Experimental Evidence for Three Universality Classes for Reaction Fronts in Disordered Flows

Atis, Severine; Dubey, Awadhesh K.; Salin, D.; Talon, Laurent; Doussal, Pierre Le; Wiese, Kay Joerg

doi:10.1103/physrevlett.114.234502

Cited by 46 publications

(62 citation statements)

References 43 publications

(18 reference statements)

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“…Flows in porous and fractured media exhibit complex spatiotemporal dynamics [1][2][3][4][5][6][7]. Avalanches and non-Gaussian intermittent velocity fluctuations [8][9][10][11][12][13][14][15][16][17] can arise from the medium heterogeneous structure, which may involve a very wide range of spatial scales, from nanometer pore size to kilometer field scales.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

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We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of μ and v on the statistical properties of the velocity V , the spatial average of the local front velocities over a window of lateral size . We have varied from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V (t) present very strong fluctuations which evolve systematically with the parameters μ, v, and . We have verified that the non-Gaussian fluctuations of the global velocity V (t) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by N eff = / c (the ratio of the lateral size of the measuring window to the correlation length c ∼ 1/ √ μv). The large correlated excursions of V (t) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents-independent of μ, v, and . Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξ S and maximum durations ξ T of global avalanches are not controlled by the same mechanism. While ξ S are also determined by / c , like the amplitude fluctuations of V (t), ξ T and the temporal correlations of V (t) evolve much more strongly with imposed flow rate v than with fluid viscosity μ.

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Section: Introductionmentioning

confidence: 99%

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

2016

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“…Non-equilibrium dynamics is ubiquitous in nature, and takes diverse forms, such as avalanche motion in magnets and vortex lines [1, 2] ultraslow relaxation in glasses [3, 4], unitary evolution towards thermalization in isolated quantum systems [5], coarsening in phase ordering kinetics [6], and flocking in living matter [7]. Prominent examples are growth phenomena, which abound in physics [8, 9, 11, 12], biology [8, 13,14], and beyond [15]. As some of these systems try to reach local equilibrium or stationarity, a great variety of behaviors can occur, such as aging dynamics and memory of past evolution [1, 4, 6,16].…”

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“…A universal behavior then emerges, unifying many growth phenomena into a few universality classes, irrespective of their microscopic details. The most generic one, for local growth rules, is the celebrated Kardar-Parisi-Zhang (KPZ) class, now substantiated by many experimental examples, such as growing turbulence of liquid crystal [9][10][11], propagating chemical fronts [15], paper combustion [12] and bacteria colony growth [13]. For one-dimensional interfaces growing in a plane, as studied in many experiments, it is characterized by the following KPZ equation [17]:…”

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Memory and Universality in Interface Growth

2017

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Recently, very robust universal properties were shown to arise in one-dimensional growth processes with local stochastic rules, leading to the Kardar-Parisi-Zhang universality class. Yet it has remained essentially unknown how fluctuations in these systems correlate at different times. Here we derive quantitative predictions for the universal form of the two-time aging dynamics of growing interfaces and we show from first principles the breaking of ergodicity that the KPZ time evolution exhibits. We provide corroborating experimental observations on a turbulent liquid crystal system, as well as a numerical simulation of the Eden model, and we demonstrate the universality of our predictions. These results may give insight into memory effects in a broader class of far-from-equilibrium systems.Introduction. Non-equilibrium dynamics is ubiquitous in nature, and takes diverse forms, such as avalanche motion in magnets and vortex lines [1, 2] ultraslow relaxation in glasses [3, 4], unitary evolution towards thermalization in isolated quantum systems [5], coarsening in phase ordering kinetics [6], and flocking in living matter [7]. Prominent examples are growth phenomena, which abound in physics [8, 9, 11, 12], biology [8, 13,14], and beyond [15]. As some of these systems try to reach local equilibrium or stationarity, a great variety of behaviors can occur, such as aging dynamics and memory of past evolution [1, 4, 6,16]. How universal and generic are these behaviors is a fundamental question [16].One important example of growth arises when a stable phase of a generic system expands into a non-stable (or meta-stable) one, in presence of noise. While spreading, the interface separating the two phases develops many non-trivial geometric and statistical features. A universal behavior then emerges, unifying many growth phenomena into a few universality classes, irrespective of their microscopic details. The most generic one, for local growth rules, is the celebrated Kardar-Parisi-Zhang (KPZ) class, now substantiated by many experimental examples, such as growing turbulence of liquid crystal [9][10][11], propagating chemical fronts [15], paper combustion [12] and bacteria colony growth [13]. For one-dimensional interfaces growing in a plane, as studied in many experiments, it is characterized by the following KPZ equation [17]:

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“…Instead, in non-Eikonal regimes, it monotonically decelerates reversing the motion for a critical adverse flow20. In the case of porous media flows, the front is observed to remain frozen for a wide range of counter velocities before starting to move downstream for relative high adverse flows2627.…”

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Finite-size effects on bacterial population expansion under controlled flow conditions

Tesser

Zeegers

Clercx

et al. 2017

Sci Rep

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The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra, advection induced, dispersal factor. We designed and assembled a dedicated microfluidic device to control and quantify the expansion of populations of E. coli bacteria under both co-flowing and counter-flowing conditions, measuring the front speed at varying intensity of the imposed flow. At variance with respect to the case of classic advective-reactive-diffusive chemical fronts, we measure that almost irrespective of the counter-flow velocity, the front speed remains finite at a constant positive value. A simple model incorporating growth, dispersion and drift on finite-size hard beads allows to explain this finding as due to a finite volume effect of the bacteria. This indicates that models based on the Fisher-Kolmogorov-Petrovsky-Piscounov equation (FKPP) that ignore the finite size of organisms may be inaccurate to describe the physics of spatial growth dynamics of bacteria.

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Experimental Evidence for Three Universality Classes for Reaction Fronts in Disordered Flows

Cited by 46 publications

References 43 publications

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

Memory and Universality in Interface Growth

Finite-size effects on bacterial population expansion under controlled flow conditions

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