Viscous Fingering During Air-Driven Displacement of a Shear-Thickening Fluid in a Hele–Shaw Cell: Capillary, Rheological, and Geometric Effects

Viscous fingering is a canonical nonlinear interfacial instability that arises when a less viscous fluid displaces a more viscous one under an adverse viscosity contrast. Despite extensive investigations into the effects of fluid properties, operating conditions, and rheology, systems involving a shear-thickening displaced phase remain largely unexplored. Here, three-dimensional numerical simulations of immiscible air–fluid displacement in a Hele–Shaw cell are performed to elucidate how interfacial tension, air-inlet velocity, and gap-depth gradient regulate instability evolution. Increasing interfacial tension strengthens the Laplace-pressure barrier, suppresses shear-induced necking and pinch-off, and preserves finger topology; however, it intensifies flow diversion and delays the advancement of the central finger. Increasing the inlet velocity markedly amplifies the local interfacial shear rate and triggers pronounced shear thickening. The resulting viscous-resistance barrier redistributes momentum toward paths of least hydraulic resistance, directly promoting tip splitting and severe topological breakup. Even a small gap-depth gradient reorganizes the local hydraulic resistance and pressure field. Positive and negative gradients induce resistance-reduction and throttling effects, respectively, generating pronounced pressure shielding that governs asymmetric momentum transfer and preferential flow-path selection. These findings identify the capillary, rheological, and geometric mechanisms controlling viscous fingering during the air-driven displacement of shear-thickening fluids. Because such instabilities compromise the integrity of geological-fracture seals and the operating efficiency of semi-solid flow batteries, this study provides a mechanistic basis for stabilizing immiscible displacement and optimizing industrial fluid-transport systems.