We explore the stabilization mechanism of the fluid-fluid interface in the radial Hele-Shaw cell, displacing a non-Newtonian fluid. It is possible to stabilize the interface following a non-linear injection rate, Q ~ t-(2- n)/(2+ n), which is related to the displaced fluid rheology (ᵅB;: power-law index). This suggests the absence of fingering at constant injection when n ~ 2. We propose a quantitative criterion to control the pattern formation and suppress fingering, through the dimensionless parameter J as a function of the physical and operating parameters, which is applicable for a generalised shear thinning fluid. The parameter J is related to the capillary number in the context of the power-law fluid, relating to the viscous and interfacial forces. The fingering morphology at higher order modes are affected by non-linear effects. The results are non-intuitive and we have shown a feasible approach towards long term fingering stabilization

We experimentally investigate the interplay of viscous fingering and fracturing in a radial Hele–Shaw cell displacing a non-Newtonian (shear-thickening) fluid. We have used cornstarch suspension of different compositions (39%–48% w/w dispersed in water–CsCl solution), and the rheology of the suspension exhibits shear thickening behavior beyond a shear rate of 1 s−1. We observe the transition from viscous fingering to dendritic fracturing morphology beyond a critical weight fraction of cornstarch suspension. We analyze the plot of the fraction of injected phase to displaced phase as a function of injected volume for different weight fractions of cornstarch suspension. The injection pressure of the invading fluid (air or oil) used in the present work has no significant effect on the transition from viscous fingering and fracturing patterns. The transition of the pattern is possible if the injection pressure (and consequently the flow rate) is increased. The width of the finger decreases with the injection pressure of the invading fluid and widens with the injected volume due to the reduced local shear rate beyond a critical size. The width of the dendritic fracturing decreases with the injection pressure of invading fluid but increases with the injected volume.

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