Lagrangian–Lagrangian simulations of solid–liquid flows in a bead mill

Solid–fluid multiphase flows are often encountered in chemical engineering operations, such as bead milling, slurry transport, and mixing. Numerical simulation is a promising approach for the design and investigation of operational conditions. In previous studies, an Eulerian–Lagrangian coupling method was developed for solid–liquid flows. However, it is difficult to apply this method to moving boundary problems because of the excessive calculation costs due to adaptive mesh or sliding mesh. To solve the difficulty, a Lagrangian–Lagrangian coupling method has been developed, which couples the Discrete Element Method (DEM) for the solid phase and the Moving Particle Semi-Implicit (MPS) method for the fluid phase. It can successfully calculate solid–fluid flows and has been validated, although it has been applied only to two-dimensional systems. In the present study, we develop a three-dimensional DEM–MPS method and apply it to bead mill systems, and show the effectiveness of the method. The simulation results, namely, the solid particle distribution and velocity are compared with experimental results and we thus demonstrate the validity of the method.