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The leading-order far-field scattered flow produced by a particle in aparallel-wall channel under creeping flow conditions has a form of theparabolic velocity field driven by a 2D dipolar pressure distribution. We showthat in a system of hydrodynamically interacting particles, the pressuredipoles contribute to the macroscopic suspension flow in a similar way as theinduced electric dipoles contribute to the electrostatic displacement field.Using this result we derive macroscopic equations governing suspensiontransport under the action of a lateral force, a lateral torque or amacroscopic pressure gradient in the channel. The matrix of linear transportcoefficients in the constitutive relations linking the external forcing to theparticle and fluid fluxes satisfies the Onsager reciprocal relation. Thetransport coefficients are evaluated for square and hexagonal periodic arraysof fixed and freely suspended particles, and a simple approximation in aClausius-Mossotti form is proposed for the channel permeability coefficient. Wealso find explicit expressions for evaluating the periodic Green's functionsfor Stokes flow between two parallel walls.

An analysis of the far-field response to external forcing of a suspension in Stokes flow in a parallel-wall channel