We introduce a coupled smoothed particle hydrodynamics-discrete element method (SPH-DEM) to describe the two-way interaction between the two phases of a solid-liquid flow. To validate the model, we simulated two test problems: a solid-liquid counter-flow in a periodic box and particle settlement. The simulations correctly predicted the dynamics, and the results showed good agreement with the theory. The developed model was then applied to simulate the slurry coagulation process to examine the coagulation efficiency. When the rotational speed exceeded the normal range, the coagulation rate decreased with time, even though the rate was high during the early stage due to the size separation effect of the particles. Given this result, overly fast stirring appears to have an adverse effect on the coagulation efficiency. The model is applicable to the design of various types of solid-liquid flows.