Laminar fluid flow, particle transport and permeate flux behavior in crossflow membrane filters
Wiesner, Mark R.
Doctor of Philosophy
Similarity solutions for axial and lateral velocity profiles, pressure gradients and wall skin friction are derived for the laminar, isothermal single phase flow of incompressible fluids in channels having porous boundaries. Results from a finite difference solution to the vorticity-stream function formulation of the Navier-Stokes equations are compared with previously reported perturbation, asymptotic, similarity and infinite series solutions. Initial transport of non-interacting particles suspended in laminar flow in the membrane far-field is reported to be accurately predicted by trajectory theory. RTDs obtained in response to pulse inputs in slow axial crossflows and high permeation rates appear to reveal a minimum in back-transport for 7 $\mu$m particles in the range of experimental conditions investigated here. Back-transport of smaller particles is due to Brownian diffusion whereas shear-induced diffusion appears to control the behavior of larger macrocolloids. The effects of suspension concentration, shear rate, Particle Size Distribution (PSD) and initial permeation rate on permeate flux are reported. Existing transient models based on shear-induced diffusion and particle adhesion as well as the steady state inertial lift model are found inadequate in predicting experimental observations of the specific permeate flux during the laminar crossflow filtration of narrow PSD suspensions. Under the range of experimental conditions investigated here, smaller particles deposit preferentially in the cake. Also, under identical experimental conditions higher permeate fluxes are obtained during the filtration of suspensions with a higher average particle size. Hence, pretreatment aimed at coagulating smaller particles could have a beneficial impact on permeate flux production. In all cases, specific resistances of cakes are higher in the crossflow mode compared to the dead-end mode. Also, cake specific resistances increased with shear and decreased with increasing permeation rate. Cumulative resistance to permeation is reported to increase on application of shear even without particle feed. Thus, even though cake mass decreases with increasing shear, it may not result in higher permeate flux. Therefore, pilot scale testing may still be necessary to evaluate the fouling potential of feed waters as well as in optimizing the operation of existing crossflow membrane filters.
Environmental science; Chemical engineering; Civil engineering