Flame propagation in random media

Provatas, Nikolas; Ala-Nissilä, Tapio; Grant, Martin; Elder, K. R.; Piché, L.

doi:10.1103/physreve.51.4232

Cited by 41 publications

(35 citation statements)

References 11 publications

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“…In order to use the theoretical prediction, Eq. (9), we measured the growth velocity of the radius of individual nucleation centers for various concentrations, and found it to be in agreement with previous results [9,10], i.e. R(t) ∼ t.…”

Section: Figsupporting

confidence: 77%

“…Such continuum reaction-diffusion equations have been used extensively in physics, chemistry, biology and engineering to describe a wide range of phenomena from pattern formation to combustion. However, the connection of reaction-diffusion equations to nucleation and interface growth has received little attention.In a recent study of slow combustion in disordered media, Provatas et al [9,10] showed that flame fronts exhibit a percolation transition, consistent with mean field theory, and that the kinetic roughening of the reaction front in slow combustion is consistent with the KardarParisi-Zhang (KPZ) [11] universality class. In this paper we make a further connection between slow combustion started by spontaneous fluctuations, and the classical theory of the nucleation and growth of droplets from a metastable phase.…”

mentioning

confidence: 88%

“…In a recent study of slow combustion in disordered media, Provatas et al [9,10] showed that flame fronts exhibit a percolation transition, consistent with mean field theory, and that the kinetic roughening of the reaction front in slow combustion is consistent with the KardarParisi-Zhang (KPZ) [11] universality class. In this paper we make a further connection between slow combustion started by spontaneous fluctuations, and the classical theory of the nucleation and growth of droplets from a metastable phase.…”

mentioning

confidence: 88%

“…This can also be seen from Eq. (9). At early times the structure factor follows approximately ∼ t 5 , and for late times it falls off exponentially.…”

Section: Figmentioning

confidence: 99%

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Karttunen

Provatas

Ala-Nissilä

et al. 1998

Journal of Statistical Physics

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We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good argeement with theoretical predictions.PACS numbers: 64.60. My,05.40.+j,82.40.Py,68.10.Gw The kinetic process by which first-order phase transitions take place is an important subject of longstanding experimental and theoretical interest [1]. Nucleation is the most common of first-order transitions, and remains of a great deal of interest [2][3][4][5][6]. There are two fundamentally different cases, homogeneous and heterogeneous nucleation. Homogeneous nucleation is an intrinsic process where embryos of a stable phase emerge from a matrix of a metastable parent phase due to spontaneous thermodynamic fluctuations. Droplets larger than a critical size will grow while smaller ones decay back to the metastable phase [7,8]. More commonplace in nature is the process of heterogeneous nucleation. There, impurities or inhomogeneities catalyze a transition by making growth energetically favorable.Here we show that the concepts of nucleation and growth can be usefully applied to understand some aspects of slow combustion. We use a phase-field model of two coupled reaction-diffusion equations to study the nucleation and growth of combustion centers in twodimensional systems. Such continuum reaction-diffusion equations have been used extensively in physics, chemistry, biology and engineering to describe a wide range of phenomena from pattern formation to combustion. However, the connection of reaction-diffusion equations to nucleation and interface growth has received little attention.In a recent study of slow combustion in disordered media, Provatas et al. [9,10] showed that flame fronts exhibit a percolation transition, consistent with mean field theory, and that the kinetic roughening of the reaction front in slow combustion is consistent with the KardarParisi-Zhang (KPZ) [11] universality class. In this paper we make a further connection between slow combustion started by spontaneous fluctuations, and the classical theory of the nucleation and growth of droplets from a metastable phase.We generalize the model of Provatas et al. by including an uncorrelated noise source η(x, t), as a function of position x and time t. The model then consists of equations of motion for the temperature field T (x, t) and the local concentration if reactants C(x, t). The temperature satisfiesThe first term on the right-hand-side accounts for thermal diffusion, with diffusion constant D, the second term gives Newtonian cooling due to coupling with a heat bath of background temperature T 0 , with rate constant Γ, and the third term R(T, C) is the exothermic reaction rate as a function of temperature and concentration o...

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Section: Figsupporting

confidence: 77%

mentioning

confidence: 88%

mentioning

confidence: 88%

“…This can also be seen from Eq. (9). At early times the structure factor follows approximately ∼ t 5 , and for late times it falls off exponentially.…”

Section: Figmentioning

confidence: 99%

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Karttunen

Provatas

Ala-Nissilä

et al. 1998

Journal of Statistical Physics

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“…We have recently shown that asymptotic TKPZ behavior can be obtained in careful experiments on slow combustion fronts in paper [11,12], as predicted theoretically [6,13]. In an earlier experiment [14] x 0.71͑5͒ was found and interpreted in terms of the moving phase of the DPD model.…”

Section: Scaling and Noise In Slow Combustion Of Papermentioning

confidence: 83%

Scaling and Noise in Slow Combustion of Paper

et al. 2000

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Scaling, propagation, and kinetic roughening of flame fronts in random media

et al. 1995

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We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.

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Flame propagation in random media

Cited by 41 publications

References 11 publications

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Scaling and Noise in Slow Combustion of Paper

Scaling, propagation, and kinetic roughening of flame fronts in random media

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