Shear-induced migration in concentrated suspensions: particle mass conservation, contact pressure and jamming
Résumé
A two-velocity biphasic model is presented to describe particle migration in mono-disperse suspensions of neutrally buoyant particles. Compared to previous migration models, introduction of a second velocity variable ensures rigorous mass conservation for the particle phase. In addition, the upper bound on particle volume fraction (jamming limit) is rigorously imposed through a non-smooth complementarity condition and the introduction of a particle contact pressure. The model is applied to an axisymmetric Poiseuille flow and solved using a finite-element method. For that purpose, a specific, fully implicit algorithm based on non-smooth optimisation tools is developed and validated. Preliminary comparisons with experimental data from the literature show promising agreement. In particular, the model properly captures the formation of an inner plug region, in which the material is saturated and jammed.
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