Mass Transfer Resistances

Membrane-controlled mass transfer provides the simplest operational condition for porous membrane systems with pressure as the driving force. Equation (12.39) is often written in the form of Darcy's Law (Darcy 1856):

n Rm with:

for laminar flow as resistance of membrane Rm. Jp is only controlled by the clean, non-blocked membrane and shows linear behavior (Fig 12.4). A further hydraulic resistance due to pore blocking and adsorption Rf can be considered:

During a membrane filtration process, the solute concentration at the membrane surface rises; and when the concentration c3 exceeds the solubility limit crystallization occurs. A gel layer, also known as a sludge cake, is formed by the deposit of solids as well as by the growth of bacteria (see Fig. 12.5 in the next section and Fig. 12.9 in Section 12.4.3). Practice normally shows non-linear behavior because the gel layer controls mass transport (Fig. 12.4).

Gel layer or sludge cake formation is often found above a so-called critical flux (see Section 12.5). The accumulated material simply adds a further resistance Rc for the sludge cake to the resistance of the free or blocked membrane:

Fig. 12.4 Permeate flux plot as a function of pressure difference.

respectively: √Ąp

n Rx

0 0

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