Dead-end filtration experiments on model dispersions: comparison of VFM data and the Kozeny–Carman model

Permeate flux decline is a major item when considering pressure driven membrane filtration. The decline is a result of the deposition of (dispersed) feed materials as a layer on the membrane surface. This means loss of production of permeate or, when applying a higher compensating pressure, loss of energy. A number of characterization techniques such as SDI (Silt Density Index) and MFI (Modified Fouling Index) are available to study such effects by using a dead-end filtration set-up. A more recent technique, VFM (Vito Fouling Measurement), is described in [1,2]. VFM is a pragmatic characterization method which presents dead end flux decline results as a graph or as a table formatted “multi value index”. To the author’s opinion it is very difficult to squeeze the complex permeate flux decline behaviour of a real feed into a one number “model” such as SDI or MFI without losing crucial information or even missing a crucial zone within the complete set of data. In this paper it is demonstrated that, even for a simple situation of a model dispersion of ceramic powders in water, it is improbable to achieve a correct mathematical description of the hydraulic conditions during cake formation on a membrane surface. Therefore, a universally applicable mathematical model which predicts in an accurate way the flux decline, for a real feed with a complex composition, seems impracticable. This argues in favour of the experimental approach, such as the VFM.

Experimental results from VFM measurements on “model” dispersions of SiC powders show that a Kozeny–Carman approach to model the hydraulic resistance Rf vs. permeate volume is founded on two crucial parameters: the Kozeny constant and the cake porosity. The Kozeny “constant” kc however is reported in the literature to show values in reality which differ from the value of 5. In this paper the effect of a scatter of +20% and –20% on this value was investigated. In literature even larger value dispersions are mentioned. The investigated spread of 40% on the kc value invokes a first important constraint on the model approach. Regarding the porosity of the cake it was shown that physically relevant values fail in order to obtain a good fit with the experimental results. This imposes even a larger constraint on the model approach. It is therefore believed that the theoretical model needs additional correction coefficients for obtaining a good fit. As a result, the VFM method seems to be a valid candidate as well as a pragmatic characterization method for the determination of basic permeate flux decline data of a feed as well as a method to produce the data needed for modelling the layer resistance Rf(V) by curve fitting. Acknowledgment The authors would like to thank Rabah Mouazer at Vito for discussions on the cake porosity and the experiments performed on mixtures of SiC powders in order to determine the characteristics of the mixtures as mentioned in Table 4. Rabah Mouazer is researching gel casting of ceramic materials.