Batch rotor-stator mixers are widely employed on the bench scale in the chemical and pharmaceutical process industries to demonstrate a variety of emulsion and dispersion processes, that must be scaled to geometrically or dynamically (continuous rather than batch) different equipment on the pilot scale. When the process fluid dynamics plays a significant role, a reasonable approach is to simulate both the bench and pilot scale flow field and deformation rate phenomena and match these on both scales to extrapolate bench scale data with respect to the number of mill head passes and shear rate history.

To this end, we are simulating the flow field in a Silverson L4R batch rotor-stator mixer with the milling head located off-axis in a 2 liter vessel. Since water is the working fluid, the flow is turbulent. We use a RANS formalism with a k - epsilon turbulence model and wall functions. Due to the importance of the rotor-stator interaction, a sliding mesh CFD technique must be employed. While time periodic convergence is relatively rapid close to the mill head, the pumping capacity is low. As a result, it is not possible with current computational resources to compute until a fully converged solution is reached throughout the entire tank. This is of little consequence if the goal is to understand rotor-stator interactions. However, it is a major barrier to allowing one way coupled particle tracking throughout the vessel, to determine the shear history and circulation time distribution of tracked particles.

At a moderate distance from the mixing head the effect of rotor-stator interactions is not felt, so the flow appears steady in time. A time periodic region, centered on the mill head can be defined by interrogating a sliding mesh solution for the entire tank. Beyond this region, the flow field is well described by an MRF simulation technique. As a result, the following hybrid technique can be used to significantly reduce the computational expense of particle tracking simulations. Based on mixing head geometry/placement, vessel size/geometry, rotor speed and physical properties, the largest possible time periodic region can be defined. We then begin with an accurate, fully converged MRF solution, which always holds beyond the time periodic (outer) region and provides boundary conditions for a sliding mesh solution within the time periodic (inner) region. The sliding mesh algorithm is then begun for the inner region. This inner region is relatively small in volume, so convergence is rapid. The inner and outer solutions are then super imposed to provide a seamless time dependent velocity field for particle tracking trials. A single, repeatable period (in this case 90 degrees due to 4 rotor blades) of this simulation can be continually repeated as input to a fast particle tracking algorithm. Our previously reported computationally efficient tracking algorithm, which accounts for all of the forces acting on particles, can then calculate the trajectories of thousands of particles for numerous impeller revolutions to yield statistics for circulation time distribution and shear rate history.

We will demonstrate the hybrid velocity field CFD technique and particle tracking algorithm, and report the results of our simulations for several different cases. We will discuss our future plans in the context of our progress to date and what can realistically be accomplished in the short term.