Control and suppression of viscous fingering displacing non-Newtonian fluid with time-dependent injection strategies

Abstract

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

Interfacial instabilities in confined displacements involving non-Newtonian fluids

“…We would like to refer the reader to the literature involving lifting Hele-Shaw cells, wherein the cell gap is time dependent [88,89] and inertial effects influence the growth of the emergent interfacial patterns [90]. Injecting the displacing fluid at a non-uniform rate [91,92] or using a tapered Hele-Shaw cell [93] have been reported to control the viscous fingering instability for both Newtonian and non-Newtonian displacements. A multiport lifted Hele-Shaw cell with multiple source holes was used to engineer complex interlinked meshes [94], while experiments with rotating Hele-Shaw cells were performed to study densitydriven instabilities [95].…”

Effect of Ionic Surfactants on the Electrokinetic Control of Viscous Fingering

“…Overall, it is desirable to be able to control the intrinsic instability in order to manipulate processes and maximize their output. The rheological properties of the resident fluid (e.g., viscosity) are usually a determining factor toward the stability of the system but are hard to change for most applications. , …”

“…Passive control methods include the use of spatially varying permeability or a tapered cell geometry − and elastic membranes . Active control strategies are achieved through the use of external forces such as electric fields, time-dependent injection rates, time-dependent cell gap, or a combination of these methods. ,− …”

“…The rheological properties of the resident fluid (e.g., viscosity) are usually a determining factor toward the stability of the system but are hard to change for most applications. 9,10 Many researchers have studied both passive and active control of viscous fingering using Hele−Shaw cells. A Hele− Shaw cell is a sandwich of two plates separated by a thin gap ( ( m)), which represents porous media flows 11,12 while allowing for optical access to characterize the displacement.…”