2008/04/30 by Jerzy Bławzdziewicz, J. Blawzdziewicz, Eligiusz Wajnryb +1 · 21 citations
Chemistry · Engineering · Materials Science · Physics and Astronomy · #Classical mechanics #Electrostatics and Colloid Interactions #Flow (mathematics) #Material Dynamics and Properties #Mechanics #Microfluidic and Bio-sensing Technologies #Open-channel flow #Physics #Pressure gradient #Stokes flow #cond-mat.soft
paper · pdf · doi:10.1063/1.2976306
published in Physics of Fluids 20(9) (American Institute of Physics) · 23 pages, 12 figures
arxiv created 2008/08/13 · openalex publication_date 2008/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The leading-order far-field scattered flow produced by a particle in a parallel-wall channel under creeping-flow conditions has a form of the parabolic velocity field driven by a two-dimensional dipolar pressure distribution. We show that in a system of hydrodynamically interacting particles, the pressure dipoles contribute to the macroscopic suspension flow in a similar way as the induced electric dipoles contribute to the electrostatic displacement field. Using this result we derive macroscopic equations governing suspension transport under the action of a lateral force, a lateral torque, or a macroscopic pressure gradient in the channel. The matrix of linear transport coefficients in the constitutive relations linking the external forcing to the particle and fluid fluxes satisfies the Onsager reciprocal relation. The transport coefficients are evaluated for square and hexagonal periodic arrays of fixed and freely suspended particles, and a simple approximation in a Clausius–Mossotti form is proposed for the channel permeability coefficient. We also find explicit expressions for evaluating the periodic Green’s functions for the Stokes flow between two parallel walls.