Staverman coefficient

Reflection or Staverman coefficient Rejection coefficient (Equation 4)... 

The negative ratio of what are known as the two phenomenological coefficients, Lpo and Lp, is called the selectivity, reflection, or Staverman coefficient. 

The Staverman coefficient s has not, to date, been theoretically calculated. Experimentally, it has been found with cellophane 600 membranes and poly(oxyethylenes) of different molar masses that the Staverman coefficients decreases more or less linearly from a value of 1 for molar masses greater than 6000 g/mol to s = 0 for Af = 62 g/mol. 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

Indeed, Rolf Treckmann, then a colleague from the Chemical Engineering Department of Bayer AG, pointed out to me some expressions for combinatorial contributions of activity coefficients, as they are often used in chemical engineering—and especially to the Staverman-Guggenheim (SG) term given in... 

The combinatorial part of the activity coefficient [Equation (3C-2)1 is known as the Staverman-Guggenheim form. This term is intended to account for size and shape effects. The residual contribution accounts for interactions among groups. The Staverman-Guggenheim term has been shown to predict an exaggerated degree of nonideality for systems where the residual contribution is zero (Kikic et al., 1980). Predictions for such systems are expected to be less accurate. 

Za.Air., where a. is the Staverman reflection coefficient have been 1 1 1... 

To obtain the complete activity coefficient, only the residual term from the UNIT AC model, Equation [4.4.87], has to be added. An attempt to incorporate differences in shape between solvent molecules and polymer segments was made by Kontogeorgis et al. by adding the Staverman correction term to obtain ... 

The effective osmotic pressure of a solution can be calculated by including a term called Staverman s reflection coefficient, symbolized by o, in the osmotic pressure equation, so that... 

Fractionation by liquid liquid phase separation relies on the molar mass dependence of the distribution coefficient which, in terms of the Flory-Huggins-Staverman theory [8 13] (FHS), reads... 

In this Section, it is implicitly assumed that the mass transport resistance at the fluid-membrane interface on either side of the membrane is negligible. Also the following is information that is made available publicly by the membrane manufacturers, when not otherwise noted. As in technical processes, mass transport across semipermeable medical membranes is conveniently related to the concentration and pressme driving forces according to irreversible thermodynamics. Hence, for a two-component mixture the solute and solvent capacity to permeate a semipermeable membrane under an applied pressure and concentration gradient across the membrane can be expressed in terms of the following three parameters Lp, hydraulic permeability Pm, diffusive permeability and a, Staverman reflection coefficient (Kedem and Katchalski, 1958). All of them are more accurately measured experimentally because a limited knowledge of membrane stmcture means that theoretical models provide rather inaccurate predictions. 

The Staverman reflection coefficient, o, measures the extent to which the membrane rejects a given solute purely transported by convection. Solutes fully rejected by the membrane feature o = 1. Solutes freely permeating the membrane feature ct = 0. Membrane rejection toward a given solute is experimentally assessed in the course of pure filtration experiments in terms of its rejection coefficient R, or its sieving coefficient S, with S = —R being the permeate-to-retentate solute concentration ratio. In fact, R is related to a as follows (Spiegler and Kedem, 1996) ... 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

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