Film flow of a suspension down an inclined plane

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Abstract
A method is developed for simulating the film flow of a suspension of rigid particles with arbitrary shapes down an inclined plane in the limit of vanishing Reynolds number. The problem is formulated in terms of a system of integral equations of the first and second kind for the free-surface velocity and the traction distribution along the particle surfaces involving the a priori unknown particle linear velocity of translation and angular velocity of rotation about designated centres. The problem statement is completed by introducing scalar constraints that specify the force and torque exerted on the individual particles. A boundary-element method is implemented for solving the governing equations for the case of a two-dimensional periodic suspension. The system of linear equations arising from numerical discretization is solved using a preconditioner based on a particle-cluster iterative method recently developed by Pozrikidis (2000 Engng Analysis Bound. Elem. 25, 19-30). Numerical investigations show that the generalized minimal residual (GMRES) method with this preconditioner is significantly more efficient than the plain GMRES method used routinely in boundary-element implementations. Extensive numerical simulations for solitary particles and random suspensions illustrate the effect of the particle shape, size and aspect ratio in semi-finite shear flow, and the effect of free-surface deformability in film flow.

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