Summary
A set of linear partial differential equations governing particle/fluid two phase parallel flows is developed based on a stress sharing continuum model. The equations are solved in closed form for parallel plate and circular ducts. Some interesting features of the solutions are that the fluid phase leads the particle phase in an average sense for horizontal flows, the transition from upward average relative velocity to downward average relative velocity occurs at neutral buoyancy in vertical flows with no particle/wall interactions, the average relative velocity is downward for upward flows of negatively buoyant suspensions, and that wall boundary layers are produced by particle/wall interactions.
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Vellanki, N.S., Peddieson, J. & Munukutla, S. Application of a stress sharing model to simulation of particle/fluid parallel flow. Acta Mechanica 181, 169–184 (2006). https://doi.org/10.1007/s00707-005-0294-3
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DOI: https://doi.org/10.1007/s00707-005-0294-3