Miscible displacements in Hele–Shaw cells: Nonmonotonic viscosity profiles

Schafroth, D.; Goyal, N.; Meiburg, Eckart

doi:10.1016/j.euromechflu.2006.09.001

Cited by 20 publications

(10 citation statements)

References 16 publications

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“…1(b) and 1(c)], which is consistent with theoretical predictions [22]. Figure 2 shows that the locally unstable region of the nonmonotonic viscosity profile [27,28] is located behind the reaction zone. This explains why fingers extend behind the interface as seen in the experiments [ Figs.…”

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confidence: 78%

Experimental evidence of reaction-driven miscible viscous fingering

et al. 2012

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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.

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confidence: 78%

Experimental evidence of reaction-driven miscible viscous fingering

et al. 2012

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“…The flow is then expected to be unstable in the case of the monotonically increasing and non-monotonic viscosity profiles but stable in the case of the monotonically decreasing profiles. In this sense, the present study bears some similarities with earlier ones dealing with nonmonotonic viscosity profiles (Manickam & Homsy 1993;Loggia et al 1995;Loggia, Salin & Yortsos 1998;Pankiewitz & Meiburg 1999;De Wit, Bertho & Martin 2005;Schafroth, Goyal & Meiburg 2007). However, there is a fundamental difference arising from the important role of chemistry.…”

Section: Monotonic Versus Non-monotonic Viscosity Profilessupporting

confidence: 61%

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

et al. 2010

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When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction-diffusion-convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by R b and R c representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

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“…It is key to the model that the spatial scale of all flow features is much greater than the gap widthb of the Hele-Shaw cell, and that the Peclet number defined in terms of the gap width, the displacement velocity and the solutal concentration is not large. If these criteria are not satisfied then the flow becomes fully three-dimensional [12] and the gap-averaged equations defined below are no longer valid: the three-dimensional Stokes equations must be considered instead, leading to significantly different stability results [13]. Our analysis below will generally deal with relatively large length-and time-scales so this restriction is not crucial, but it should be borne in mind throughout.…”

Section: Introductionmentioning

confidence: 99%

The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell

Pritchard

2009

European Journal of Mechanics - B/Fluids

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We investigate the viscous instability of a miscible displacement process in a recti-linear geometry, when the viscosity contrast is controlled by two quantities whichdiuse at dierent rates. The analysis is applicable to displacement in a porousmedium with two dissolved species, or to displacement in a Hele-Shaw cell with twodissolved species or with one dissolved species and a thermal contrast. We carry outasymptotic analyses of the linear stability behaviour in two regimes: that of smallwavenumbers at intermediate times, and that of large times.An interesting feature of the large-time results is the existence of regimes in whichthe favoured wavenumber scales with t−1/4, as opposed to the t−3/8 scaling foundin other regimes including that of single-species ngering. We also show that theregion of parameter space in which the displacement is unstable grows with time,and that although overdamped growing perturbations are possible, these are neverthe fastest-growing perturbations so are unlikely to be observed. We also interpretour results physically in terms of the stabilising and destabilising mechanisms actingon an incipient nger

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Miscible displacements in Hele–Shaw cells: Nonmonotonic viscosity profiles

Cited by 20 publications

References 16 publications

Experimental evidence of reaction-driven miscible viscous fingering

Experimental evidence of reaction-driven miscible viscous fingering

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell

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