The numerical analysis of particle-size distribution of clusters in shear flow at one-dimensional closed system and three-dimensional open system

Abstract

Aimed at optimizing the resin-molding process, a method for numerically analyzing aggregation and dispersion behavior of the filler in resin composite was proposed. The flow of a resin composite during molding was calculated by using computational fluid dynamics (CFD), and particle-size distribution (PSD) of the cluster in each computational domain of the CFD model was estimated by solving the population balance equation (PBE). The proposed numerical-analysis method is based on the thixotropy model of Usui et al. In the thixotropy model, PSD is calculated by taking into account the aggregation and dispersion rate of the cluster by Brownian coagulation, shear coagulation, and shear breakage. Shear-breakage rate of the cluster is evaluated by solving the energy balance of bonding energy of the primary particles cut at the breakage and the drag applied to the cluster by the flow of the fluid. The composite viscosity was calculated using Krieger and Dougherty’s model based on apparent-solid-volume fraction estimated from the calculated PSD. To solve the PBE at low calculation cost, it was discretized using the fixed-pivot technique of Kumar and Ramkrishna. The proposed method was incorporated into the general-purpose CFD software FLOW-3D®, and its accuracy was proved.