A differentially weighted Monte Carlo method for two-component coagulation

The direct simulation Monte Carlo (DSMC) method for population balance modeling is capable of retaining the history of each simulation particle and is thus able to deal with multivariate properties in a simple and straightforward manner. As opposed to conventional DSMC approaches that track equally weighted simulation particles, a differentially weighted Monte Carlo method is extended to simulate two-component coagulation processes and is thereby able to simulate the micromixing of the components. A new feature of the method for this bivariate population balance modeling is that it is possible to specify how the simulation particles are distributed over the compositional axis. This allows us to obtain information about particles in those regions of the size and composition distribution functions where the non-weighted MC methods place insufficient simulation particles to obtain an inaccurate solution. The new feature results in lower statistical noise for simulating two-component coagulation, which is validated by using two-component coagulation cases for which analytical solutions exist (a discrete process with sum kernel for initial monodisperse populations and a process with constant kernel for initial polydisperse populations).