(494b) Application of the Numerical Fractionation Technique to Population Balance Models of Simultaneous Agglomeration and Breakage

The numerical fractionation technique for population balance modeling divides the population into generations and models population evolution by the evolution of each generation’s moments.  One of the attractions of the method is the avoidance of closure issues by evaluating the rate kernels at each generation’s number mean size.  The method has been applied to problems in polymerization and to particle problems involving nucleation, growth and coagulation.  In this paper, the method is extended to treat particle breakage, and is applied to a set of test problems for breakage alone with a range of fragment distribution parameters, and various combinations of simultaneous coagulation and breakage for both Brownian and turbulent coagulation kernels.  The results, expressed in terms of the moment trajectories, are compared to moment models based on closures employing either polynomial interpolation (MOMIC) or quadrature (DQMOM).

We find that when breakage is included, either on its own or with coagulation, it is no longer sufficient to evaluate the rate kernels at each generation’s number mean, but that the kernel’s size-dependence must be included explicitly in (at a minimum) the breakage moment integrals and a means of model closure provided.  Thus, one of the advantages of the numerical fractionation method is lost when breakage is included in the model.  Furthermore, we find that while the modified model works well for coagulation-breakage problems involving 0^th-order coagulation kernels (i.e., the Brownian kernel), it has significant difficulty handling similar problems with 1^st-order coagulation kernels (i.e., the turbulent kernel).  By contrast, the two other methods produce results in reasonable agreement with one another in nearly all cases.