Controlling Viscous Fingering Using Time-Dependent Strategies

Abstract

Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. We report theoretical and experimental results on a time-dependent control strategy by manipulating the gap thickness b(t) in a lifting Hele-Shaw cell in the power-law form b(t)=b(1)t(1/7). Experimental results show good quantitative agreement with the predictions of linear stability analysis. By choosing the value of a single time-independent control parameter, we can either totally suppress the viscous fingering instability or maintain a series of nonsplitting viscous fingers during the fluid displacement process. In addition to the gap thickness of a Hele-Shaw cell, time-dependent control strategies can, in principle, also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tension between the two fluids.

Control of radial miscible viscous fingering

“…Discussions and conclusion-Depending upon the application, controlling fingering instabilities is of paramount importance, such as mixing can be increased by increasing the instability; whereas for an improved oil recovery or separation process, instability should be suppressed. VF in immiscible systems are controllable by modifying the geometry [29,30], using time dependent strategies [17,18]. Though all these control mechanisms may be directly inapplicable in miscible VF [31], in this paper, we investigate a stability mechanism in miscible VF based on the principle of stabilisation in immiscible flows.…”

Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depth

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The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1].

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Flow instabilities of time‐dependent injection schemes in immiscible displacements

“…The term C ij is only applicable at the grid points intersected by the interface (irregular grid points), and its value is derived from the two jump conditions described by Equations (14) and (15). The term C ij is only applicable at the grid points intersected by the interface (irregular grid points), and its value is derived from the two jump conditions described by Equations (14) and (15).…”

“…The first experimental studies that attempted to understand this instability were carried out by Hill et al [1,2] In a seminal work, Saffman and Taylor examined the case of an immiscible displacement and provided a mathematical model for the development of the instability. [15] Extensive reviews of studies on viscous fingering instabilities were given by Homsy, [16] Yortsos, [17] and McCloud and Maher. [14] A recent study examined strategies to control the instability using a time-dependent gap thickness.…”