A methodology, called the aggregate transport model, is presented that can a priori predict both the pressure-independent permeation flux and yield of target species for the microfiltration of poly-disperse solutions. The model captures the phenomenon of critical shear rate. Beyond the critical shear rate (expressed as a ratio of shear rate to permeation flux), the transmission of proteins drops sharply as a result of cake classification. The widely reported benefits of operating at uniform transmembrane pressure and constant wall concentration follow from this method. The methodology is general in nature and can be used predictively to obtain an optimal balance between flux and yield of target species during the microfiltration of many commercial polydisperse suspensions. In the accompanying paper we test this model for microfiltration of transgenic whole goat milk.