Fluctuating hydrodynamics of multi-species reactive mixtures

Bhattacharjee, Anup Kumar; Balakrishnan, Kaushik; Garcia, Alejandro L.; Bell, John B.; Donev, Aleksandar

doi:10.1063/1.4922308

Cited by 45 publications

(64 citation statements)

References 133 publications

(303 reference statements)

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“…We show that under realistic experimental conditions, the amplitude of concentration fluctuations is small compared to the macroscopic concentration differences that generate them, the ratio being of the order of 1/10 4 if the gradient extends over lengths of the order of millimeters. For this reason, we argue that they are not likely to give rise to measurable effects in chemical reactions or in the growth of crystals (although the macroscopic concentration gradient itself can affect the reaction-diffusion behavior of the system [24,25]). …”

Section: Introductionmentioning

confidence: 99%

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

2016

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Diffusion in liquids is accompanied by nonequilibrium concentration fluctuations spanning all the length scales comprised between the microscopic scale a and the macroscopic size of the system, L. Up to now, theoretical and experimental investigations of nonequilibrium fluctuations have focused mostly on determining their mean-square amplitude as a function of the wave vector. In this work, we investigate the local properties of nonequilibrium fluctuations arising during a stationary diffusion process occurring in a binary liquid mixture in the presence of a uniform concentration gradient, ∇c 0 . We characterize the fluctuations by evaluating statistical features of the system, including the mean-square amplitude of fluctuations and the corrugation of the isoconcentration surfaces; we show that they depend on a single mesoscopic length scale l = √ aL representing the geometric average between the microscopic and macroscopic length scales. We find that the amplitude of the fluctuations is very small in practical cases and vanishes when the macroscopic length scale increases. The isoconcentration surfaces, or fronts of diffusion, have a self-affine structure with corrugation exponent H = 1/2. Ideally, the local fractal dimension of the fronts of diffusion would be D l = d − H , where d is the dimensionality of the space, while the global fractal dimension would be D g = d − 1. The transition between the local and global regimes occurs at a crossover length scale of the order of the microscopic length scale a. Therefore, notwithstanding the fact that the fronts of diffusion are corrugated, they appear flat at all the length scales probed by experiments, and they do not exhibit a fractal structure.

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Section: Introductionmentioning

confidence: 99%

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

2016

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“…Here we adopt the canonical form for the rate of chemical reactions [19,32]. Propensity density functions are expressed as [12]…”

Section: Generalized Law Of Mass Actionmentioning

confidence: 99%

“…Hence, our proposed algorithm combines discrete processes (CME for reactive processes) and continuous processes (FHD for transport processes); a similar idea has been used for the simulation of the Boltzmann equation [9][10][11]. The use of the CME enables us to correctly capture large fluctuations of composition, going beyond the Gaussian approximation inherent in the chemical Langevin equation (CLE) used in our prior work [12]. While our previous work on reaction-diffusion systems [4] also employed the CME, it was restricted to dilute solutions.…”

Section: Introductionmentioning

confidence: 99%

Fluctuating hydrodynamics of reactive liquid mixtures

Kim

Nonaka

Bell

et al. 2018

The Journal of Chemical Physics

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Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.

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“…Further work regarded fluctuations in the highly heterogeneous diffusive mixing of water and glycerol [91], the effect of confinement on the dynamics of fluctuations in a binary mixture [30], or the impact of giant fluctuations on the initial development of a doubly-diffusive gravitational instability in a ternary mixture [92,93]. The computational algorithms have further been extended to study giant nonequilibrium fluctuations in the presence of surface tension [94], chemical reactions [95], as well as electrostatic effects for electrolyte solutions [96]; the predictions made by the simulations have yet to be confirmed experimentally.…”

Section: Numerical Simulations Of Nonequilibrium Fluctuation Experimentsmentioning

confidence: 99%

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids

et al. 2016

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Abstract. Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q −4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the onset of fluctuations during transient diffusion. We envision to parallel these experiments with state of the art multi-scale simulations.

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Fluctuating hydrodynamics of multi-species reactive mixtures

Cited by 45 publications

References 133 publications

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

Fluctuating hydrodynamics of reactive liquid mixtures

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids

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