A Hydrodynamic Model for Electroosmosis
| Autor: | Barry R. Breslau, Irving F. Miller |
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| Rok vydání: | 1971 |
| Předmět: | |
| Zdroj: | Industrial & Engineering Chemistry Fundamentals. 10:554-565 |
| ISSN: | 1541-4833 0196-4313 |
| DOI: | 10.1021/i160040a003 |
| Popis: | A hydrodynamic model fur electroosmosis in ion-exchange membranes has been developed, based on the unidirectional flow of macroscopic spheres in a homogeneous bounded medium. Corrections have been incorporated to account for the influence of the matrix, viscosity changes due to ion-solvent interaction, and the molecular size of the ionic sphere. Measurements of membrane properties have been made on both cation- and anion-exchange membranes in a variety of ionic states. Calculated electroosmotic coefficients (solvent transference numbers) were found to agree with most experimentally measured values within &5%. The results indicate that membrane pore structure is well approximated by a model employing parallelplate pores and that ions are partially stripped of their hydration sheath while within the membrane. of the many phenomena which take place across ion-. exchange membranes, electroosmosis is one that has evoked particular interest for many years. In spite of the many experimental and theoretical studies on electroosmosis (the movement of solvent from an ionic solution across an electrically conducting barrier in response to an electric current), one finds wide variance between predictions based on mechanistic models and experiment. The reasons for these discrepancies are reasonably well understood, at least qualitatively. On the other hand, various models based on irreversible thermodynamics (Katchalsky and Kedem, 1962; Kedem and Katchalsky, 1963; Spiegler, 1958), while providing a basis for the description of transport phenomena across membranes, provide little or no insight into the mechanism by which such transport occurs. The classical mechanistic theory of electroosmosis, due to Helmholtz (1879), Lamb (1888), Perrin (1904), and Smoluchowski (1914), assumes the existence of an electrical double layer adjacent to the cylindrical pore walls, whose dimensions are small compared to the pore diameter. The fluid in the core of the pore is assumed to be essentially bulk fluid. This model, while qualitatively verified for such wide pore systems as clay plugs, was shown to exhibit systematic deviations when applied to membrane systems by Manegold and Solf (1931) in studies on collodion diaphragms of graded pore size. Schmid (1950, 1951, 1952, 1965) and Schmid and Schmarz (1951, 1952) were able to explain some of these deviations by ignoring the double layer and postulating an even distribution of ions in the pore, with certain of the ions immobilized. In particular, the Schmid theory, was able to explain the previously unexplained facts observed by Manegold and Solf that the electroosmotic permeability was proportional to the pore size and to the hydraulic permeability, while the electroosmotic pressure was independent of pore size. However, Despic and Hills (1956), working with copolymers of methacrylic acid and ethylene glycol dimethacrylate, showed that the Schmid theory was inapplicable to highly cross-linked, highly charged ion-exchange membrane systems. Other workers who came to similar conclusions include Graydon and Stewart (1955, 1957), Oda and Yaivataya (1955, 1956,1957), R'inger, Ferguson, and Kunin (1956), Mackie and Meares (1959), and many others. So far, a model for the process which does explain observations made with highly charged ion-exchange membrane systems has not been found. In this contribution, a new model for electroosmosis is developed from a hydrodynamic point of view. This model, specifically applicable to highly cross-linked, highly charged ion-exchange membrane systems, assumes that ions may be represented as spherical particles moving in a continuous medium, with the membrane matrix forming the boundary of the medium. Appropriate equations are derived which relate the forces acting on the ion, the solvent medium, and the matrix, taking account of ion-solvent interactions. After certain approximations are made, the equations are used to predict pore sizes and electroosmotic transport for a variety of membrane ionic states, and these predictions are then compared to experiment. Electroosmotic Model |
| Databáze: | OpenAIRE |
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