The effect of a crosslinking chemical reaction on pattern formation in viscous fingering of miscible fluids in a Hele–Shaw cell

Abstract

Viscous fingering can occur in fluid motion whenever a high mobility fluid displaces a low mobility fluid in a Darcy type flow. When the mobility difference is primarily attributable to viscosity (e.g., flow between the two horizontal plates of a Hele-Shaw cell), viscous fingering (VF) occurs, which is sometimes termed the Saffman-Taylor instability. Alternatively, in the presence of differences in density in a gravity field, buoyancy-driven convection can occur. These instabilities have been studied for decades, in part because of their many applications in pollutant dispersal, ocean currents, enhanced petroleum recovery, and so on. More recent interest has emerged regarding the effects of chemical reactions on fingering instabilities. As chemical reactions change the key flow parameters (densities, viscosities, and concentrations), they may have either a destabilizing or stabilizing effect on the flow. Hence, new flow patterns can emerge; moreover, one can then hope to gain some control over flow instabilities through reaction rates, flow rates, and reaction products. We report effects of chemical reactions on VF in a Hele-Shaw cell for a reactive step-growth cross-linking polymerization system. The cross-linked reaction product results in a non-monotonic viscosity profile at the interface, which affects flow stability. Furthermore, three-dimensional internal flows influence the long-term pattern that results.

Chemo-Hydrodynamic Patterns and Instabilities

“…The cross-linked reaction product is more viscous which results in a non-monotonic viscosity profile at the interface, affecting flow stability. In particular, the numerically predicted fact that fingers extend preferentially at the back of the reaction zone where the less viscous injected reactant displaces the locally produced more viscous product while the frontal part of the reaction zone is stabilized is recovered in the experiments (Bunton et al (2017)).…”

“…The case of reactions inducing a non-monotonic increasing viscosity profile with a maximum (zone III of Figure 3) has been recently studied in Hele-Shaw cells in the case of a step-growth cross-linking polymerization reaction (Bunton et al (2017), Stewart et al (2018)). In absence of reaction, the invading solution is less viscous than the displaced one and VF is obtained.…”

Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth

“…In contrast, viscous fingers can be regarded as nonreactive wormholes ( ) where growth occurs only at the tip. Chemical reactions may also alter the rheology of the fluid leading to viscous instabilities (Bunton et al, ; Nagatsu et al, ).…”

Mixing and finger morphologies in miscible non-Newtonian solution displacement

“…Den Chen, 1989). Miscible fluid displacement has also been studied in both linear (Boschan et al, 2003;Malhotra et al, 2015;Mishra et al, 2010) and radial (Bunton et al, 2017;C. Y. Chen et al, 2010;J.…”