A population balance-Monte Carlo method for particle coagulation in spatially inhomogeneous systems

Insight into the spatiotemporal evolution of particle size distribution (PSD) is very useful in many natural and engineering systems in which the multiphase fields are spatially inhomogeneous and complicated dynamic processes of particle population, e.g., coagulation between particles, occur with field-dependent rates. Traditional population balance modeling (PBM) is usually used to simulate spatially homogeneous dynamic processes, only obtaining the time evolution of PSD. In this paper, we presented an algorithm to predict the spatiotemporal evolution of PSD accounting for mutual coupling of particle population and hydrodynamics. The differentially-weighted Monte Carlo method for PBM is used to simulate coagulation behavior of particles in each grid that is considered to be spatially homogeneous, and the transport behavior of fluid and particles towards neighbor grids that are spatially inhomogeneous are described by general conservation equations of multiphase flows. The simulation strategy is based on the selection of a time step within which the fluid transport, the particle transport and the particle dynamics are uncoupled and then separately simulated. A limiting case of the coarse high-inertia particles whose motion is independent of surrounding fluid is chosen to validate the population balance-Monte Carlo (PBMC) method for the spatiotemporal evolution of PSD. The computational time is found to be less by a factor of 10 compared to the direct numerical simulation (DNS), yielding reasonably closer predictions of spatiotemporal particle size distributions.

► We propose an algorithm to couple population balance and Eulerian–Lagrangian model. ► The spatiotemporal evolution of particle size distribution function is predicted. ► The mutual coupling of the particle dynamics with the hydrodynamics is considered. ► The CFD–PBMC model yields reasonably closer prediction to Direct Numerical Simulation. ► The computational expense of CFD–PBMC is less by a factor of 10 than that of DNS.