Confined Brownian motion

Faucheux, Luc P.; Libchaber, Albert

doi:10.1103/physreve.49.5158

Cited by 190 publications

(192 citation statements)

References 11 publications

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“…Indeed, hydrodynamic interactions with the bounding surface have to be accounted for if the particles are moving in a liquid, and the diffusion coefficient is not expected to be constant anymore. Instead, theoretical [19] and experimental [20,21,22] works have revealed that the mobility is in fact a function of position -or, more precisely, of the distance to the surface. In addition, the diffusion coefficient may also be time-dependent when the bounding surface is soft, like a liquid-liquid interface or a fluid membrane.…”

Section: Resultsmentioning

confidence: 99%

A note on confined diffusion

Bickel

2007

Physica A: Statistical Mechanics and its Applications

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Abstract.The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion inside a sphere. In both cases, the short-time behaviour of the mean square displacement is obtained.

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Section: Resultsmentioning

confidence: 99%

A note on confined diffusion

Bickel

2007

Physica A: Statistical Mechanics and its Applications

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“…Condition (4) can be obtained by applying to immobile particles the forces and torques opposite to those given by equation (3). Thus, the resistance and mobility coefficients ζ and ν satisfy the following relation…”

Section: Particles In Parabolic Flowmentioning

confidence: 99%

“…A recent, considerable interest in particle motion in confined geometries has been stimulated by development of new experimental techniques [2,3,4,5,6,7] and by emerging applications, such as the microfluidic devices [8] and technologies for production of microstructured materials by a self-assembly process [9,10].…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls

Bhattacharya¹,

Bławzdziewicz²,

Wajnryb³

2006

Physics of Fluids

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We study hydrodynamic interactions of spherical particles in incident Poiseuille flow in a channel with infinite planar walls. The particles are suspended in a Newtonian fluid, and creeping-flow conditions are assumed. Numerical results, obtained using our highly accurate Cartesian-representation algorithm [Physica A xxx, xx, 2005], are presented for a single sphere, two spheres, and arrays of many spheres. We consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall. We find that the pair hydrodynamic interactions in this wall-bounded system have a complex dependence on the lateral interparticle distance due to the combined effects of the dissipation in the gap between the particle surfaces and the backflow associated with the presence of the walls. For immobile particle pairs we have examined the crossover between several far-field asymptotic regimes corresponding to different relations between the particle separation and the distances of the particles from the walls. We have also shown that the cumulative effect of the far-field flow substantially influences the force distribution in arrays of immobile spheres. Therefore, the far-field contributions must be included in any reliable algorithm for evaluating many-particle hydrodynamic interactions in the parallel-wall geometry.

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“…4,5 The diffusion of a sphere in confined geometries has been extensively studied through experiments. Several geometries have been considered, such as a single planar wall, [6][7][8][9] two parallel walls, [10][11][12] and a cylindrical cavity. 13 The results clearly show that the dependence of the translational diffusion coefficients on particle position reflects the hydrodynamic interactions that the particle experiences under confinement, for which theoretical predictions are well established.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

Corato

Greco

D’Avino

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested in PHYSICS 142, 194901 (2015) Hydrodynamics and Brownian motions of a spheroid near a rigid wall In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement. C 2015 AIP Publishing LLC. [http://dx

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Confined Brownian motion

Cited by 190 publications

References 11 publications

A note on confined diffusion

A note on confined diffusion

Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

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