TY - JOUR

T1 - Multiscale modeling of a free-radical emulsion polymerization process

T2 - Numerical approximation by the Finite Element Method

AU - Urrea-Quintero, Jorge Humberto

AU - Marino, Michele

AU - Hernandez, Hugo

AU - Ochoa, Silvia

N1 - Funding Information: We thank the anonymous reviewers of this work for their valuable comments and suggestions that helped improving the quality of this manuscript. Jorge-Humberto Urrea-Quintero gratefully acknowledges COLCIENCIAS for the financial support via the Doctoral Scholarship 727–2015 granted. Lkewise, the gratitude is extended to the Institute of Continuum Mechanics - IKM at Leibniz Universität Hannover, Germany, for hosting him as visiting researcher. Particularly, to Prof. Dr.-Ing. habil. Dr. h.c. mult. Dr.-Ing. E. h. Peter Wriggers for the financial support provided during the internship period at IKM. M. Marino acknowledges that this work has been carried out within the framework of the SMART BIOTECS alliance between the Technical University of Braunschweig and the Leibniz University of Hannover (Ministry of Science and Culture of Lower Saxony, Germany) and to the program “Rita Levi Montalcini” for young researchers (Ministry of Education, University and Research, Italy).

PY - 2020/9/2

Y1 - 2020/9/2

N2 - 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.

AB - 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.

KW - Finite Element Method

KW - Fokker-Planck equation

KW - Free-radical polymerization

KW - kMC

KW - PDE/ODEs-kMC multiscale systems

KW - Statistical modeling

UR - http://www.scopus.com/inward/record.url?scp=85083004179&partnerID=8YFLogxK

U2 - 10.1016/j.compchemeng.2020.106974

DO - 10.1016/j.compchemeng.2020.106974

M3 - Article

AN - SCOPUS:85083004179

VL - 140

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

M1 - 106974

ER -