratio μr between displacing and displaced fluids and their interfacial tension σ on finger morphology is investigated. It is shown that there exist four distinct finger patterns, depending upon the viscosity ratio, μr, and Ca′, the modified capillary number for constant flow rate, or ΔP⋅W/σ, for constant driving pressure difference. Morphology diagrams are developed to identify the ranges of the dimensionless parameters corresponding to the various finger patterns. The simulation results are validated with experiments.