A model equation for the gravielectric effect in electrochemical cells

The Role of the Gravitational Field in Generating Electric Potentials in a Double-Membrane System for Concentration Polarization Conditions

Electric potentials referred to as the gravielectric effect (∆ΨS) are generated in a double-membrane system containing identical polymer membranes set in horizontal planes and separating non-homogenous electrolyte solutions. The gravielectric effect depends on the concentration and composition of the solutions and is formed due to the gravitational field breaking the symmetry of membrane complexes/concentration boundary layers formed under concentration polarization conditions. As a part of the Kedem-Katchalsky formalism, a model of ion transport was developed, containing the transport parameters of membranes and solutions and taking into account hydrodynamic (convective) instabilities. The transition from non-convective to convective or vice versa can be controlled by a dimensionless concentration polarization factor or concentration Rayleigh number. Using the original measuring set, the time dependence of the membrane potentials was investigated. For steady states, the ∆ΨS was calculated and then the concentration characteristics of this effect were determined for aqueous solutions of NaCl and ethanol. The results obtained from the calculations based on the mathematical model of the gravitational effect are consistent with the experimental results within a 7% error range. It has been shown that a positive or negative gravielectric effect appeared when a density of the solution in the inter-membrane compartment was higher or lower than the density in the outer compartments. The values of the ∆ΨS were in a range from 0 to 27 mV. It was found that, the lower the concentration of solutions in the outer compartments of the two-membrane system (C0), for the same values of Cm/C0, the higher the ∆ΨS, which indicates control properties of the double-membrane system. The considered two-membrane electrochemical system is a source of electromotive force and functions as an electrochemical gravireceptor.

Evaluation of Transport Properties and Energy Conversion of Bacterial Cellulose Membrane Using Peusner Network Thermodynamics

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the R^r version of the Kedem-Katchalsky-Peusner formalism (KKP) for the concentration polarization (CP) conditions of solutions, the osmotic and diffusion fluxes as well as the membrane transport parameters were determined, such as the hydraulic permeability (L_p), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner (Rijr) coefficients resulting from the KKP equations to assess the transport properties of the membrane based on the calculated dependence of the concentration coefficients: the resistance, coupling, and energy conversion efficiency for aqueous ethanol solutions. The transport properties of the membrane depended on the hydrodynamic conditions of the osmotic diffusion transport. The resistance coefficients R11r, R22r, and Rdetr were positive and higher, and the R12r coefficient was negative and lower under CP conditions (higher in convective than nonconvective states). The energy conversion was evaluated and fluxes were calculated for the U-, F-, and S-energy. It was found that the energy conversion was greater and the S-energy and F-energy were lower under CP conditions. The convection effect was negative, which means that convection movements were directed vertically upwards. Understanding the membrane transport properties and mechanisms could help to develop and improve the membrane technologies and techniques used in medicine and in water and wastewater treatment processes.

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential (Δψs) generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations (Ci/Ce) at the membrane/concentration boundary layers. We present the calculation procedure (Ci/Ce) based on novel equations derived in the paper containing the transport parameters of the membrane (Lp, σ, and ω), solutions (ρ, ν), concentration boundary layer thicknesses (δl, δh), concentration Raileigh number (RC), concentration polarization factor (ζs), volume flux (Jv), mechanical pressure difference (ΔP), and ratio of known solution concentrations (Ch/Cl). From the resulting equation, Δψs was calculated for various combinations of the solution concentration ratio (Ch/Cl), the Rayleigh concentration number (RC), the concentration polarization coefficient (ζs), and the hydrostatic pressure difference (ΔP). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m⁻³ (Cl) was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m⁻³ (Ch). It is shown that (Δψs) depends on the value of one of the factors (i.e., ΔP, Ch/Cl, RC and ζs) at a fixed value of the other three.

Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia

The results of experimental studies of volume osmotic fluxes (Jvkr) and fluxes of dissolved substances (Jkr) in a system containing a synthetic Nephrophan® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions Jvk and Jk depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), Jvkr and Jkr depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the Jvk and Jk flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (ΦSk), while Jvkr and Jkr-to assess the global production of entropy for concentration polarization conditions (ΦSkr). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient ζir was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

The Investigation of Time-dependent Solute Transport through Horizontally Situated Membrane: The Effect of Configuration Membrane System

This paper presents an experimental and theoretical investigation ofsolute transport through a horizontally situated membrane. Theexperimental investigation was carried out by the laserinterferometric method in association with a computer system ofinterference image analysis. On the basis of this analysis thicknessof near-membrane layers, solution concentration drops on these layersas well as diffusion fluxes of diluted substance are determined.Different fluxes of the soluble substance are observed depending onthe configuration of the system. The results of the experimental andtheoretical investigation of diffusion fluxes are conformable inrespect of measurement error, with one adjustment parameter, i.e. thesolute partition coefficient.

Membrane Transport Generated by the Osmotic and Hydrostatic Pressure. Correlation Relation for Parameters L(p), σ, and ω

Standard approach to membrane transport generated by osmotic andhydrostatic pressures, developed by Kedem and Katchalsky, is based onprinciples of thermodynamics of irreversible processes. In this paper wepropose an alternative technique. We derive transport equations from fewfairly natural assumptions and a mechanistic interpretation of the flows.In particular we postulate that a sieve-type membrane permeability isdetermined by the pore sizes and these are random within certain range.Assuming that an individual pore is either permeable or impermeable tosolute molecules, the membrane reflection coefficient depends on the ratioof permeable and impermeable pores. Considering flows through permeableand impermeable pores separately, we derive equations for the total volumeflux, solute flux and the solvent flux across the membrane. Comparing themechanistic equations to the Kedem-Katchalsky equations we find the formereasier to interpret physically. Based on the mechanistic equations we alsoderive a correlation relation for the membrane transport parameters L(p),σ, and ω. This relation eliminates the need for experimentaldetermination of all three phenomenological parameters, which in somecases met with considerable difficulties.

Gravitational effects in a passive transmembrane transport: the flux graviosmotic and gravidiffusive effects in non-electrolytes

In this paper the classification ofthe gravitational effects in a passive transmembranetransport is presented. Among these effects there arethe flux and force gravitational effects (fluxgraviosmotic effect, osmotic pressure graviosmoticeffect, flux gravidiffusive effect, osmotic pressuregravidiffusive effect, voltage gravielectric effectand current gravielectric effect). The volume fluxgraviosmotic and solute flux gravidiffusive effectsmodel equations for a single-membrane system areelaborated. These models for binary and ternarynon-electrolyte solutions have been verified using anexperimental data volume and solute fluxes forosmotic-diffusion cell with horizontally mountedmembrane. In the experimental set-up, water was placedon one side of the membrane. The opposite side of themembrane was exposed to binary or ternary solutions ofdensities greater than that of water (aqueous glucoseor glucose-0.2 mole/l aqueous ethanol) and binary andternary solutions of densities larger than that ofwater (aqueous ethanol or ethanol-0.05 mole/l aqueousglucose). These experimental results are interpretedin terms of the convective instability that increasesthe diffusive permeability coefficient of junction:boundary layer/membrane/boundary layer.

Thermodynamic model equations for heterogeneous multicomponent non-ionic solution transport in a multimembrane system

Non-equilibrium thermodynamic model equations for non-ionic and heterogeneous n-component solution transport in a m-membrane system are presented. This model is based on two equations. The first one describes the volume transport of the solution and the second the transport of the solute. Definitions of the hydraulic permeability, reflection and diffusive permeability coefficients of the m-membrane system and relations between the coefficients of the m-membrane system and the respective membranes of the system are also given. The validity of this model for binary and ternary solutions was verified, using a double-membrane cell with a horizontally mounted membrane. In the cell, volume and solute fluxes were measured as a function of concentration and gravitational configuration.

A model equations of the volume transport of multicomponent and heterogeneous non-ionic solutions in double-membrane system

The volume flows model equation for a double-membrane system, in which two membranes separate three compartments (l,m,r) containing the heterogeneous, non-ionic n-component solutions is elaborated. In this system the solution concentrations fulfill the condition Clk > Cmk > Crk. The inter-membrane compartment (m) consists of the infinitesimal layer of solution. The volume of compartment m and external compartments (l and r) fulfill the conditions Vm→ 0 and Vl =Vr→∞ respectively. The linear dependences of the volume flux on concentration differences in binary solutions and nonlinear - in ternary solutions, were obtained. This model for binary and ternary non-electrolyte solutions is discussed. It is shown, that the double-membrane system has rectifying and amplifying properties for osmotic transport and mechanical pressure.