Viscous fingering in reaction-diffusion systems

Wit, A. De; Homsy, G. M.

doi:10.1063/1.478774

Cited by 112 publications

(87 citation statements)

References 31 publications

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“…The exact dependence of the viscosity on concentrations B and C still needs to be specified. Following earlier studies (Tan & Homsy 1986;De Wit & Homsy 1999a, 1999bAzaiez & Singh 2002;Gérard & De Wit 2009), an exponential dependence is adopted. The logarithm of the viscosity is thus taken to be a linear combination of the concentrations.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In the case of immiscible flows, this instability, known as the Saffman-Taylor instability, can also be modified by reactions that change the surface tension at the fluid interface (Jahoda & Hornof 2000;Fernandez & Homsy 2003). Several works have moreover addressed theoretically the coupling between VF and autocatalytic reactions (De Wit & Homsy 1999a, 1999bSwernath & Pushpavanam 2007Ghesmat & Azaiez 2009) without however corresponding experimental confirmations as autocatalytic reactions are more prone to change density rather than viscosity (De Wit 2001;De Wit et al 2003). In the context of chromatographic applications, adsorption-desorption phenomena have also been shown to influence VF patterns (Mishra, Martin & De Wit 2007).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2010

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“…Recently, reaction driven viscosity changes have been shown numerically to lead to new spatiotemporal dynamics of viscous fingering in chemical bistable autocatalytic systems providing traveling fronts between solutions of different viscosity. [6][7][8] Unfortunately the predicted nonlinear dynamics have not been observed to date mainly because autocatalytic reactions are usually performed in aqueous solutions for which the viscosity hardly changes with concentrations of solutes. The only striking evidence of chemically driven viscous fingering for miscible autocatalytic systems occurs in polymeric systems where the monomer solution and the polymer matrix can have quite strong differences in viscosity.…”

Section: Introductionmentioning

confidence: 99%

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Wit

2004

Physics of Fluids

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Nonlinear interactions between chemical reactions and Rayleigh-Taylor type density fingering are studied in porous media or thin Hele-Shaw cells by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the density of miscible solutions. In absence of flow, the reaction-diffusion system features stable planar fronts traveling with a given constant speed v and width w. When the reactant and product solutions have different densities, such fronts are buoyantly unstable if the heavier solution lies on top of the lighter one in the gravity field. Density fingering is then observed. We study the nonlinear dynamics of such fingering for a given model chemical system, the iodate-arsenious acid reaction. Chemical reactions profoundly affect the density fingering leading to changes in the characteristic wavelength of the pattern at early time and more rapid coarsening in the nonlinear regime. The nonlinear dynamics of the system is studied as a function of the three relevant parameters of the model, i.e., the dimensionless width of the system expressed as a Rayleigh number Ra, the Damköhler number Da, and a chemical parameter d which is a function of kinetic constants and chemical concentration, these two last parameters controlling the speed v and width w of the stable planar front. For small Ra, the asymptotic nonlinear dynamics of the fingering in the presence of chemical reactions is one single finger of stationary shape traveling with constant nonlinear speed VϾv and mixing zone WϾw. This is drastically different from pure density fingering for which fingers elongate monotonically in time. The asymptotic finger has axial and transverse averaged profiles that are self-similar in unit lengths scaled by Ra. Moreover, we find that W/Ra scales as Da Ϫ0.5 . For larger Ra, tip splittings are observed.

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“…Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36], medium heterogeneity [32,[37][38][39][40], gravity [41][42][43][44][45][46], chemical reactions [3,[47][48][49], absorption [50], and flow configuration [51][52][53][54][55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56].…”

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confidence: 99%

Interface evolution during radial miscible viscous fingering

2015

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We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t 1 2 , as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability. A large number of natural and industrial flow processes depend on both the degree and the rate of mixing between fluids, such as chemical reactions [1][2][3][4], combustion [5], microbial activity [6], and enhanced oil recovery [7]. In such mixing-driven systems, the flow responsible for fluid displacement reflects the heterogeneity of the host medium structure [8][9][10][11] or the physical properties of the fluids, such as density [3,12,13] or viscosity [14,15]. Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36] [50], and flow configuration [51-55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56]. While the dynamics of the interface between two miscible fluids is crucial to explain and predict the rate of mixing [1,16], a solid understanding of the temporal evolution of the viscously unstable fl...

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Viscous fingering in reaction-diffusion systems

Cited by 112 publications

References 31 publications

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

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

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Interface evolution during radial miscible viscous fingering

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