The “laminar” shear flow of a particle-fluid mixture is studied using the two-fluid model, which is based on equations of conservation of mass and momentum for each material. The equations are applied to plane parallel flow, where the equations or mixture axial momentum and an equation for the concentration across the channel are derived. An asymptotic solution to the equations is derived which shows that the particles move to the center of the channel, forming a core which does not shear. The core is surrounded by clear fluid layers where all the shear occurs.

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