Electro-osmotic Coefficient Research Articles

Correlations between electroosmotic coefficients and hydraulic permeability in nafion membranes

The correlation between the electroosmotic coefficient and the hydraulic permeability of Nafion 125 membranes in alkali chloride and hydroxide solutions is analyzed by means of current theories on charged membranes. The dependence of these transport coefficients on both the electrolyte concentration and counterion (cation) nature is also discussed.

On electroosmosis and related phenomena

We describe the transport processes occurring in a conducting liquid system with a diaphragm separating two subsystems of equal temperature and composition, but with different values of pressure and electric potential, in terms of measurable quantities. We show how these quantities are correlated to the (partly non-measurable) phenomenological coefficients of the conventional linear relations of non-equilibrium thermodynamics. We establish some general equations and inequalities relating to the permeation coefficients, the electric conductance, the electroosmotic coefficient and the streaming conductance. We also derive the laws governing the evolution in time of our system for both potentiostatic and galvanostatic conditions and thus complete the description of the irreversible processes possible in the system at hand. We finally present results of recent measurements on aqueous potassium chloride solutions (for molalities between 10 −4 mol/kg and 10 −1 mol/kg and for temperatures between 15°C and 35°C) with silver—silver chloride electrodes and a glass filter disk. We carry through a check of Onsager's reciprocity relation and of an inequality fixing an upper limit for the absolute value of the electroosmotic coefficient.

Irreversible thermodynamics of transport processes through porous media composed of particles of different size

An experimental investigation on liquids transport through porous media is described. Porous diaphragms of Pyrex glass particles, whose sizes were in three ranges, between 150 and 500 μm, as well as water, methyl-, ethyl-, and isopropyl alcohols have been used to perform the hydrodynamic and electroosmotic experiments. The hydrodynamic flow is linearly dependent on the pressure difference and independent on the direction of the flow. The dependence of L 11 on the size of the particles forming the porous diaphragm agrees with that predicted by the classic theory of the electrokinetic phenomena. The electroosmotic coefficient L 12 has been found to decrease as the particle size increases, this being verified for all the permeants used. This fact is explained on the basis of the Anderson and Koh's model.

Electrical and electroosmotic transport behavior of asymmetric cellulose acetate membranes. I. Transport behavior in dialysis-osmosis experiments

Using an asymmetric cellulose acetate (CA) membrane annealed at 82.5°C and the linear relationships of the thermodynamics of irreversible processes, the electrical and electroosmotic transport coefficients such as R e, l ep, and l pe as well as the hydrodynamic permeability, l p, have been determined as functions of the NaCl concentration, c s. The electroosmotic coefficient, l pe, and the so called “pressure-membrane potential” (pmp) coefficient, l ep, have been found to be strongly dependent on the external salt concentration. At larger NaCl concentrations both coefficients even change their sign being positive for c s < 0.07 mole/liter and negative for c s > 0.07 mole/liter. The positive values of l ep and l pe at concentrations c s < 0.07 mole/liter are in agreement with the cation exchange property of CA membranes. Furthermore, the hydrodynamic permeability, l p, and the electrical resistance, R e, of the asymmetric cellulose acetate membrane have been measured. The sign reversal of l ep and l pe is discussed by applying the finely porous membrane model to the two-layer membrane and taking into account the weak cation-exchange character of cellulose acetate membranes. The discussion indicates that both the weak cation-exchange character as well as the asymmetry of the cellulose acetate membrane are responsible for the significant sign reversal of the electrokinetic transport coefficients l ep and l pe at larger concentrations. Moreover, the value of the measured electrical resistance supports the idea of the two-layer model for the asymmetric cellulose acetate membrane.

Hydraulic and electro-osmotic permeability coefficients. Technical note : Sundaram, P N J Geotech Engng Div ASCE, V105, NGT1, Jan 1979, P89–92

Hydraulic and electro-osmotic permeability coefficients. Technical note : Sundaram, P N J Geotech Engng Div ASCE, V105, NGT1, Jan 1979, P89–92

Hydraulic and Electro-Osmotic Permeability Coefficients

Knowledge of hydraulic and electro-osmotic permeability coefficients is required to assess the amount and time rate of consolidation by electro-osmosis. Usually, the coefficients are determined separately. In one method, the pore water is allowed to rise in a vertical tube at the open cathode under a constant voltage gradient. The final electro-osmotic equilibrium head at the cathode is used to estimate the electro-osmotic equilibrium head at the cathode is used to estimate the electro-osmotic permeability, k e , from a knowledge of the hydraulic permeability coefficient, k h .

Electroosmosis of methanol-water and methanol-heavy water mixtures

The electroosmotic and hydrodynamic permeability of methanol and of methanol-H 2O and methanol-D 2O mixtures across a Dowex 1 (Cl − form) membrane have been measured at 30°C. The conductance of the membrane equilibrated with the permeant has also been measured. A phenomenological analysis of the results indicates that the hydrodynamic permeability coefficients of the mixtures are of comparable magnitudes whereas electroosmotic permeability coefficients are significantly different. It is shown that H 2O and D 2O do not form identical double layers at the membrane-permeant interface.

The hyperfiltration streaming potential as a tool in the characterization of polyelectrolyte membranes

A phenomenological expression for the hyperfiltration streaming potential is presented and discussed in the light of recent model calculations. Criteria for membrane homogeneity are defined utilizing the equivalent pore radius calculated from the electroosmotic coefficient, and the hydraulic permeability. Hyperfiltration streaming potential and water flow data for collodion polyvinylamine membranes are compared to electroosmotic and osmotic results for the same membrane. The homogeneity criteria are used to show that at one atmosphere the membrane contains parallel paths for water and ion flow, while at elevated pressure only a single path exists for both species.

Hyperfiltration by polyelectrolyte membranes. I. Analysis of the streaming potential

The streaming potential developed by a polyelectrolyte membrane during hyperfiltration has been analyzed through two approaches: (i) a phenomenological approach and (ii) calculations based on a combination of the TMS (Teorell, Meyer and Sievers) model and the equations of irreversible thermodynamics. Assuming concentration independent phenomenological coefficients, the streaming potential measurable by reversible electrodes can be shown to include the electro-osmotic coefficient and the transport number of the nonreversible ion. By means of the model, local flow equations are integrated over the membrane thickness in order to account for any concentration dependence. In this manner the hyperfiltration streaming potential has been calculated and plotted as a function of both flow rate and net applied pressure. By comparison of the electro-osmotic coefficients calculated from the model treatment of both hyperfiltration and electro-osmosis, the existence of overall Onsager symmetry is demonstrated. The equations are shown to correctly predict the effects of co-ion mobility and external salt concentration on the electro-osmotic coefficient and the streaming potential.

The effect of some growth-regulating compounds upon electroosmotic measurements, transcellular water flow, and Na, K, and Cl influx in Nitella flexilis

By using a small, constant, applied current on a cell of Nitella in artificial pond water, it was possible to compare the effect of different growth-regulating compounds on the apparent electroosmotic water coupling in the cell wall – membrane complex. Indoleacetic acid (IAA) at first enhanced the electro-osmotic effect and then ceased to alter it, but began to change the asymmetric transcellular water flow. Gibberellic acid (GA), when added to IAA, increased this effect, while abscissic acid (ABA) added to IAA decreased it. Some compounds like naphthaleneacetic acid (NAA), alar-83, skatol, or ABA alone, had no effect on the electroosmotic (eo.) coefficient; but NAA, skatol, ABA (alone) changed the asymmetric water flow (basic flow) and some ion influxes. Light-degraded IAA acted in a manner very similar to skatol, which suggests that IAA is quickly converted to skatol in the cell in the presence of light. With light–dark transitions or with IAA, the electroosmotic coefficient changed in a manner parallel to passive ion (Na+ and K+) influx, but was not related to basic flow or Cl− influx changes.Under controlled conditions of low constant current applied to a test cell, it has been shown that a change in apparent eo. coefficient upon auxin addition is largely a reflection of change in the true electroosmotic properties of the cell membrane at the positive end of the cell.

A Hydrodynamic Model for Electroosmosis

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

Fixed charge density effective to membrane phenomena

Transference number of counterions in charged membranes with various concentrations of KCl solution were measured both by the Hittorf and by the emf methods. Two transference numbers obtained for a given membrane differed from each other in their magnitudes, notably in concentrated salt solution. Theoretical equation for the transference number of cations in a negatively charged membrane was derived on the basis of the thermodynamics of irreversible processes in conjunction with an approximate hydrodynamic equation for the movement of the local center of mass. The derived equation illustrates that the transference number obtained by the Hittorf method is composed of two terms; one associated with the movement of individual ion species relative to the local center of mass, and the other with the mass flow. The first term was evaluated with use of our previous results on mobilities and activities of mobile ions in a charged membrane for the same system studied here. Comparison between theoretical and experimental values revealed that the transference number relative to the mass movement was practically the same as that determined from the emf method. The second term of the Hittorf transference number of counterions could be evaluated from the data on the electroosmotic coefficient for the system. It was found that the contribution to the observed Hittorf transference number of the term associated with the mass movement predominates in the concentrated salt solution, and that the marked depression of charge density effective to hydrodynamic properties of the membrane was attributed to decrease of amounts of the counterions carried by the mass flow.

Measurements of Electro-osmosis inNitella translucens

Determinations of the electro-osmotic efficiency (models H2O per Faraday) in Nitella translucens have been made under different conditions. Associated tracer measurements show that the main path of current flow ins through the cell, and not in the cell wall external to the membrane, but that the measured influxes of Na and K can account for only a small fraction of the current. The electro-osmotic coefficient increases markedly at very low currents in the light (to as high as 700 H2O/F), is decreased in the dark, in the presence of low concentrations of N-dichlorophenyl-N′, N′ -dimethyl urea (DCMU) or of carbonyl cyanide m-chlorophenylhydrazone (CCCP) and on the addition of I mM NaHCO3 to the bathing solution; the efficiency is higher at 10.5 °C than at 22 °C. Electro-osmosis, generated by a difference in membrane potential at the two ends of the cell bathed by different solutions, gave values of the electro-osmotic coefficient similar to those characteristic of low applied currents.The results suggest that the cell membrane, and not only the cell wall, shows electro-osmotic properties. A simplified analysis of the system shows that the electro-osmotic coefficient measured depends on conditions at each end of the cell and is not simply a property of the cation added at the end of the cell at which positive current enters.

Correlation of Measurements of Electroosmosis and Streaming Potentials in Ion Exchanger Membranes

AbstractMeasurements of streaming potentials have been carried out at 25 °C in systems with ion exchanger membranes of the phenol sulfonic acid formaldehyde type with external KC1 solutions of concentrations 0.01, 0.03, 0.1 and 0.3 N using a pressure pulse method. The concentration polarization on account of reverse osmosis was eliminated by studying the time variation of the measured potential and applying a theoretical formula for extrapolation to time zero.It is shown on a simple model system that electroosmosis experiments may give erroneous results on account of concentration polarization even if the apparent electroosmotic coefficient is independent of the current density. Electroosmosis experiments were carried out in a stirred cell, and the values were found to be consistent with the streaming potential values in the corresponding systems.It is concluded that streaming potential measurements are the more promising for accurate and fast determination of the electrokinetic cross coefficient.

Osmotic Flows in Charged Membranes. II. Thermo-Osmosis

Thermo-osmotic flow rates of an electrolyte solution through a porous charged membrane separating two solutions which are at different temperatures but have the same concentration is studied theoretically, using a capillary model for the membrane. The assumptions used are that the Debye-Hückel approximation is applicable for the ion distribution in the double layer formed near the fixed charges on the capillary wall, and that the thickness of the double layer is much smaller than the capillary radius. The steady-state solutions of a set of differential equations derived are obtained subject to appropriate external conditions. It is shown that plots for the flow rate of fluid against the logarithm of the concentration of the outer solution give a bell-shaped curve. This theoretical curve follows well the Carr—Sollner data of the thermo-osmosis for various electrolyte solutions. The thermo-osmosis is an electro-osmotic flow caused by the electric field which is set up in the membrane so that no net electric charge is allowed to be transported across the membrane. The dependence of the electro-osmotic coefficient on salt concentration is the primary cause for the characteristic behavior of the thermo-osmosis in charged membranes. It has been shown in Part I of this series that this effect is also responsible for the anomalous osmosis.

Osmotic flow in charged membranes

The osmotic flow through a porous charged membrane separating electrolyte solutions of different concentrations but at a constant temperature is studied theoretically, using a capillary model for the membrane. The assumptions used are that theDebye-Huckel approximation is applicable for the ion distribution in the double layer formed near the fixed charges on the capillary wall, and that the thickness of the double layer is much smaller than the capillary radius. The steady state solutions of the differential equations derived are obtained subject to the external conditions that the concentrations of the outer solutions are maintained constant and no pressure head is applied across the membrane. It is shown that the volume rate of osmotic flow is the sum of two terms, one arising from the fact that the membrane is electrically charged and the other being independent of the membrane charge and thus observable commonly both in charged and uncharged membranes. The former corresponds to whatGrim andSollner have referred to as the true anomalous osmosis. The plot of this electric part of osmosis against the logarithm of the concentration of one outer solution gives a bell-shaped curve, when the concentration ratio of the outer solutions is fixed. This theoretical curve follows well theGrim-Sollner data of the true anomalous osmosis for various aqueous electrolyte solutions. The true anomalous osmosis is an electro-osmotic flow caused by the electric field which is set up inside the membrane so that no net transport of electric charge occurs from one solution compartment to the other. The dependence of the electroosmotic coefficient on salt concentration is responsible for the characteristic behavior of the osmotic flow rates through charged membranes.

Flows Through Charged Membranes. I. Flip-Flop Current vs Voltage Relation

Flow processes in a (porous) charged membrane separating two solutions of different concentration of the same electrolyte are studied theoretically, using a capillary model for the membrane and the Debye—Hückel approximation for the calculation of ion distributions in the double layer formed near fixed charges on the capillary wall. Steady-state solutions to the continuity equations derived are obtained subject to the external conditions that there is the passage of a constant forced electric current I through the membrane, the salt concentrations on both sides of the membrane are held constant, and a constant pressure is imposed on the more concentrated solution. The results yield a characteristic I vs transmembrane potential Δφ relation, which consists of two nearly straight lines of different slopes involving a discontinuous transition between them. This feature well compares to the experimental data obtained recently by Tasaki et al. with sintered glass membranes and thought by them to be significance in relation to the physiology of nerve excitation. It is shown that, in the framework of the theory presented, the occurrence of a discontinuous change in I at a certain particular potential mainly stems from the dependence of the electro-osmotic coefficient on salt concentration. The probable causes for the discrepancies between theory and experiment are discussed briefly.