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