In a subsequent paper, the critical point condition will be discussed and the results of the first two papers illustrated with real systems, that is, the spinoidal and critical points of pure components and mixtures will be determined using typical equations of state. NOTATIONjugate coordinate of xj LITERATURE CITEDBeegle, B. L., M. Modell, and R. C. Reid, "Legendre Transforms andAn experimental study of the ultrafiltration of several ionic inorganic solutes, using a negatively-charged membrane, is detailed. Both single salt and multi-salt systems are investigated in a continuous flow, thin channel unit, with an average transmembrane pressure difference of 2.76 X lo5 N/m2 and a channel Reynolds number of 2800. The solute rejection is predictable to some extent in terms of Donnan ion exclusion theory, and the water flux is dictated by the combined effects of osmotic pressure and membrane-cation interaction.In the single salt experiments, the anion rejections can be related to the inlet (feed) concentration by power functions of the form: rejection = 1 -K Cia, in which 0 < a < 1.0. The power a is 0.4 for chloride salts, 0.25 for monovalent oxyanion salts, and 0.1 for divalent oxyanion salts, but a is independent of the cation present (Na+, Ca2+, or La3+). The constant K is generally a function of both the anion (except in the case of sod2-, HPOd2-, and Cr042-) and the cation, being determined by such factors as ion charge density and membrane-cation interaction. The membrane resistance to water flux is found to depend on cation charge and cation radius. For systems containing two or more salts, the presence of a divalent anion decreases the rejection of the monovalent anion. For multi-salt systems, a rejection of Ca2+ plus Mg2+ of 0.82 and a water flux of 12.9 X cm/s (27.2 gal/ft2-day) are achieved at a transmembrane pressure difference of 4.10 X lo5 N/m2 (4.1 atm), indicating that the process has considerable potential for industrial water softening. SCOPEUltrafiltration is a pressure-activated membrane process charged anisotropic membrane9 has been used primarily and is generally carried out at low pressures of about for the separation of modest molecular weight organic lo5 to lo6 N/m2. Ultrafiltration with conventional un-solutes, organic macromolecules, and colloids from
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