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Membrane twhnology 39

the extent to which rejected material accumulates in the interfacial
region.

These two factors are, of course, interlinked: a high driving force yields high
flux and a high rate of rejected material collecting on the membrane surface,
which then needs to be dispersed rapidly if the process is not to grind to a halt. In
extractive and dialytic processes, CP tends to deplete the permeating species at
the membrane, which in electrodialysis has the effect of increasing electrical
resistancc and decreasing permselectivity.

2.2.4 Critical flux
The critical flux concept was originally presented by Field et al. (1995). These
authors stated that: “The critical flux hypothesis for microfiltration is that on
start-up there exists a flux below which a decline of flux with time does not occur;
above it, fouling is observed”. Two distinct forms of the concept have been
defined. In the strong form, the flux obtained during sub-critical flux is equated to
the clean water flux obtained under the same conditions. However, clean water
fluxcs arc rarely attained for most real feedwaters due to irreversible adsorption
of some solutes. In the alternative weak form, the sub-critical flux is the flux
rapidly established and maintained during the start-up of the filtration, but does
not necessarily equate to the clean water flux. Alternatively, stable filtration
operation, i.e. stable permeability for an extended period of time, has been
defined as sub-critical operation even when preceded by an initial decline in flux
(Howell, 1995). Such conditions would be expected to lead to lower critical
flux values than those obtained for absolutly constant permeability operation
(i.e. from t=O), however, since an initial permeability decline implies foulant
deposition.
A number of slightly different manifestations of sub-critical flux operation
have been proposed, largely depending on the method employed. The most
microscopically precise definition equates the critical flux to that flux below
which no deposition of colloidal matter takes place. Kwon and Vigneswaran
(1998) equated the critical flux to the lift velocity as defined by lateral migration
theory (Table 2.12: Section 2.3.2), as introduced by Green and Belfort (1980).
This rigorous definition is difficult to apply because of the relative complexity
of the determination of the lift velocity, particularly for heterogeneous matrices.
On the other hand, experimental determination of critical flux by direct
observation of material deposition onto the membrane has been conducted using
model homodispersed suspensions of polystyrene latex particles (Kwon and
Vigneswaran, 1998), and some authors have also used mass balance
determinations (Kwon eta]., 2000).
Given the limitations of applying particle hydrodynamics to the identification
of the critical flux in real systems, recourse generally has to be made to
experimental determination. By plotting flux against the transmembrane
pressure it is possible to observe the transition between the linearly pressure-
dependent flux arid the onset of fouling, where deviation from linearity