Predicting optimal back-shock times in ultrafiltration hollow fibre modules through path-lines

Predicting optimal back-shock times in ultrafiltration hollow fiber modules II: Effect of inlet flow and concentration dependent viscosity

“…This approximation is best when the time between back-shock is so long that the concentration field just before a back-shock is applied, in the periodic solution, is close to the steady-state solution. In [33], it was seen that using a time between back-shocking of 5 s was long enough for the flux, and thereby the concentration field, to be close to the steady-state value before initiating the back-shock. Hence, all simulations in this section have been done with this value of the time between back-shocking, t 5 s bbs = .…”

“…As a model of the flux through the membrane, we use the solution diffusion model [34] -the same model as in [27,33] …”

“…Mathematical modeling and computational fluid dynamics are increasingly being used to gain understanding of cause and effect in membrane filtration [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Of these the following papers concern back-shocking [28][29][30][31][32][33].…”

“…In [33], the focus is on back-shocking of concentration polarization in ultrafiltration. Here, an estimate was given for the optimal back-shock time depending on the working parameters.…”

“…The assumption used in [33] that the velocity tangential to the membrane is linear as a function of distance from the membrane is obviously not correct in hollow fibres for large distances away from the membrane. Instead, the full Navier-Stokes equation should be solved along with the continuity equation for both solvent and solute.…”