Models of Flux Decline

Equation (10.6) can be rearranged and differentiated with respect to time to give  

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Passage of bacteria through membrane Analysis of deposits ATR, FTIR, measuring fouling in real time Measuring concentration polarization Mathematical modeling of flux decline... 

Lee, Y. and Clark, M.M., Modeling of flux decline during crossflow ultraflltration of colloidal suspensions, J. Membr. Sci., 149, 181, 1998. 

Aydiner C., Demir I., Yildiz E., Modeling of flux decline in crossflow microfiltration using neural networks the case of phosphate removal. Journal of Membrane Science, 2005,248(1-2), 53-62. 

Curdo S, Calabro V, lorio G (2006b), Reduction and control of flux decline in cross-flow membrane processes modeled by artificial neural networks , /. Membrane ScL, 286(1-2), 125-132. 

The phenomenon of fouling is very complex and difficult to describe theoretically. Even for a given solution, fouling will depend on physical and chemical parameters such as concentration, temperature, pH, ionic strength and specific interactions (hydrogen bonding, dipole-dipole interactions). However, reliable values of flux decline are necessary for process design. The flux may also be described by a resistances-in-series model, in which a resistance of a cake layer is in series with the membrane resistance. The flux can be described by... 

Also included are sections on how to analyze mechanisms that affect flux feature models for prediction of micro- and ultrafiltration flux that help you minimize flux decline. Descriptions of cross-flow membrane filtration and common operating configurations clarify tf e influence of important operating parameters on system performance. Parameters irdlucnc irxj solute retention properties during ultrafiltration arc identified and discussed or treated in detail. 

The basis for the experiments as carried out was that the flux decline with time, which is an easily measured quantity, could be correlated with the foulant film growth by the model of Eq. (2), or some other appropriate semi-empirical model. In this way the fouling film thickness could be deduced indirectly. To show this we write from Eqs. (5)-(7)... 

In Figures 8 and 9 are shown the data for the dependence of the characteristic film buildup time t on Apg and U. In accord with the model, t is found to be independent of U, with only a very weak dependence on Apg indicated. This latter result could in part be a function of experimental inaccuracy. The data reduction for t introduces no assumptions beyond that needed to draw the exponential flux decline curves such as those shown in Figures 2 and 3. However, an error analysis shows that the maximum errors relative to the exponential curve fits occur at the earlier times of the experiment. This is seen in the typical error curve plotted in Figure 10. The error analysis indicates that during the early fouling stage the relatively crude experimental procedure used is not sufficiently accurate or possibly that the assumed flux decline behavior is not exponential at the early times. In any case, it follows that the accuracy of the determination of 6f is greater than that for t. 

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... 

This model has been successful in describing flux decline during dead-end filtration of particulate suspensions, but is not appropriate for application to crossflow filtration where the feed solution continuously recirculates [158]. Also, neither the occurrence of macromolecules and colloidal particles diffusion nor the influence of solute-solute and solute-membrane interactions on flux decline is considered in this model [42,59,159]. 

Despite the numerous efforts in understanding the fouling mechanisms and the influence of operating parameters involved that lead to flux decline in filtration systems, there remain significant gaps in the present knowledge on this phenomenon. To date, none of the theoretical models, and their numerous modified forms, and empirical models sufficiently explain the influence of membrane-solute interactions and solute-solute interactions on real dairy systems. 

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). 

Moaddeb and Koros (1997) described the deposition of silica on polymeric MF membranes as non-uniform. This means that cake characterisation is difficult as a cracks could vary the results. Meagher et al (1996) stated that attractive interaction between membranes and particles would cause a flux decline, even if the particles were aggregated. Aggregation reduced the flux decline if there was no attraction between the membranes and colloids. The authors outlined the restrictions of the gel polarisation model, as the porosity of the deposit is not accounted for in the model. It was also suggested that the resistance of the gel layer is more important than the particle-surface interaction (what is often referred to as adsorption). 

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