Resistance cake layer

External fouling is caused by the formation of a cake layer of cells or other materials on the membrane surface, leading to a reduction in permeate flux (defined as the volume of permeate produced per time and membrane area). Internal fouling is caused mainly by proteins and particles smaller than membrane pores. Proteins and protein aggregates can adsorb or deposit at the pore entrance or inside the pores and cause pore blockage or narrowing, leading to increased hydraulic resistance (2). 

Fig. 1. shows the steady-state permeate flux with respect to various stirrer speeds and surface charge densities. As the stirrer speed was faster, the higher permeate flux was observed because of the higher shear stress at the surface of a cake layer. The permeate flux was proportional to the surface charge density of microspheres, in the case of the higher surface charge density, the repulsive force became larger and the cake resistance decreased. 

To understand the flux decline in pressure-driven membrane operations, a number of models were developed. Two of the most widely smdied models are the resistance model and the concentration polarization model. The resistance model is the oldest and is based on the cake filtration theory, where it is assumed that a cake layer of rejected particles, which are too large to enter the membrane pores, is formed. The frictional drag due to permeation through these immobile particles leads to additional hydraulic resistance [21]. The cake layer and the membrane are considered as two resistances in series, and the permeate flux is described by Darcy s Law as... 

A permeate flux declines in the presence of solute due to membrane fouling. A decrease in flux is a result of several phenomenons including adsorption of macromolecules to membrane surface involving pore blocking, concentration polarization, and formation of a gel-like cake layer within the membrane pores (50). Several models have been used to describe solute fouling, among them are hydraulic resistance, osmotic pressure, gel polarization, and film models (51,52). 

The solvent flux (J) is typically described by the equation J = AP/Rj. The total resistance to flow (Rj) is expressed as the sum of two resistances, R i + Rc, where Rm is the resistance due to the membrane and R is the cake-layer resistance. The resistance Rra can be determined by measuring the pure-water flux on an imfouled membrane, one limiting case corresponding to maximum solvent flux. This case is independent of feed flowrate. As Rc increases, the flux becomes independent of AP. This is illustrated in the Figure 9.8. 

Laine et al. (1990) used a hydrophobic and a hydrophilic membrane to remove turbidity, organic matter, and THMPs from lake water. UF was compared to coagulation-tUF, PAC+UF, and coagulation-t-PAC+UF. While no THMPs were removed with UF alone, 30% rejection was achieved with coagulation as pretreatment, and 85% with PAC pretreatment. Additionally, the resistance of the cake layer was improved significantly if two pretreatments were applied. Baudin and Anselme (1995) applied a combination of PAC and UF for river water treatment. PAC was added to a recirculation loop to obtain a higher adsorption efficiency ( Cristal process). Taste and odours were successfully removed, and the process performed better than conventional GAC treatment. 

For incoDopressible filtration the cake concentration remains constant, thus for each unit volume of suspension filtered the filter cake volume increases by a uniform and constant amount. likewise the filtrate volume is uniform and constant with respect to each volume of suspension filtered. The rate of cake deposition will not, however, be uniform because each new element of filter cake increases the total resistance to the passage of filtrate fi om the new cake layer and eventually through the filter medium Thus the rate of filtration declines, as shown in Figure 2.4, vtiien filtering at constant pressure. The uniform relation between cake volume and filtrate volume is illnstrated in Figure 2.5. The constant of proportionality P can be used to give an equation for cake depth, at any instant in time ... 

Cake pick-up can be strongly influenced by the reastance of the medium which predetermines the initial filtrate velocity and the drag forces created by the latter, whidi stabilise the cake layers. Figure 11.11 shows the influence of medium resistance on the rate of cake fittradon, to that er ected fl om liquid flow, plotted against agitator speed. 

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