Phase diagram of sustained wave fronts opposing the flow in disordered porous media

Saha, Sandeep; Atis, Severine; Salin, D.; Talon, Laurent

doi:10.1209/0295-5075/101/38003

Cited by 24 publications

(29 citation statements)

References 30 publications

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“…The essential experimental picture [13] is reproduced and we identified a clear criterium that allows to discriminate between the possible scenarios shown in Fig.1. Supported by excellent agreement with ab initio simulations used to model the experiments [24], this validates the hypothesis that the depinning transition is controlled by a limited number of events, randomly spread over the medium.…”

supporting

confidence: 77%

Strong pinning of propagation fronts in adverse flow

Gueudré¹,

Dubey

Talon

et al. 2014

Phys. Rev. E

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Reaction fronts evolving in a porous medium exhibit a rich dynamical behaviour. In presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive numerical simulations of the hydrodynamic equations confirm the experimental observations. Here we propose a stylized model, predicting two possible outcomes of the experiments for large adverse flow: either the front develops a sawtooth shape, or it acquires a complicated structure with islands and overhangs. A simple criterion allows to distinguish between the two scenarios and its validity is reproduced by direct hydrodynamical simulations. Our model gives a better understanding of the transition and is relevant in a variety of domains, when the pinning regime is strong and only relies on a small number of sites.PACS numbers: 82.33.Ln In the systems separated in distinct phases, the dynamics is controlled by the behaviour of the propagating fronts. Those fronts pervade a broad variety of domains in physics, ranging from chemotaxis [1] and plasma physics [2] to flames front [3] or epidemics, therefore triggering much activity in their modelling (for a recent review, see [4]). One of the cornerstones in this field is the celebrated Fisher-KPP theory, describing the front propagation in reaction-diffusion systems [5]. However, this approach was limited to systems with no advection, i.e. not undergoing any fluid flow, despite its physical importance. Coherent fluid-like motion strongly impacts the dynamics of the fronts [6] and remains a challenging problem, whether because of the appearance of turbulence [7], or because of the influence of a disordered media [8,9]. One natural disordered environment for propagation fronts is a porous medium. Some examples were investigated in the petrol industry and aeronautics with attempts to address the evolution of a flame front in a gas filter [10,11]. Recently, experiments on selfsustained chemical reactions have allowed a fine and controlled examination of the propagation fronts in porous medium, revealing some striking features by direct observation [12,13].The experimental setup employs an autocatalytic reaction invading a cell filled with a solution of reactants. To reproduce porosity, the cell also contains a mixture of glass spheres of different sizes. The reaction starts at the bottom of the cell and, in the absence of advection flow, develops into an almost flat front propagating upwards with constant chemical speed |V χ | = D m α/2 and width χ = D m /|V χ |, D m being the molecular diffusion constant and α the reaction rate. In presence of an adverse flow injected from the top at speed U , the porosity generates a fixed random velocity map of the fluid with short range correlations of characteristic length d . A rich dynamical phase diagram is observed as a function of the flow velocity U , the control parameter of the experiment (see Fig

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supporting

confidence: 77%

Strong pinning of propagation fronts in adverse flow

Gueudré¹,

Dubey

Talon

et al. 2014

Phys. Rev. E

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“…We first recall briefly the origin of the directed percolation mapping. As discussed in previous work [23], the interface is able to propagate wherever the local flow velocity is lower than the chemical velocity (i.e., |U | < V χ ), but it can be blocked if the velocity is higher. A necessary condition to be pinned is the existence of a blocking (|U | > V χ ) path transverse to the flow direction, which defines a percolation criterion.…”

Section: Appendix: Directed Percolationmentioning

confidence: 70%

“…As a consequence of the flow opposing the front, static fronts have been found depending on the intensity of the the mean flow velocity U that is negative by convention. In previous studies [22][23][24] we have demonstrated that, depending on U , the system display three propagating regimes. If the flow magnitude is high enough, the front recedes downstream.…”

Section: Introductionmentioning

confidence: 80%

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Avalanches dynamics in reaction fronts in disordered flows

et al. 2017

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We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

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“…A klorit-tetrationát reakciót termosztált edényben lejátszatva, függőle-gesen lefelé haladó front esetén azt tapasztalták, hogy a porozitás csökkenésével az alakzatra jellemző maximális hullámszám értéke csökkent. D. Salin és csoportja is végzett néhány kísérletet pórusos közegű frontreakciók esetén [61][62][63], ám ezekben a front ellenében, vagy éppen a vele megegyező irányban történő reaktáns-áramoltatás hatását vizsgálták a jodát-arzénessav rendszerben. A közeg kialakításához kétféle méretű gyöngy keverékét használ-ták, és megállapították, hogy a permeabilitás növekedésével nőtt a front terjedési sebessége.…”

Section: A Pórusos Közeg áRamlást Befolyásoló Hatásaunclassified

A konvektív instabilitás tanulmányozása homogén és pórusos közegben a klorit-tetrationát rendszerben

Schuszter¹

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Phase diagram of sustained wave fronts opposing the flow in disordered porous media

Cited by 24 publications

References 30 publications

Strong pinning of propagation fronts in adverse flow

Strong pinning of propagation fronts in adverse flow

Avalanches dynamics in reaction fronts in disordered flows

A konvektív instabilitás tanulmányozása homogén és pórusos közegben a klorit-tetrationát rendszerben

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