WebOct 1, 2016 · A population balance model of the combined cooling-antisolvent addition system is developed and a moments model used in optimal control strategies with … WebNov 12, 2024 · We have developed two population balance equation (PBE) models to describe secondary nucleation by attrition: one as a breakage phenomenon and the other as a boundary condition of the PBE. ... Kumar, R.; Kumar, J. Numerical simulation and convergence analysis of a finite volume scheme for solving general breakage …
arXiv:2110.01374v1 [math.NA] 15 Sep 2024
WebApr 11, 2024 · The general form of the equation is a mass balance equation, in which end population = starting population ± natural increase ± net migration, where natural … WebFor this special case, a generalized population balance equation is employed to describe polydispersity in the velocity and other internal coordinates (such as the particle size.) check att texts online
Population Balance Equation - an overview ScienceDirect …
WebNatural Sciences Publishing WebJun 15, 2024 · Thus, the final expression of MC FVS for solving a simultaneous coagulation-fragmentation equation takes the following form:(10)nip+1=nip+Δtp(12∑i=1I∑(j,k)∈ϒiβj,knjpnkpΔujΔuk(uj+uk)ωi,j,k−∑i=1I∑j=1Iuiβi,jnipnjpΔuiΔuj+∑i=1Iui∑k=iISknkpΔuk∫ui−1/2gkib(u,uk)du−∑i=1IΩiSinip),where(11)ωi,j,k=uj+ukui,(12)Ωi=1ui∑k=1iuuk∫uk−1/2gkib(u,ui)du,i=1,2,⋯,I. Population balance equations (PBEs) have been introduced in several branches of modern science, mainly in Chemical Engineering, to describe the evolution of a population of particles. This includes topics like crystallization, leaching (metallurgy), liquid–liquid extraction, gas-liquid dispersions like water … See more Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r … See more Monte Carlo methods , discretization methods and moment methods are mainly used to solve these equations. The choice depends on the application and computing infrastructure. See more check attribute python