Multiscale modeling of a free-radical emulsion polymerization process: Numerical approximation by the Finite Element Method

Abstract

A multiscale modeling description of free-radical polymerization processes is presented. The polymerization process is described at the macroscale by coupling the Fokker-Planck Equation (FPE) for the particle size distribution (PSD) prediction at the mesoscale with a kinetic Monte Carlo (kMC) simulation at the microscale. The finite element method is adopted to solve the mesoscopic scale to capture the nonlinear evolution of the PSD, successfully facing challenges related to accuracy and computational cost in the FPE numerical solution. Additionally, the proposed model captures the evolution of the average number of free-radicals and secondary nucleation rate at the microscopic level. The control of the secondary nucleation rate is in fact critical to satisfactorily obtain high quality structured polymer particles. Finally, a closed-form model is developed at the microscopic scale to handle the curse of dimensionality. Simulations to evaluate the capabilities of the proposed numerical scheme and sensitivity analyses with respect to the system inputs and uncertainties in the initial condition of the PSD are performed.