International Max Planck Research School for Analysis, Design and Optimization in Chemical and Biochemical Process Engineering Magdeburg "The Dynamics of the Becker-Döring System of Nucleation Theory applied in Process Engineering"
In this project we study the Becker-Döring model mathematically and numerically. This model describes nucleation process of droplets in gas, crystals in solutions or liquid droplets in a crystalline solid such as Gallium Arsenide (GaAs). It is a special case of the discrete coagulation-fragmentation equations. It has several applications including suspensions, aerosols, enantiomer crystallization etc. One of the objectives is to extend some results on existence and uniqueness of solutions. Furthermore, efficient computation of solutions through metastable phases is a big challenge due to a very large system of equations required to exhibit the metastability. Our aim is to provide a computationally efficient numerical method for solving the model. Regarding efficient computation, one possibility could be model reduction in such a way that over all balances like mass conservation and the total number of aggregates are accurate enough. The model reduction idea relies on considering computation of only a few concentrations. This leads to the inconsistency of the moments, that is, poor prediction of total aggregates and break down of mass conservation. In order to overcome inconsistency of the numerical method one can use the idea of the cell average technique [An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation, Powder Technology 182, 2008, Pages 81-104] which is well known for solving a general aggregation-breakage equation. This technique predicts the complete density distribution as well as the moments of the distribution very accurately by considering only a few grid points for the computation.
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