Emergence of transient reverse fingers during radial displacement of a shear-thickening fluid

Abstract

A highly sheared dense aqueous suspension of granular cornstarch particles displays rich nonlinear rheology. We had previously demonstrated the growth and onset of interfacial instabilities when shear-thinning cornstarch suspensions were displaced by a Newtonian fluid, and had suggested methods to maximise displacement efficiency [Palak, R. Sathayanath, S. K. Kalpathy and R. Bandyopadhyay, Colloids Surf. A Physicochem. Eng. Asp., 629 (2021) 127405]. In the present work, we explore the miscible displacement of a dense aqueous cornstarch suspension in its discontinuous shear-thickening regime in a quasi-two-dimensional radial Hele-Shaw cell. We systematically study the growth kinetics of the inner interface between water and the cornstarch suspension, and also of the outer interface between the suspension and air. In addition to the growth of interfacial instabilities at the inner interface, we observe a transient withdrawal of the suspension and the formation of fingering instabilities at the outer interface. We demonstrate that these `reverse fingering' instabilities are extremely sensitive to the injection flow rate of water, the gap of the Hele-Shaw cell and the concentration of the displaced cornstarch suspension, {and emerge irrespective of immiscibility between the fluid pair. We believe that as the cornstarch suspension dilates due to the high shear rate imposed by the displacing fluid, the outer suspension-air interface responds with a restoring force, resulting in the penetration of air into the suspension and the formation of reverse fingers. We note that the growth of reverse fingers significantly reduces the displacement efficiency of the suspension. Finally, we demonstrate a correlation in the growth of inner and outer interfacial patterns by computing the velocity with which stresses propagate in the confined dense suspension. Our findings are useful in understanding the flow of granular materials through constrained geometries and can be extended to study stress propagation in shear-thickening materials due to a sudden imposition of high shear rate, such as in impact behaviour.