Fingering of Chemical Fronts in Porous Media

Wit, A. De

doi:10.1103/physrevlett.87.054502

Cited by 143 publications

(49 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 82%

“…Change of the instability in time The classical non-reactive VF is known to weaken in time when diffusion smoothes out unstable viscosity gradients (Tan & Homsy 1986;De Wit et al 2005). Chemical reactions are obviously changing this picture as readily seen in figure 8 for R b = 0.…”

Section: Unstable Initial Reactant Front (Rmentioning

confidence: 93%

“…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%

See 2 more Smart Citations

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

et al. 2010

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Monotonic Versus Non-monotonic Viscosity Profilessupporting

confidence: 82%

Section: Unstable Initial Reactant Front (Rmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…The case R = 0, or equivalently δ → ∞, in (3.10) yields 12) which corresponds to the pure RT instability of a layer of A above the pure solvent where B 0 = 0, which is always unstable (see Manickam &Homsy 1995 andDe Wit 2001). Such a situation has been studied experimentally in Hele-Shaw cells by Fernandez et al (2002) for instance.…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…One quantity that would make sense to follow in time would be the mean flux obtained by averaging the flux along the transverse coordinate. Even in that case, one would, in addition, need to make ensemble average of this mean flux on several simulations made for a single set of parameters but different noise seeding the initial condition (De Wit, Bertho, Martin 2005). To perform a parametric study of the scalings of such statistical ensemble averages of mean fluxes is beyond the scope of the present paper.…”

Section: Nonlinear Simulationsmentioning

confidence: 99%

Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells

2011

Self Cite

View full text Add to dashboard Cite

Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are theoretically studied in porous media and Hele-Shaw cells (two glass plates separated by a thin gap). Beyond the classical Rayleigh-Taylor (RT) and double diffusive (DD) instabilities that can affect such two-layer stratifications right at the initial time of contact, diffusive-layer convection (DLC) as well as delayed-double diffusive (DDD) instabilities can set in at a later time when differential diffusion effects act upon the evolving density profile starting from an initial step-function profile between the two miscible solutions. The conditions for these instabilities to occur can therefore be obtained only by considering time evolving base-state profiles. To do so, we perform a linear stability analysis based on a quasi-steady-state approximation (QSSA) as well as nonlinear simulations of a diffusion-convection model to classify and analyse all possible buoyancy-driven instabilities of a stratification of a solution of a given solute A on top of another miscible solution of a species B. Our theoretical model couples Darcy's law to evolution equations for the concentration of species A and B ruling the density of the miscible solutions. The parameters of the problem are a buoyancy ratio R quantifying the ratio of the relative contribution of B and A to the density as well as δ, the ratio of diffusion coefficients of these two species. We classify the region of RT, DD, DDD and DLC instabilities in the (R, δ) plane as a function of the elapsed time and show that, asymptotically, the unstable domain is much larger than the one captured on the basis of linear base-state profiles which can only obtain stability thresholds for the RT and DD instabilities. In addition the QSSA allows one to determine the critical time at which an initially stable stratification of A above B can become unstable with regard to a DDD or DLC mechanism when starting from initial step function profiles. Nonlinear dynamics are also analysed by a numerical integration of the full nonlinear model in order to understand the influence of R and δ on the dynamics.

show abstract

The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows

Anna

Dentz

Tartakovsky

et al. 2014

Geophysical Research Letters

View full text Add to dashboard Cite

International audienceThe mixing dynamics resulting from the combined action of diffusion, dispersion, and advective stretching of a reaction front in heterogeneous flows leads to reaction kinetics that can differ by orders of magnitude from those measured in well-mixed batch reactors. The reactive fluid invading a porous medium develops a filamentary or lamellar front structure. Fluid deformation leads to an increase of the front length by stretching and consequently a decrease of its width by compression. This advective front deformation, which sharpens concentration gradients across the interface, is in competition with diffusion, which tends to increase the interface width and thus smooth concentration gradients. The lamella scale dynamics eventually develop into a collective behavior through diffusive coalescence, which leads to a disperse interface whose width is controlled by advective dispersion. We derive a new approach that quantifies the impact of these filament scale processes on the global mixing and reaction kinetics. The proposed reactive filament model, based on the elementary processes of stretching, coalescence, and fluid particle dispersion, provides a new framework for predicting reaction front kinetics in heterogeneous flows

show abstract

Fingering of Chemical Fronts in Porous Media

Cited by 143 publications

References 38 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

Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells

The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows

Contact Info

Product

Resources

About