EMoM: Exact method of moments—Nucleation and size dependent growth of nanoparticles

Abstract

In this study we present a reformulation for a broad class of population balance equations that model nucleation and size dependent growth. This formulation enables the definition of new numerical methods, which have two advantages compared to existing schemes in the literature (e.g. finite volume type methods and methods based on the evolution of moments): i) higher precision due to non-smoothing and ii) less run-time in comparison to finite volume algorithms of equivalent accuracy. The described formulation represents the solution of the considered balance equation in terms of the solution of a scalar integral equation, which can then be exploited to establish efficient numerical solvers. The computation of a solution of an initial boundary value problem in space-time is thus reduced to a scalar integral equation, which considerably reduces the computational effort required for its approximation. The integral equation describes the exact evolution of the third moment of the solution, justifying the name for this method: the exact method of moments (eMoM).