Membrane filtration theory

Land (1987) has reviewed and discussed theories for the formation of saline brines in sedimentary basins. We will summarize his major relevant conclusions here. He points out that theories for deriving most brines from connate seawater, by processes such as shale membrane filtration, or connate evaporitic brines are usually inadequate to explain their composition, volume and distribution, and that most brines must be related, at least in part, to the interaction of subsurface waters with evaporite beds (primarily halite). The commonly observed increase in dissolved solids with depth is probably largely the result of simple "thermo-haline" circulation and density stratification. Also many basins have basal sequences of evaporites in them. Cation concentrations are largely controlled by mineral solubilities, with carbonate and feldspar minerals dominating so that Ca2+ must exceed Mg2+, and Na+ must exceed K+ (Figures 8.8 and 8.9). Land (1987) hypothesizes that in deep basins devolatilization reactions associated with basement metamorphism may also provide an important source of dissolved components. 

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... 

With membrane filtration techniques, analytes can be concentrated on the membranes if the molecular diameter is bigger than that of the pores of the membrane. Analytes are dissolved in a buffer containing ions that are smaller than the pores of the membrane. The buffer ions pass through the membrane, and the analytes with sizes bigger than the membrane pores are concentrated at the membrane. In theory, the degree of concentration is only limited by the ratio of the initial sample volume to the surface of the membrane, and the solubility limit of the samples. 

Elimelech, M. Bhattachaijee, S. (1998) A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory. 

The MFI is based upon cake filtration theory that particles are retained on the membrane surface during filtration. According to the resistance in series model, the reduction in flux due to the presence of cake layer and the additional resistance from the membrane under constant operating filtration can be described as ... 

TRENDS IN MEMBRANE FILTRATION TECHNOLOGY THEORY AND APPLICATION... 

The Realizable k-e model ensures the positivity of normal stresses ( realizable ) by making the empirical constants of k-e turbulence model, C, a function of the mean flow (mean deformation) and the turbulence (/c, ) while the Boussinesq theory used in the standard and RNG k-e model allows for negative normal stresses. The Realizable k-e model is more accurate in the prediction of the spreading rate of both planar and round jets. Kang et al (2008) used a Realizable k-e model to simulate the hydrodynamics in the membrane filtration zone of pilot and full-scale MBRs. 

In reverse osmosis membranes, the pores are so smaH, in the range 0.5— 2 nm in diameter, that they ate within the range of the thermal motion of the polymer chains. The most widely accepted theory of reverse osmosis transport considers the membrane to have no permanent pores at aH. Reverse osmosis membranes are used to separate dissolved microsolutes, such as salt, from water. The principal appHcation of reverse osmosis is the production of drinking water from brackish groundwater or seawater. Figure 25 shows the range of appHcabHity of reverse osmosis, ultrafiltration, microfiltration, and conventional filtration. 

While the development of codeposition theories was essentially dormant, the understanding of the kinetics of particle deposition from suspensions was rapidly evolving. The omnipresence of the interaction of particles with surfaces [70] and the importance to deep-bed granular filtration, deposition of paints, fouling of coolant circuits, chemical reactors and membranes, led to careful theoretical and experimental investigations of the mechanism of deposition. The theory is most advanced in the area of filtration and a number of comprehensive reviews exist [71-73]. It is striking that of... 

The sole purpose of using the membrane is to separate the solute from the water molecules. Whereas MF, UF, and NF may be viewed as similar to conventional filtration, only done in high-pressure modes, the RO process is thought to proceed in a somewhat different way. In addition to operating similar to conventional filtration, some other mechanisms operate during the process. Several theories have been advanced as to how the separation in RO is effected. Of these theories, the one suggested by Sourirajan with schematics shown in Figures 8.6a and 8.6b is the most plausible. 

Dip coating is analogous to a slip casting process for making ceramic parts. The membrane deposition behavior by slip casting can be described by a theory of colloidal filtration for incompressible cakes [Aksay and Schilling, 1984] and compressible cakes [Tiller and Tsai, 1986). The theory predicts that the thickness of the consolidated layer, L, is given by... 

Gowman and Ethier [49,50] developed an automated laser-based refractometric technique to measure the solute concentration gradient during dead-end filtration of a biopolymer solution. This paper attempts to reconcile theory with experimental data. The refractometric technique may be useful to other researchers working on quantification of membrane fouling. 

The concentration polarization model, which is based on the stagnant fihn theory, was developed to describe the back-diffusion phenomenon during filtration of macromolecules. In this model, the rejection of particles gives rise to a thin fouling layer on the membrane surface, overlaid by a concentration polarization layer in which particles diffuse away from the membrane surface, where solute concentration is high, to the bulk phase, where the solute concentration is low [158]. At steady state, convection of particles toward the membrane surface is balanced by diffusion away from the membrane. Thus, integrating the onedimensional convective-diffusion equation across the concentration polarization layer gives... 

It has been shown recently [11] that the experimental hydraulic resistance of such a composite structure can be much larger than the theoretical resistance obtained by simply summing the resistances of the different layers. As an interpretation, the existence of highly resistant transition boimdary layers due to infiltration between adjacent media of drastically different particle sizes has been suggested (Fig. 12.3). In order to check this theory, infiltrated and nonin-filtrated Ti02 membranes deposited on a-alumina support have been prepared. Scanning electron micrograph of their interfaces is shown in Fig. 12.4. From them, complementary resistances have been measured. 

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