The forces and couples acting on two nearly touching spheres in low-Reynolds-number flow

Jeffrey, David J.; Onishi, Yoshimoto

doi:10.1007/bf00952109

Cited by 67 publications

(36 citation statements)

References 6 publications

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“…Although the lubrication argument is obviously valid for the nondeforming rigid objects, its validity for the deformable surfaces has not been proved yet. Furthermore, most of the precedent studies have considered the hydrodynamic interaction either between two rigid spheres or between two deformable drops, but have not considered the interaction between two coated spheres yet (6,11,16). These are the primary thrust of the present study.…”

Section: Introductionmentioning

confidence: 96%

“…Meanwhile, the hydrodynamic contribution to the interaction forces between two spheres coated with thin deformable liquid films must be considered to estimate the net molecular interaction forces. Since the molecular interaction forces begin to act at a very close proximate, the hydrodynamic force can be calculated by the lubrication theory (16). When the molecular force between two interacting spheres is measured, SFA uses, in fact, two crossing cylindrical surfaces of an identical size instead of two spherical surfaces (14).…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic Interaction between Spheres Coated with Deformable Thin Liquid Films

Yang

Leal

Kim

2002

Journal of Colloid and Interface Science

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Hydrodynamic Interaction between Spheres Coated with Deformable Thin Liquid Films

Yang

Leal

Kim

2002

Journal of Colloid and Interface Science

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“…However, most of these methods encounter severe numerical difficulties when particle separations become small. When the interstitial gap between particles decreases, the analytical solutions for the interstitial traction become nearly singular resulting in extremely stiff differential systems [5][6][7]. In these cases, interstitial tractions are typically underpredicted resulting in the relative particle velocities being overpredicted by most numerical, mesoscopic methods [8].…”

Section: Introductionmentioning

confidence: 99%

Accurate treatment of lubrication forces between rigid spheres in viscous fluids using a traction-corrected boundary element method

Zhu

Ingber

2009

Engineering Analysis with Boundary Elements

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“…For a sphere translating towards a stationary sphere, Jeffrey (1982) combined the work of Cooley and O'Neill (1969) with numerical calculations and deduced a brief formula proportional to ε −1 for normal force acting on the moving sphere. For the other three motions, Jeffrey and Onishi (1984) extended the work of O'Neill and Majumdar (1970) and obtained asymptotic expressions of the forces and torques acting on the spheres. Above all, the formulae were obtained based on the assumption of Stokes flow.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

Zhou

Jin

Tian

et al. 2017

International Journal of Multiphase Flow

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: Models for hydrodynamic force and torque Finite particle Reynolds number Near-wall effect Particle-resolved simulation Sub-grid scale model Eulerian-Lagrangian simulation a b s t r a c t This research work is aimed at proposing models for the hydrodynamic force and torque experienced by a spherical particle moving near a solid wall in a viscous fluid at finite particle Reynolds numbers. Conventional lubrication theory was developed based on the theory of Stokes flow around the particle at vanishing particle Reynolds number. In order to account for the effects of finite particle Reynolds number on the models for hydrodynamic force and torque near a wall, we use four types of simple motions at different particle Reynolds numbers. Using the lattice Boltzmann method and considering the moving boundary conditions, we fully resolve the flow field near the particle and obtain the models for hydrodynamic force and torque as functions of particle Reynolds number and the dimensionless gap between the particle and the wall. The resolution is up to 50 grids per particle diameter. After comparing numerical results of the coefficients with conventional results based on Stokes flow, we propose new models for hydrodynamic force and torque at different particle Reynolds numbers. It is shown that the particle Reynolds number has a significant impact on the models for hydrodynamic force and torque. Furthermore, the models are validated against general motions of a particle and available modeling results from literature. The proposed models could be used as sub-grid scale models where the flows between particle and wall can not be fully resolved, or be used in Lagrangian simulations of particle-laden flows when particles are close to a wall instead of the currently used models for an isolated particle.

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The forces and couples acting on two nearly touching spheres in low-Reynolds-number flow

Cited by 67 publications

References 6 publications

Hydrodynamic Interaction between Spheres Coated with Deformable Thin Liquid Films

Hydrodynamic Interaction between Spheres Coated with Deformable Thin Liquid Films

Accurate treatment of lubrication forces between rigid spheres in viscous fluids using a traction-corrected boundary element method

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

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