Experimental evidence of reaction-driven miscible viscous fingering

Abstract

An experimental demonstration of reaction-driven viscous fingering developing when a more viscous solution of a reactant A displaces a less viscous miscible solution of another reactant B is presented. In the absence of reaction, such a displacement of one fluid by another less mobile one is classically stable. However, a simple A + B → C reaction can destabilize this interface if the product C is either more or less viscous than both reactant solutions. Using the pH dependence of the viscosity of some polymer solutions, we provide experimental evidence of both scenarios. We demonstrate quantitatively that reactive viscous fingering results from the buildup in time of nonmonotonic viscosity profiles with patterns behind or ahead of the reaction zone, depending on whether the product is more or less viscous than the reactants. The experimental findings are backed up by numerical simulations. Viscous fingering (VF), also often referred to as the Saffman-Taylor instability, appears when a fluid with a given viscosity displaces another more viscous and hence less mobile one in porous media. This hydrodynamic instability has been largely studied both theoretically and experimentally [1][2][3][4] because of the beauty and generic character of the ramified patterns produced but also because of its practical consequences. VF is indeed observed in applications as diverse as hydrology [5,6] [21,22] has, however, suggested that reactions could even destabilize the classically stable reverse situation of a more viscous fluid displacing a less viscous one. To do so, it has been predicted that the product of the reaction must have a viscosity either larger or smaller than the viscosity of the reactants.In this work we present experimental evidence of such reaction-driven VF destabilization of a more viscous liquid displacing a less viscous one. We show quantitatively that the classically stable interface between a viscous reactant A pushing a less viscous aqueous solution of another reactant B can be destabilized by the buildup through a reaction of nonmonotonic viscosity profiles in time. The experimental study is carried out using aqueous solutions of polymers, chosen mainly because of their viscosity dependence on pH. If a solution of such a polymer A displaces less viscous dyed water, no instability is obtained and the interface remains planar. However, upon addition of a pH changing reactant B in the displaced water, an A + B → C neutralization reaction generates a product C either more viscous than the polymer A or less viscous than the solution of B triggering reactioninduced fingering. We provide experimental realization of both scenarios, and explain the origin of the destabilization by quantitative measurements of viscosities and numerical simulations. We also highlight the difference between VF patterns depending on whether the reaction generates respectively a maximum or a minimum in the spatial viscosity profile.

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

“…We directly compare the spatio-temporal evolution of the concentration fields in the reactive cases to the analogous non reactive scenarios obtained by neglecting kinetic terms in Eqs. (13)- (15). A consistent comparison is made by using the same general conditions and parameters (R a = 2.5, δ a = 0.64) both in the non reactive and reactive cases, the latter ones also considering the parameters for the species C, R c = 2.3, and δ c = 0.48.…”

“…13,14 This change in turn can affect the flows but in some cases can also more drastically modify the patterns or even trigger an instability in an otherwise stable system. 15 In the case of buoyancy-driven instabilities, such a chemo-hydrodynamic coupling has already been well studied for traveling autocatalytic fronts (see Refs. [16][17][18] and references therein) and combustion problems.…”

Experimental study of a buoyancy-driven instability of a miscible horizontal displacement in a Hele-Shaw cell

“…There is however increased interest in understanding the properties of such thin stripes either to suppress them or to avoid confusing them with other patterns due to other instabilities. Recent work has indeed demonstrated that chemical reactions that change the viscosity of polymer solutions [12][13][14] can generate patterns at the interface between miscible solutions even in the viscously stable case of a more viscous injected fluid displacing a less viscous one. In such reaction-induced viscous fingering, 14 the pattern-forming role played by reactions modifying the viscosity in situ can only be appreciated if the underlying non-reactive displacement is stable, which is not trivial when the above mentioned stripes come into play.…”

Introduction to the Focus Issue: Chemo-Hydrodynamic Patterns and Instabilities

“…[9][10][11][12][13][14][15][16][17] For A þ B ! C fronts, complex buoyancy- 18,19 or viscosity-driven patterns [20][21][22] can develop when miscible solutions containing initially separated A and B reactants are put into contact with each other. These convective patterns have been shown to have stability properties 21,22 and symmetries 18 different from those in non-reactive systems.…”

“…C fronts, complex buoyancy- 18,19 or viscosity-driven patterns [20][21][22] can develop when miscible solutions containing initially separated A and B reactants are put into contact with each other. These convective patterns have been shown to have stability properties 21,22 and symmetries 18 different from those in non-reactive systems. Finally, a third class of model systems consists of immiscible RDC fluid-fluid systems in the presence of species which are either restricted to the fluid-fluid interface or can cross the interface, and which may also undergo chemical reactions.…”