Complex Pattern Formation and Viscous Fingering Stabilization in Radial Flow

Interfacial fluid instabilities are ubiquitous in Nature and are responsible for many important phenomena. In some cases, they play a constructive role like in the redistribution of energy in a system but, in some other cases, the role is destructive and may pose a serious threat to technical or industrial applications. In most cases, these fluids involve reactants that are known to modify the instability itself.

Fingering instabilities are special cases of fluid instabilities that occur when a high mobility fluid displaces a low mobility one [1]. Processes like enhanced oil recovery or other fluid displacements in porous media, such as chromatography, are examples in which the existence of fingering instability is crucial for the overall extraction performance. At a laboratory scale, these instabilities are studied in experimental arrangements known as Hele-Shaw cells. A particularity of these cells is that the flow inside them is representative of the flow in porous media.

In this work, we propose a chemical system likely to produce instabilities. We endow it with the appropriate chemical reactions at the interface that make it possible to control the activation or deactivation of the fingering instability at will. In particular, we consider two different fluids with different viscosities and analyze the displacement of one fluid by the other injected into a radial Hele-Shaw cell. We studied two different scenarios depending on which fluid is used as displacing/displaced solution [2].

In the first case, where the most viscous fluid displaces the less viscous one (initially stable configuration), pattern formation is observed when the characteristic flow and reactive timescales are similar. The patterns show complex dynamics in which fingers not only grow but move forward/backward. In the second case (initially unstable configuration), the unfavorable mobility ratio produces complex wormhole structures similar to those observed in dissolving rock fractures [3,4]. The displacement stabilizes when flow, diffusive, and reactive timescales are comparable.

We extensively characterized and numerically modeled both scenarios. Our results establish the basis to control fluid instabilities that may arise in a broad variety of contexts.  

REFERENCES:

[1] Homsy, G. M. (1987). Viscous fingering in porous media. Annual review of fluid mechanics, 19(1), 271-311.

[2] Escala, D. M., & Muñuzuri, A. P. (2021). A bottom-up approach to construct or deconstruct a fluid instability. Scientific reports, 11(1), 1-16.

[3] Szymczak, P., & Ladd, A. J. C. (2009). Wormhole formation in dissolving fractures. Journal of Geophysical Research: Solid Earth, 114(B6).

[4] Kalia, N., & Balakotaiah, V. (2007). Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks. Chemical Engineering Science, 62(4), 919-928.