Stochastic descriptions of the dynamics of interacting brownian particles

Tough, R.J.A.; Pusey, P. N.; Lekkerkerker, H. N. W.; Broeck, C. Van den

doi:10.1080/00268978600102291

Cited by 60 publications

(21 citation statements)

References 29 publications

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“…The approach to analysis of the microstructure of flowing Brownian suspensions was pioneered by Batchelor [1]. This approach considers directly the probability distribution function governing the configurations in the suspension, and this essentially statistical mechanical approach develops the Smoluchowski partial differential equation (PDE) analysis of the pair correlation function, which is statistically equivalent to the Langevin stochastic PDE [2,3], upon which discreteparticle simulations tools used in this work are based. The Smoluchowski approach has proven useful for description of the steady shear flow of hard-sphere suspensions in the dilute limit at low Pe [4][5][6][7] and at high Pe [8].…”

Section: Introductionmentioning

confidence: 99%

Unsteady shear flows of colloidal hard-sphere suspensions by dynamic simulation

Marenne¹,

Morris²,

Foss³

et al. 2017

Journal of Rheology

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The rheology during the start-up and cessation of simple shear flow has been investigated for near hard-sphere colloidal suspensions. Simulations augmented by theoretical analysis are used to determine how the non-Newtonian stress development and relaxation depend on the microstructure. Accelerated Stokesian dynamics (ASD) and Brownian dynamics (BD) simulations are used for 0.05 Pe 500 in concentrated freely flowing suspensions; the P eclet number defining the ratio of shear to thermal motion is Pe ¼ 3pg_ ca 3 =kT with g the suspending fluid viscosity, _ c the shear rate, and kT the thermal energy. Theoretical predictions based on the Smoluchowski equation for dilute suspensions are made, and these are primarily used for comparison with results from BD simulations in which hydrodynamic interactions are neglected. For suspensions with hydrodynamics, simulations by ASD are used to probe start-up and flow cessation over a large range of Pe; these studies focus on solid volume fraction / ¼ 0:4, with more limited examinations at other /. The use of both BD and ASD simulations allows us to discriminate hydrodynamic interaction effects on the suspension rheology. The Brownian stresses computed by either method exhibit overshoots of their steady state value during the start-up of shear flow. The overshoots occur at strain amplitudes which depend on Pe, and the overshoot is described by a model based on extension of the concept of cage-breaking from glass dynamics. Results from the relaxation of a sheared suspension show that the distortion of the pair distribution function from its equilibrium form has a fast radial relaxation and a slow angular relaxation. The various rheometric functions (relative viscosity; first and second normal stress differences) are found to respond on different timescales, reflecting their different dependences on the flow-induced structure. A re-examination of steady shear flow allows us to find normal stress differences which tend properly toward zero at small Pe, unlike prior work; the discrepancy is found to be due to finite size scaling, as small simulations used in prior work resulted in excessively large normal stress responses at small Pe. V

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Section: Introductionmentioning

confidence: 99%

Unsteady shear flows of colloidal hard-sphere suspensions by dynamic simulation

Marenne¹,

Morris²,

Foss³

et al. 2017

Journal of Rheology

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“…Both forms of diffusion have been studied in a wide variety of physical contexts, including continuum [3][4][5][6][7][8][9][10] and lattice [11][12][13] models. Exact analytical results for the diffusion coefficient of interacting particles are however typically limited to a perturbation expansion, for example in the density of the particles.…”

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confidence: 99%

Diffusion of Interacting Particles in Discrete Geometries

et al. 2013

Self Cite

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We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical expressions are obtained in the absence of correlations, showing that the self-diffusion can exceed the transport diffusion if the free-energy function is concave. The effect of correlations is elucidated by comparison with numerical results. Quantitative agreement is obtained with recent experimental data for diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8.PACS numbers: 05.40. Jc, 05.60.Cd, 66.30.Pa The equality of inertial and gravitational mass played a crucial role in Einstein's discovery of general relativity. Similarly, Einstein's work on Brownian motion is based on the identity of the transport-and self-diffusion coefficients for noninteracting particles [1], leading eventually through Perrin's experiments [2] to the vindication of the atomic hypothesis. In general, however, diffusion of interacting particles is described by two different coefficients. The transport-diffusion coefficient D t quantifies the particle flux j appearing in response to a concentration gradient dc/dx:The self-diffusion coefficient D s describes the mean squared displacement of a single particle in a suspension of identical particles at equilibrium: x 2 (t) ∝ D s t. An alternative way for measuring this coefficient is by labeling, in this system at equilibrium, a subset of these particles (denoted by * ) in a way to create a concentration gradient dc * /dx of labeled particles under overall equilibrium conditions. The resulting flux j * of these particles reads:Both forms of diffusion have been studied in a wide variety of physical contexts, including continuum [3][4][5][6][7][8][9][10] and lattice [11][12][13] models. Exact analytical results for the diffusion coefficient of interacting particles are however typically limited to a perturbation expansion, for example in the density of the particles. The effect of correlations is notoriously difficult to evaluate in continuum models, especially when hydrodynamic interactions come into play, while they can play a dominant role, for example, in lattice models with particle exclusion constraints.In this Letter, we introduce a physically relevant model, for which exact analytical results can be obtained at all values of the concentration and for any interaction. It describes the diffusive hopping of interacting particles in a compartmentalized system, see Fig. 1 for a schematic representation. It is assumed that the relaxation inside each cavity is fast enough to establish a local equilibrium, described by a free-energy function characterizing the confinement and interaction of the particles. This model describes diffusion in confined geometries [14]. Of particular interest are microporous materials [15,16] [21][22][23][24][25][26], it was found that the self-diffusion could exceed the transport diffusion, a result confirmed by ...

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“…(8) in the text, give the correct form for the MSD1 and the best estimation for the mean square displacements. The SE approach gives also the best estimation for the energy.…”

Section: Numerical Calculationsmentioning

confidence: 99%

On Algorithms for Brownian Dynamics Computer Simulations

Brańka¹

1998

CMST

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Several Brownian Dynamics numerical schemes for treating stochastic differential equations at the position Langevin level are analyzed from the point of view of their algorithmic efficiency. The algorithms are tested using model colloidal fluid of particles interacting via the Yukawa potential. Limitations in the conventional Brownian Dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical and static quantities can be achieved with an algorithm based on the stochastic expansion and second-order stochastic Runge-Kutta algorithms. Mutual merits of the second-order algorithms are discussed.

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Stochastic descriptions of the dynamics of interacting brownian particles

Cited by 60 publications

References 29 publications

Unsteady shear flows of colloidal hard-sphere suspensions by dynamic simulation

Unsteady shear flows of colloidal hard-sphere suspensions by dynamic simulation

Diffusion of Interacting Particles in Discrete Geometries

On Algorithms for Brownian Dynamics Computer Simulations

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