A non-local extension of the Phillips model for shear induced particle migration
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We present a simple and natural extension of Phillips’ model (Phillips in Phys Fluids A 4(1):30–40, 1992) for shear induced particle migration in concentrated suspensions. It is based on considering an effective deformation rate as it is experienced by a solid particle of finite size. In this way the solid fraction does not converge anymore to the maximum packing in the centre of Poiseuille-like flows where the deformation rate vanishes, and the steady state concentration profile becomes dependent on the particle diameter a. In addition, the migration rate in the extended model scales with an, where 2 < n < 3 in contrast to the strict a2-scaling of the original Phillips-model.
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