Population balance models morphology

Despite the commercial importance of PVC particle morphology to its end-use applications, there has been little work done on the development of quantitative models relating the size evolution of primary particles in terms of process conditions. Kiparissides [57] developed a population balance model to describe the time evolution of the primary particle size distribution as a function of the process variables, such as temperature and ionic strength of the medium. However, for the solution of the population balance model, the coalescence rate constant between the primary particles needs to be known. This, in turn, requires the calculation of electrostatic and steric stabilization forces acting on these particles. 

The value of this example lies in showing how the population balance framework, viewed in suitably abstract terms can accommodate even the detail of spatial morphology of the particles. The author is not aware of such models in the literature. 

The important feature of the MEL model is the acclimation of vegetation to maintain a nutritional balance when faced with changes in resource availability, Vc, Vn. By acclimation authors (Bastetter etal, 1997) mean any process that results in a compensatory redistribution of uptake effort in response to a deviation from optimal element ratios in biomass. These processes include not only physiological and morphological responses of individual plants, such as changes in enzyme concentrations in tissue and root shoot ratios, but also genetic adaptation of populations and competitive replacement of species by other species with more favorable distribution of uptake efforts. This aspect is essentially important for the time scale of response. 

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