Dynamic wetting effects in finite mobility ratio Hele-Shaw flow

TL;DR

This study investigates how dynamic wetting influences fluid displacement in Hele-Shaw cells, revealing delays in finger bifurcation and changes in finger morphology due to wetting effects, especially at high capillary numbers.

Contribution

It introduces a boundary element method with a Picard scheme to model dynamic wetting effects in finite mobility ratio flows, highlighting their impact on finger formation.

Findings

Dynamic wetting delays finger bifurcation.

High capillary numbers alter bifurcation modes.

Wetting reduces finger interaction and competition.

Abstract

In this paper we study the effects of dynamic wetting on the immiscible displacement of a high viscosity fluid subject to the radial injection of a less viscous fluid in a Hele-Shaw cell. The displaced fluid can leave behind a trailing film that coats the cell walls, dynamically affecting the pressure drop at the fluid interface. By considering the non-linear pressure drop in a boundary element formulation, we construct a Picard scheme to iteratively predict the interfacial velocity and subsequent displacement in finite mobility ratio flow regimes. Dynamic wetting delays the onset of finger bifurcation in the late stages of interfacial growth, and at high local capillary numbers can alter the fundamental mode of bifurcation, producing vastly different finger morphologies. In low mobility ratio regimes, we see that finger interaction is reduced and characteristic finger breaking mechanisms are delayed but never fully inhibited. In high mobility ratio regimes, finger shielding is reduced when dynamic wetting is present. Finger bifurcation is delayed which allows the primary fingers to advance further into the domain before secondary fingers are generated, reducing the level of competition.