Page 66 - Membranes for Industrial Wastewater Recovery and Re-Use

46 Membranes for Industrial Wastewater Recovery and Re-use

Table 2.9 Expressions developed to describe, for dynamic behaviour, dead-end and cross-
flow filtration
_____
Model Equationa Reference
~~
Dead-endfiltration
--4doA
Pore blocking J = 10 exp(7) Hermia (1982)
model
lo
Pore constriction J = Herinia (1982)
model

J = (
Cake formation Hermia(1982)
model

Cross-flowfiltration
Shear-induced J = 10 Romero and Davis
diffusion from (1988)
thick layers

Brownian (1) = 1.31(F)1'3($- fortpks Song(1998), after Song
diffusion and Elimelech (1 99 5)
1
from thick
layers (I) =; [rt)Jss(x)dx + [I. - X(t)]J(t) fort < t,,

3kT
APc =-NE.
4m3

a ab,. no. of pores blocked per filtrate volume passed opere, foulant volume deposited within pores per
filtrate volume passed adep fraction of foulant depositing on membrane: A, filter area, Jo J I,,, flux
initially, at time t, at equilibrium; np, no. of pores: rp pore radius; R,, membrane resistance: (E: operating
pressure difference: (Pc, critical pressure difference (pressure required for cake to form); t. filtration time;
tss. steady-state filtration time (time after which flux is constant): X. distance of the front of the dynamic
layer from the entrance: 170. bulk suspensionviscositp
0 the propensity of the rejected (solute) species to diffuse (Le. their diffusivity),
0 the notional thickness of the stagnant region, and
0 the rate at which solute species are added to the stagnant region.

The first of these relates to the solute itself, and principally to its size. The latter
two factors, on the other hand, are determined mainly by operating conditions.
The thickness of the stagnant region (6) can be determined from: