Modeling a batch foam fractionation process

A mathematical model of a batch foam fractionation process has been developed based on analogies to a distillation model. The model is tested for the foam fractionation of the aqueous protein solution obtained from kudzu (Pueraria lobata) vine retting broth. This broth is most likely comprised of cellulases and pectinases. Time-varying trajectories of measured total protein levels are fitted to the model such that localized distribution coefficients (K's) are determined at each stage, at 15-minute intervals, for the six-stage equilibrium model. This is the identification part of the model building. The distribution coefficients relate to the postulated local equilibrium between the rising foam stream and the descending liquid drainage stream. This is apparently the first time that such values have been determined directly from a dynamic foaming process. The K values are averaged to around 1.4 since they are approximately the same at each determined time point and position within the dilute protein solution (presumably governed by Henry's Law). The simulation part of the model building uses the time averaged K's to generate foamate (collapsed foam) protein concentrations which are compared with the sampled experimental data.