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Colloidal suspensions have a rich rheology and can exhibit shear-thinning aswell as shear-thickening. Numerical simulations recently suggested thatshear-thickening may be attributed to the inertia of the colloids, besides thehydrodynamic interactions between them. Here, we consider the ideal limit of adense bath of soft colloids following an underdamped Langevin dynamics. We usea mean-field equation for the colloidal density to get an analytical expressionof the drag force felt by a probe pulled at constant velocity through thesuspension. Our results show that inertia can indeed induce shear-thickening byallowing density waves to propagate through the suspension.

Mean-field microrheology of a very soft colloidal suspension: inertia induces shear-thickening