In this paper, we consider the three dimensional flow of granular materials and a viscous fluid in a channel. We use Mixture Theory to treat this problem as a two-component system : One component is the solid particles (granular materials), such as sand, coal particles or red blood cells; the solid particles are modeled as a generalized Reiner-Rivlin type fluid derived by Massoudi , which not only considers the effects of volume fraction but also has a viscosity which is shear rate dependent. The other component, the host fluid, is assumed to behave as a linear viscous fluid, such as water, oil or plasma. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the hindrance function is suggested. For studying this two-component system numerically, a three dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data  show good agreement.
Channel Flow of a Mixture of Granular Materials and a Fluid
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Wu, W, Aubry, N, & Massoudi, M. "Channel Flow of a Mixture of Granular Materials and a Fluid." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 7A: Fluids Engineering Systems and Technologies. San Diego, California, USA. November 15–21, 2013. V07AT08A033. ASME. https://doi.org/10.1115/IMECE2013-65385
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