Osmotic pressure model

Osmotic pressure models can be developed from a very fundamental basis. For example, it is becoming possible to predict the rate of ultrafiltration of proteins starting from a knowledge of the sequence and three-dimensional structure of the molecule 19). 

Womans, J. G., Nakao, S. and Smolders, C. A. Journal of Membrane Science 20 (1984) 115. Flux limitation in ultrafiltration osmotic pressure model and gel layer model. 

In the case of the osmotic-pressure model, the rigorous theory allowed the conclusion that at high applied transmembrane pressure, the permeate flux increased as a cube root of the pressure, so that the limiting flux was never reached ... 

Danckwerts P.V., Significance of liquid film coefficients in gas absorption. Industrial Engineering and Chemistry 43 1951 460-1470. Denisov C.A., Theory of concentration polarization in cross-flow ultrafiltration Cel-layer model and osmotic-pressure model. Journal of Membrane Science 91 1994 173-187. 

The solvent and ion selectivity behavior of Na+ and K+ forms of Linde A have been measured in nonaqueous and mixed media. An osmotic pressure model accurately describes ion exchange in concentrated aqueous electrolyte solutions and is extended to solvent selectivity in mixed media. Water is preferentially adsorbed over alcohols, and ethylene glycol is preferred over ethanol in accord with the derived equation... 

On the basis of the above result, it is suggested that the osmotic pressure approach may be as useful for the estimate of thermodynamic properties of simple electrolyte mixtures in mixed solvents as in aqueous media. Additional research with alkali chlorides in alcohol-water mixtures is in progress to substantiate this conclusion. The mean molal coefficient data that are published for the alkali chlorides (12) are expected to facilitate a meaningful prognosis of the osmotic pressure model. 

R. B. Barrett Solvent exchange (H O—MeOH) studies on Na-13-X have been investigated but since the external phase is electrolyte-free, the limitations you mention are not serious. Our results are in accord with the osmotic pressure model. 

A second explanation for a pressure-independent permeate rate could be a strong osmotic pressure dependence on concentration with the osmotic pressure approaching the applied pressure. This description is viable only where the osmotic pressure has meaning. In a system in which solidlike particulates coalesce, the osmotic pressure model would not be a good one. 

Table 3.1 illustrates that the separation between the different processes is not precise, as the processes overlap. Therefore, filtration and separation models are generally applicable to mote than one process. Often several phenomena are operative simultaneously and which one dominates depends on the membrane and the solute or particle in question. Concepts such as the resistance-in-series model, the osmotic pressure model or concentration polarisation are principles which are applicable to any membrane operation. These wiU be described in the MF section. 

The Osmotic Pressure Model, as shown in (3.6), is an equivalent description for macromolecules according to Wijmans et al. (1985). AfT is the osmotic pressure difference across the membrane. 

The osmotic pressure difference can usually be neglected in MF and UF, since the rejected solutes are large and their osmotic pressure small. However, even polymeric solutes can develop a significant osmotic pressure at boundary layer concentrations (Ho and Sirkar (1992)). This naturally implies that the resistance in series model (equation (3.4)) would be more appropriate in MF, while the osmotic pressure model (equation (3.6)) may be more useful in NF and RO. Both models have been applied to UF. 

Applying the osmotic pressure model, assuming negligible fouling of the membranes with Dextran and a negligible permeate concentration, the wall concentration of Dextran can be calculated using equations (7.8) and (7.9) and the relationship between osmotic pressure and Dextran concentration developed by Wijmans et al. (1985)... 

Here, a is a constant and n an exponential factor with a value greater than 1. Hence, if the concentration is high the osmotic pressure can be high as well and this concept may be used to describe concentration polarization, i.e. although the osmotic pressure of the bulk solution is still low, the concentration at the wall may have increased drastically as does the osmotic pressure (see chapter vn.5, osmotic pressure model)... 

How can the gel layer model and the osmotic pressure model, be related to each other In the gel layer model, a plot of J versus IniCj,) gives a straight line with a slope equal to -k. A similar J versus ln(c,) relationship can be obtained from the osmotic pressure model. From eq.vn - 25 the following relationship can be derived ... 

When (Art n)/(q R , k) 1, the right-hand side of eq.VII - 31 reduces to -k. Hence the osmotic pressure model gives a linear plot in the region where R can be neglected with a slope equal to -k similar to that obtained from the gel layer model. 

It should be noted that the boundary layer resistance model is equivalent to the osmotic pressure model [16] ... 

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. 

Both the outlet pressure and the feed velocity were varied in order to reproduce, as a function of and /p , values, negative pulses for TMP and positive pulses for Q, according to the already-described periodic square-wave profiles. At the interface of the channel and the membrane, it was assumed that the components of the velocity vectors were continuous, while, on the basis of the osmotic pressure model, the pressure pi, evaluated on the membrane-side , was equal to the pressure p, calculated on the channel-side , decreased by the difference of osmotic pressure. All (x,t), between the membrane surface and the permeate ... 

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