Image representation of a spherical particle near a hard wall

Cichocki, B.; Jones, R. B.

doi:10.1016/s0378-4371(98)00267-2

Cited by 121 publications

(139 citation statements)

References 29 publications

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“…(2), it follows that M xθ is positive definite, which is then also true for the matrix C. As the diagonal elements of M xθ are significantly larger than the off-diagonal element [33,38], one easily finds that trC is negative. Therefore, C has two negative eigenvalues, which we denote in the following by λ ± .…”

Section: Definition Of the Dynamic States Of Motion A Experimenmentioning

confidence: 85%

“…In order to obtain accurate results when simulating the motion of the sphere it is essential to properly calculate the mobility matrix M and the shear force F S . In our simulations we use a numerical method described by Jones et al [33,38] which allows to accurately calculate the components of the mobility matrix for a single sphere above a wall for arbitrary sphere wall distances. The values obtained by this method agree very well with the classical results given for some tabulated height values by Goldman et al [39].…”

Section: A Stokesian Dynamicsmentioning

confidence: 99%

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Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our We also investigate the effect of non-molecular parameters. In particular, we find that an increase in viscosity of the medium leads to a characteristic expansion of the region of stable rolling to the expense of the region of firm adhesion, but not to the expense of the regions of free or transient motion. Our results can be used in an inverse approach to determine single bond parameters from flow chamber data on rolling adhesion.

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Section: Definition Of the Dynamic States Of Motion A Experimenmentioning

confidence: 85%

Section: A Stokesian Dynamicsmentioning

confidence: 99%

Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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“…The single wall contributions can be integrated analytically [39,40]. Moreover, as shown in [29], the correction term δΨ(k) is easier to integrate numerically than the original highly oscillatory integrand Ψ(k).…”

Section: F Numerical Implementationmentioning

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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“…The main idea in this scheme is based on the image representation of a sphere near a hard wall proposed by Cichocki and Jones in Ref. [24]. The latter is a generalization of the result for Stokeslet derived by Blake [25].…”

Section: Virial Expansionmentioning

confidence: 99%

The intensity correlation function in evanescent wave scattering

Cichocki

Wajnryb

Bławzdziewicz

et al. 2010

The Journal of Chemical Physics

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As a first step towards the interpretation of dynamic light scattering with evanescent illumination, in order to probe dynamics near walls, we develop a theory for the initial slope of the intensity auto-correlation function for suspensions of interacting spheres. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions 1 between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory, and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments, and to develop an understanding of near-interface dynamics, at high colloid concentrations.

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Image representation of a spherical particle near a hard wall

Cited by 121 publications

References 29 publications

Dynamic states of cells adhering in shear flow: From slipping to rolling

Dynamic states of cells adhering in shear flow: From slipping to rolling

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

The intensity correlation function in evanescent wave scattering

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