Motivated by applications in oil sands processing, numerical simulations of the combined flow of yield-stress (Bingham) liquids and solid particles in a mixing tank have been performed. The conditions were such that, generally, the flow systems were in a transitional regime, between laminar and developed turbulence. The fluid flow was simulated according to a lattice-Boltzmann scheme, with the yield stress being mimicked as a highly viscous fluid for low deformation rates. Particles were assumed to move under the influence of drag, gravity, and particle-wall and particle-particle collisions. Agitation formed a cavity (active volume) around the impeller, with the rest of the tank being virtually inactive. This mobilized the particles in the cavity. In their ability to suspend and mobilize particles, agitated Bingham liquids behave markedly different from Newtonian liquids.