Slow linear shear flow past discrete particles adhered to a plane wall

Linear shear flow bounded by a plane wall is an idealization that occurs in microfluidic devices and many other applications. Perfect plane approximation neglects surface irregularities and discrete particles adsorbed at the surface. Here we study the disturbance to the linear shear flow due to the particle(s) rigidly attached to the surface. We first revisit the exact solution of O'Neill for a spherical particle in contact with an infinite plane boundary. While the original paper contains multiple typos and provides very few details of the derivation, we present detailed solution accompanied by an alternative and simpler derivation of the viscous force and the torque exerted on the particle. We further study the universal far-field behavior of the flow due to an arbitrary particle adhered to the surface, and demonstrate that it is controlled by the stress moment of magnitude depending on particle's volume and shape. Using the revised O'Neill solution, we compute the stress moment for a spherical particle. Using the far-field asymptotic form of the flow we estimate the net flow due to uniform and sparse layer of discrete adsorbates by superposition and demonstrate that it does not decay away from the plane.