Continuum random walk simulations of diffusion and reaction in catalyst particles

Drewry, H. P. G.; Seaton, Nigel A.

doi:10.1002/aic.690410415

Cited by 28 publications

(11 citation statements)

References 25 publications

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“…Ligand binding to cell surface receptors, 1,2 reactions on supported catalysts, 3 electric current through arrays of microelectrodes, 4 and water exchange in plants 5 are just a few from a long list of practical examples. Ligand binding to cell surface receptors, 1,2 reactions on supported catalysts, 3 electric current through arrays of microelectrodes, 4 and water exchange in plants 5 are just a few from a long list of practical examples.…”

Section: Introductionmentioning

confidence: 99%

Boundary homogenization for trapping by patchy surfaces

Berezhkovskii

Makhnovskii

Monine

et al. 2004

The Journal of Chemical Physics

136

171

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We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations. (c) 2004 American Institute of Physics.

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Section: Introductionmentioning

confidence: 99%

Boundary homogenization for trapping by patchy surfaces

Berezhkovskii

Makhnovskii

Monine

et al. 2004

The Journal of Chemical Physics

136

171

View full text Add to dashboard Cite

show abstract

“…A number of studies on porous media [9][10][11][12][13][14] involve the concept of mean survival time, i.e., the average travel time of a molecule in steady-state Brownian diffusion before colliding and reacting with the pore wall, under infinite surface reaction rate conditions. Some of these studies also involve the broader concept of survival probability, representing the fraction of molecules that survive ͑do not react͒ up to a certain time during the process; the survival probability has also been the focus of extensive research on diffusion-controlled reactions in nonporous environments.…”

Section: Introductionmentioning

confidence: 99%

Pore size distribution, survival probability, and relaxation time in random and ordered arrays of fibers

Tomadakis

Robertson

2003

The Journal of Chemical Physics

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We present a random walk based investigation of the pore size probability distribution and its moments, the survival probability and mean survival time, and the principal relaxation time, for random and ordered arrays of cylindrical fibers of various orientation distributions. The dimensionless mean survival time, principal relaxation time, mean pore size, and mean square pore size are found to increase with porosity, remain practically independent of the directionality of random fiber beds, and attain lower values for ordered arrays. Wide pore size distributions are obtained for random fiber structures and relatively narrow for ordered square arrays, all in very good agreement with theoretically predicted limiting values. Analytical results derived for the pore size probability and its lower moments for square arrays of fibers practically coincide with the corresponding simulation results. Earlier variational bounds on the mean survival time and principal relaxation time are obeyed by our numerical results in all cases, and are found to be quite sharp up to very high porosities. Dimensionless groups representing the deviation of such bounds from our simulation results vary in practically the same range as the corresponding values reported earlier for beds of spherical particles. A universal scaling expression of the literature relating the mean survival time to the mean pore size ͓S. Torquato and C. L. Y. Yeong, J. Chem. Phys. 106, 8814 ͑1997͔͒ agrees very well with our results for all types of fiber structures, thus validated for the first time for anisotropic porous media.

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“…In mass transfer, the same problem could describe the concentration profile c(x, y) of a chemical of diffusivity D produced by a uniform volumetric reaction rate R v in a catalyst rod ( Fig. 2(9)) [60].…”

Section: Heat and Mass Transfermentioning

confidence: 99%

“…The first passage time (or "escape time" or "survival time") describes many phenomena in science and engineering, such as the mean reaction time in Smoluchowski's theory of diffusion-controlled homogeneous reactions [30,32,63]. The two-dimensional case considered here could describe adsorbed reactants on a surface as in heterogeneous catalysis [60,64] (Fig. 2(12)).…”

Section: E Diffusion-controlled Reactionsmentioning

confidence: 99%

Exact solutions and physical analogies for unidirectional flows

Bazant¹

2016

Phys. Rev. Fluids

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Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here, the literature is unified and extended by identifying seventeen physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with non-constant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.

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Continuum random walk simulations of diffusion and reaction in catalyst particles

Abstract: To predict the effect of pore structure on the

Cited by 28 publications

References 25 publications

Boundary homogenization for trapping by patchy surfaces

Boundary homogenization for trapping by patchy surfaces

Pore size distribution, survival probability, and relaxation time in random and ordered arrays of fibers

Exact solutions and physical analogies for unidirectional flows

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