Resistance functions for two unequal spheres in linear flow at low Reynolds number with the Navier slip boundary condition

2013/02/03 by Kengo Ichiki, Ichiki, Kengo, Alexander E. Kobryn +3
Chemical Engineering · Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Rheology and Fluid Dynamics Studies #cond-mat.stat-mech #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1302.0461

arxiv created 2013/02/03 · arxiv updated 2013/02/05

Abstract

Resistance functions for two spherical particles with the Navier slip boundary condition in general linear flows, including rigid translation, rigid rotation, and strain, at low Reynolds number are derived by the method of reflections as well as twin multipole expansions. In the solutions, particle radii and slip lengths can be chosen independently. In the course of calculations, single-sphere problem with the slip boundary condition is solved by Lamb's general solution and the expression of multipole expansions, and Faxén's laws of force, torque, and stresslet for slip particle are also derived. The solutions of two-body problem are confirmed to recover the existing results in the no-slip limit and for the case of equal scaled slip lengths.

Related

• Generating, from scratch, the near-field asymptotic forms of scalar resistance functions for two unequal rigid spheres in low Reynolds number flow
• Exact Solution for Non-Newtonian Fluid Flow Beyond a Contaminated Fluid Sphere
• Newton's problem of minimal resistance under the single-impact assumption
• Impact of Spin Slip Conditions on the Axisymmetric Rotation of a Spherical Particle in a Couple Stress Fluid Within a Cavity
• Slow linear shear flow past discrete particles adhered to a plane wall