Development Of A Predictive Mathematical Model For Crossflow Filtration Of Colloidal Suspensions
Free (open access)
CJ. Richardson & V. Nassehi
The step-by-step development of a Galerkin finite element model for crossflow filtration of colloidal particles is explained. Important features of the process from both the fluid dynamical and rheological points of view are discussed and the solution methods that were adopted to provide realistic computer simulations for crossflow filtration of colloids are presented. The developed algorithm takes into account the process dependant nature of the flow regime, i.e. combined free and Darcy flows in a crossflow filter, by updating the viscosity of the fluid as a function of particle volume fraction distribution. Hence any change in the volume fraction due to filtration and any knock on effects on the rheological behaviour can be continually taken into account. The algorithm has been developed with generalized Newtonian suspensions in mind. To simulate tie filtration of a suspension the equation used to relate fluid viscosity to particle volume fraction should be defined separately. In this way a realistic model of the process can be obtained. Similarly the model has the potential to include the commonly adopted back transport models such as shear-induced diffusion. The paper includes samples of simulation results and discussions concerning their validity.