The effect of membrane potential on the development of chemical osmotic pressure in compacted clay

When clay soils are subjected to salt concentration gradients, various interrelated processes come into play. It is known that chemical osmosis induces a water flow and that a membrane potential difference develops that counteracts diffusive flow of solutes and osmotic flow of water. In this paper, we present the results of experiments on the influence of membrane potential on chemical osmotic flow and diffusion of solutes and we show how we are able to derive the membrane potential value from theory. Moreover, the simultaneous development of water pressure, salt concentration and membrane potential difference are simulated using a model for combined chemico-electroosmosis in clays. A new method for short-circuiting the clay sample is employed to assess the influence of electrical effects on flow of water and transport of solutes.     

Membrane capacitive deionization

Membrane capacitive deionization (MCDI) is an ion-removal process based on applying an electrical potential difference across an aqueous solution which flows in between oppositely placed porous electrodes, in front of which ion-exchange membranes are positioned. Due to the applied potential, ions are adsorbed in the electrodes and a product stream with a reduced salt concentration is obtained. Including the membranes in the process has two advantages: first, they block co-ions from leaving the electrodes, thereby increasing the salt removal efficiency of the process, and second, when during ion release a reversed voltage is used, counterions can be more fully flushed from the electrode region, thereby increasing the driving force for ion removal in the next cycle. Here we present pilot-plant experimental data for salt removal in MCDI as function of inlet ionic strength and flow rate. In the subsequent stage of ion release the flow rate is temporarily reduced to zero and the voltage sign reversed. This “stop-flow” operation mode results in a small and concentrated product stream. We present a theoretical process model for MCDI which describes the time-dependent electric current and effluent ion concentration, both during the deionization stage and during the subsequent stage of ion release. The process model describes the MCDI cell as a number of stirred volumes placed in-series, and includes the transport resistance of the ion-exchange membrane and of the stagnant diffusion layer in front of the membrane. Ion storage in the electrodes is described according to the equilibrium Gouy–Chapman–Stern model for the electrostatic double layer.     

Electrochemical characterization of an asymmetric nanofiltration membrane with NaCl and KCl solutions: influence of membrane asymmetry on transport parameters

Electrochemical characterization of a nanofiltration asymmetric membrane was carried out by measuring membrane potential, salt diffusion, and electrical parameters (membrane electrical resistance and capacitance) with the membrane in contact with NaCl and KCl solutions at different concentrations (10(-3)< or =c(M)< or =5 x 10(-2)). From these experiments characteristic parameters such as the effective concentration of charge in the membrane, ionic transport numbers, and salt and ionic permeabilities across the membrane were determined. Membrane electrical resistance and capacitance were obtained from impedance spectroscopy (IS) measurements by using equivalent circuits as models. This technique allows the determination of the electrical contribution associated with each sublayer; then, assuming that the dense sublayer behaves as a plane capacitor, its thickness can be estimated from the capacitance value. The influence of membrane asymmetry on transport parameters have been studied by carrying out measurements for the two opposite external conditions. Results show that membrane asymmetry strongly affects membrane potential, which is attributed to the Donnan exclusion when the solutions in contact with the dense layer have concentrations lower than the membrane fixed charge (X(ef) approximately -0.004 M), but for the reversal experimental condition (high concentration in contact with the membrane dense sublayer) the membrane potential is practically similar to the solution diffusion potential. The comparison of results obtained for both electrolytes agrees with the higher conductivity of KCl solutions. On the other hand, the influence of diffusion layers at the membrane/solution interfaces in salt permeation was also studied by measuring salt diffusion at a given NaCl concentration gradient but at five different solutions stirring rates.     

静电位阻模型在纳滤膜跨膜电位解析中的应用

采用静电位阻模型对纳滤膜的跨膜电位进行了理论解析, 考察了溶液体积通量密度、原料液浓度、阴阳离子扩散系数比、膜孔半径和膜体积电荷密度对KCl(1-1型电解质)和MgCl2(2-1型电解质)中的纳滤膜跨膜电位的影响. 研究结果表明, 随着通量密度的增大, KCl和MgCl₂的跨膜电位线性程度增强; 两种电解质的跨膜电位均随着原料液浓度和膜孔半径的增大而下降; 在不同的考察范围内, 阴阳离子扩散系数比对1-1型和2-1型电解质的跨膜电位的影响差别较大; KCl的跨膜电位随着膜体积电荷密度的变化关于零点呈现出对称性, 而MgCl₂的跨膜电位零点则出现在膜体积电荷密度为负的条件下.     

Asymmetric bipolar membrane: A tool to improve product purity

Bipolar membranes (BPMs) are catalytic membranes for electro-membrane processes splitting water into protons and hydroxyl ions. To improve selectivity and current efficiency of BPMs, we prepare new asymmetric BPMs with reduced salt leakages. The flux of salt ions across a BPM is determined by the co-ion transport across the respective layer of the membrane. BPM asymmetry can be used to decrease the co-ion fluxes through the membrane and shows that the change of the layer thickness and charge density of the corresponding ion exchange layer determines the co-ion flux. The modification of a commercial BP-1 with a thin additional cation exchange layer on the cationic side results in a 47% lower salt leakage. Thicker layers result in water diffusion limitations. In order to avoid water diffusion limitations we prepared tailor made BPMs with thin anion exchange layers, to increase the water flux into the membrane. Therefore a BPM could be prepared with a thick cation exchange layer showing a 62% decreased salt ion leakage through the cationic side of the membrane.     

Free-flow zone electrophoresis and isoelectric focusing using a microfabricated glass device with ion permeable membranes

This paper describes a microfabricated free-flow electrophoresis device with integrated ion permeable membranes. In order to obtain continuous lanes of separated components an electrical field is applied perpendicular to the sample flow direction. This sample stream is sandwiched between two sheath flow streams, by hydrodynamic focusing. The separation chamber has two open side beds with inserted electrodes to allow ventilation of gas generated during electrolysis. To hydrodynamically isolate the separation compartment from the side electrodes, a photo-polymerizable monomer solution is exposed to UV light through a slit mask for in situ membrane formation. These so-called salt-bridges resist the pressure driven fluid, but allow ion transport to enable electrical connection. In earlier devices the same was achieved by using open side channel arrays. However, only a small fraction of the applied voltage was effectively utilized across the separation chamber during free-flow electrophoresis and free-flow isoelectric focusing. Furthermore, the spreading of the carrier ampholytes into the side channels resulted in a very restricted pH gradient inside the separation chamber. The chip presented here allows at least 10 times more efficient use of the applied potential and a nearly linear pH gradient from pH 3 to 10 during free-flow isoelectric focusing could be established. Furthermore, the application of hydrodynamic focusing in combination with free-flow electrophoresis can be used for guiding the separated components to specific chip outlets. As a demonstration, several standard fluorescent markers were separated and focused by free-flow zone electrophoresis and by free-flow isoelectric focusing employing a transversal voltage of up to 150 V across the separation chamber.     

Anomalous diffusion governed by a fractional diffusion equation and the electrical response of an electrolytic cell

The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and negative ions have the same mobility and that the electric potential profile across the sample satisfies the Poisson's equation. The results cover a rich variety of scenarios, including the ones connected to anomalous diffusion.     

Study on transmembrane electrical potential of nanofiltration membranes in KCl and MgCl2 solutions

The transmembrane electrical potential (TMEP) across two commercial nanofiltration membranes (ESNA1-K and Filmtec NF) was investigated in KCl and MgCl(2) solutions. TMEP was measured in a wide range of salt concentrations (1-60 mol·m(-3)) and pH values (3-10) at the feed side, with pressure differences in the range of 0.1-0.6 MPa. A two-layer model based on the Nernst-Planck equation was proposed to describe the relation between TMEP and permeation flux. From the pattern of these curves, the information of membrane structure could be deduced. In the concentration range investigated, TMEP in KCl solutions was always positive and decreased as the salt concentration increased. The contribution of the membrane potential to the TMEP decreased. TMEP was greatly affected by the feed pH. When the feed pH increased, the mobility of cations increased, which indicated that the charges of NF membranes were more negative. The zero point of TMEP and the minimum of rejection in KCl solution were consistent and occurred at the isoelectric point of NF membranes, while in MgCl(2) solution the zero point of TMEP located at a higher pH value. The TMEP in MgCl(2) solutions changed its sign at a given concentration, and by calculating the transport number the location of the minimum rejection could be determined.     

Transport of Water and Ions Through a Clay Membrane

A model for hindered transport of water and ions is used to predict transient flow through a clay membrane caused by an initial difference in the concentration of salt solutions in reservoirs on the two sides of the membrane. Transport is assumed to be controlled by three coefficients, which are analogous to the permeability, salt diffusivity, and salt reflection coefficient of the membrane. Initial fluid motion is caused by osmosis, leading to a buildup of pressure on one side of the membrane. However, the clay forms an imperfect ion exclusion membrane and the final steady state is one of equal concentrations and pressures on the two sides of the membrane. The time-dependent differences in pressure and salt concentration across the membrane are predicted to vary as the sum of two decaying exponentials. When the salt reflection coefficient is small, one time scale governs Darcy flow through the membrane and another the diffusion of salt. Experimental results confirm the analysis. Although the salt concentration in the reservoirs was monitored in the experiments, estimates of the transport coefficients can be obtained by measuring only the pressure change across the membrane.     

Driving force for hydraulic and pervaporative transport in homogeneous membranes

Experiments were designed to demonstrate that the chemical potential gradient required for liquid transport through swollen network polymer membranes manifests itself as a concentration gradient and that the rate of transport is independent of how this gradient is established. The fluxes of various liquids through a crosslinked rubber membrane were measured in hydraulic and pervaporation modes of permeation. The pressure applied downstream in the latter act simply to fix the activity of the liquid in the downstream membrane surface. The experiments show the flux is a unique function of this activity, and it does not matter how it is established. Sorption data were used to convert these results into a plot of flux versus concentration differential across the membrane which was analyzed by Fick's law using a model for the concentration dependence of the diffusion coefficient. Measured ceiling fluxes for pervaporation for a number of liquids were found to be the same as those estimated from hydraulic permeation data. A simple mathematical representation for an ideal system is used as a pedagogical device to demonstrate the conclusions.     

Electrokinetic parameters of ion transport across isolated pepper cuticular membranes

The transport of NaCl and CaCl₂ solutions across isolated pepper cuticular membranes was studied by means of conductivity, membrane potential and diffusion experiments. Some characteristic membrane parameters such as the electrical resistance, ionic and salt permeabilities were obtained as a function of the electrolyte concentrations. Cuticle morphological asymmetry accounts for differences in membrane potential values under external reverse gradients. The influence of temperature on the membrane structure was also considered, but only small changes in the electrokinetic parameters were obtained. From the NaCl diffusion experiments two activation energies were determined (54.8 kJ/mol for temperature ranging between 15 and 35°C, and 20.6 kJ/mol for the interval of temperature between 40 and 60°C), which could be associated to thermal transitions in the molecular structure of the cuticle for the interval 30–40°C.     

Study on a novel antifouling polyamide–urea reverse osmosis composite membrane (ICIC–MPD): III. Analysis of membrane electrical properties

In this study, the electrical properties of the new polyamide–urea (ICIC–MPD) reverse osmosis composite membrane were analyzed via two self-made test cells. The electrical potential difference across membrane was measured via a perpendicular flow through mode potential difference measurement cell, and the electrical conductivity of membrane was tested by a tangential flow across mode conductivity measurement cell. Both streaming potential coefficient and gap between the upward and downward curves were determined by the plot of electrical potential difference versus up-loading and down-loading external pressure difference at both sides of membrane. It was found that pH of electrolyte solution has strong impact on streaming potential coefficient and electrical conductivity due to the dissociation of COOH group and protonation of NH₂ group of the active layer of ICIC–MPD membrane. It was also observed that both concentration of monomer 5-isocyanato-isophthaloyl chloride (ICIC) in the organic phase and contact time of organic phase with aqueous phase play an important role in salt rejection rate, gap between curves and electrical conductivity of the prepared ICIC–MPD membrane, and experimental results indicate that salt rejection rate of ICIC–MPD membrane is closely correlated to gap between curves at either polymerization condition. In addition, the effects of fouling behaviors on electrical potential difference and electrical conductivity of membrane were also discussed.     

Membrane potential across anion-exchange membranes in acidic solution system

The membrane potential across anion-exchange membranes in H2SO4 and Na2SO4 solutions was measured, and the experimental results were fitted to the theory in the 2-1 electrolyte system based on the Donnan equilibrium and the Nernst-Planck flux equations. For the Na2SO4 solution, the Donnan potential makes a significant contribution to the membrane potential, but for the H2SO4 solution, the diffusion potential significantly contributes to the membrane potential. The diffusion potential has a greater contribution to the membrane potential across AEM-2 with a high water content than that across AEM-1. These results suggest that a proton with a high mobility can move without substantial influence of electrostatic interaction in a positively charged membrane.     

Ion transport membranes based on conducting polymers

Polypyrrole membranes containing four different dopant ions were prepared galvanostatically from aqueous solutions of pyrrole (0.1 M) and the appropriate counter ion salt (0.1 M). The transport of mono-valent cations through each membrane was achieved by applying a potential gradient across the membranes. The influence of a number of set up parameters on the flux of K⁺ ions across a PPy/pTS membrane was assessed, as well as the relative selectivities of the four membrane types for the mono-valent cations; Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺.     

A mathematical study of sample modulation at a membrane inlet mass spectrometer—Potential application in analysis of mixtures

An ANSI C program that simulates the diffusion profiles of sample modulation at a membrane inlet system has been developed to study the characteristics of modulated diffusion profiles. The program produces concentration profiles within the membrane and flux values at the exit side of the membrane as a function of time. Sample concentration on the inlet side can be switched between zero and an arbitrary value with a square or asymmetric cycle. Achievement of steady-state diffusion between alternations is not required. With this computer simulation, the flux profiles of analytes through a membrane inlet have been studied as a function of diffusion coefficient, modulation frequency, and concentration. The amplitude, shape, and time lag or phase angle of the flux profile are shown to be related directly to analyte concentration and diffusivity. A method that involves a set of linear equations is proposed to resolve mixtures of diffusing analytes based on differences in the time dependence of their flux profiles.     

Simulation of flux during electro-membrane extraction based on the Nernst-Planck equation

The present work has for the first time described and verified a theoretical model of the analytical extraction process electro-membrane extraction (EME), where target analytes are extracted from an aqueous sample, through a thin layer of 2-nitrophenyl octylether immobilized as a supported liquid membrane (SLM) in the pores in the wall of a porous hollow fibre, and into an acceptor solution present inside the lumen of the hollow fibre by the application of an electrical potential difference. The mathematical model was based on the Nernst-Planck equation, and described the flux over the SLM. The model demonstrated that the magnitude of the electrical potential difference, the ion balance of the system, and the absolute temperature influenced the flux of analyte across the SLM. These conclusions were verified by experimental data with five basic drugs. The flux was strongly dependent of the potential difference over the SLM, and increased potential difference resulted in an increase in the flux. The ion balance, defined as the sum of ions in the donor solution divided by the sum of ions in the acceptor solution, was shown to influence the flux, and high ionic concentration in the acceptor solution relative to the sample solution was advantageous for high flux. Different temperatures also led to changes in the flux in the EME system.     

Simultaneous diffusion of ions and ion pairs across liquid membranes

The flux of tetrabutylammonium nitrate (Bu₄ NNO₃) across a liquid membrane of n-heptyl cyanide varies with the salt concentrations in dilute solution, but with the concentration squared in more concentrated solution. The results are consistent with a mechanism which includes parallel diffusion of ions and ion pairs. This type of behavior, which will be common in homogeneous membranes of low dielectric constant, is a form of facilitated diffusion in which the salt acts as its own carrier.     

Electrokinetic sample transport in a microchannel with spatial electrical conductivity gradients

Studies of the sample transport in a microchannel with the electrical conductivity gradient are critical to develop techniques for on-chip sample transport control. A numerical model presented in this paper, consisting of the electrical potential equation, full Navier-Stokes equation and species conservation equation, is used to simulate sample transport in a microchannel with the consideration of the conductivity gradient. There are two situations studied here, sample pumping (where sample separation is minimized by employing a high-conductivity buffer in the sample region), and sample stacking (where sample separation is expedited by using a low-conductivity buffer as the sample carrier). The effects of applied electrical potential, sample diffusion coefficient and the ratio of conductivity of the driving buffer over the sample carrying buffer are investigated by using the developed model.     

Transport of NaNO3 solutions across an activated composite membrane: electrochemical and chemical surface characterizations

Electrochemical characterization of two different samples of an activated membrane, which consists of a polymeric support containing different amounts of Di-(2-ethylhexyl) phosphoric acid as a carrier, was made by measuring the electrical resistance, salt diffusion and membrane potential for the activated membranes and the polymeric support in contact with NaNO₃ solutions. Transport parameters such as the ion transport numbers and concentration of fixed charge in the membrane, salt and ionic permeabilities at different NaNO₃ concentrations were obtained. A comparison of the different electrochemical parameters obtained with both activated membranes and the polymeric support shows how the carrier affects the transport of NaNO₃ solutions across the activated membranes. On the other hand, chemical composition of the membrane surfaces as a function of the amount of carrier was determined by X-ray photoelectron spectroscopy technique, which also allows an envisagement of the chemical bonding between the carrier and the membrane top layer (polyamide).     

Deformation effects on ionic transport in polymeric films

When a periodical deformation is applied to a cellophane film through which an ion flux is established by a concentration gradient, an electrical signal, synchronous with the deformation, can be detected on electrodes placed on both sides of the membrane. This signal was studied as a function of the amplitude and frequency of the deformation and the ionic concentration. Ionic resistance, permeability, water content and ionic concentration measurements were carried out in order to explain the particular dependence of the signal with the ionic concentration. © 1994 John Wiley & Sons, Inc.