Electro-diffusion convective

What are the mechanisms and the transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electro-osmotic drag) ... 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

Preliminaries. This entire chapter is devoted to one physical phenomenon—electro-osmotic (Teorell) oscillations. As opposed to phenomena discussed in previous chapters, electro-convection will be of importance here in its interaction with electro-diffusion. 

Generalized local Darcy s model of Teorell s oscillations (PDEs) [12]. In this section we formulate and study a local analogue of Teorell s model discussed previously. The main difference between the model to be discussed and the original one is the replacement of the ad hoc resistance relaxation equation (6.1.5) or (6.2.5) by a set of one-dimensional Nernst-Planck equations for locally electro-neutral convective electro-diffusion of ions across the filter (membrane). This filter is viewed as a homogenized aqueous porous medium, lacking any fixed charge and characterized... 

EMCPMT models wifi be described that can simulate transient electro-mechano-chemo diffusion, convection, and osmosis in one-dimensional FEMs composed of one and/or multiple layers of porous material with prescribed no(Xi) and FCD, < [ (X,) in the solid. The left (L) and right (R) interfaces are water baths containing prescribed concentrations of up to three charged species (p, m, b). Mechanical force (stress) or displacement fluid pressure, and electrical potential will also be prescribed on these interfaces. The first example is... 

Concentration resistance, Rconc- The third factor determining the nature of the deposit is mass transport. The corresponding resistance is referred to as the concentration resistance, Rconc, which results from the depletion of the electro-active species at the cathode surface, caused by mass-transport limitation. The mechanism of mass transport of the electro-active species (either charged or uncharged) could be diffusion, convection or migration, or some combination of these mechanisms. For the simple onedimensional case (corresponding to semi-infinite linear diffusion) at steady state, the rate of mass transport, expressed as the current density, can be written as... 

To take into account the role of surface-active species the transport equations in the bulk and at surfaces for each of them (i = 1,2,...,AO are studied (Dukhin et al. 1995, Danov et al. 1999). In the bulk the change of concentration, C/, is compensated by the bulk diffusion flux, j bulk convective flux, C/V, and rate of production due to chemical reactions, (see Fig. 1). The bulk diffusion flux includes the flux driven by external forces (e.g. electro-diffusion), the molecular diffusive and thermodiffusion fluxes. The rate of production, r/,... 

Many practical processes (foaming, emulsification, dispersing, wetting, washing, solubilization) are influenced by the rate of adsorption from surfactant solutions. This rate depends on whether the adsorption takes place under diffusion, electro-diffusion, barrier, or convective control. The presence of surfactant micelles, which serve as carriers, and a reservoir of surfactants can strongly accelerate the kinetics of adsorption see Secs. 

Valdes models the electro-deposition of Brownian particles on a RDE, by solving the steady-state convective diffusion equation ... 

A fundamental fuel cell model consists of five principles of conservation mass, momentum, species, charge, and thermal energy. These transport equations are then coupled with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. Such convection—diffusion—source equations can be summarized in the following general form... 

This technique represents the transposition of classical polyacrylamide or agarose gel electrophoresis into a capillary. Under these conditions, the electro-osmotic flow is relatively weak. In this approach, the capillary is filled with an electrolyte impregnated into a gel that minimises diffusion and convection phenomena. In contrast to its use for proteins that are fragile and thermally unstable, CGE is ideal for separating the more rugged oligonucleotides. 

In PEMFC systems, water is transported in both transversal and lateral direction in the cells. A polymer electrolyte membrane (PEM) separates the anode and the cathode compartments, however water is inherently transported between these two electrodes by absorption, desorption and diffusion of water in the membrane.5,6 In operational fuel cells, water is also transported by an electro-osmotic effect and thus transversal water content distribution in the membrane is determined as a result of coupled water transport processes including diffusion, electro-osmosis, pressure-driven convection and interfacial mass transfer. To establish water management method in PEMFCs, it is strongly needed to obtain fundamental understandings on water transport in the cells. 

This section analyzes the response of a charge transfer process under conditions of finite linear diffusion which corresponds to a thin layer cell. This type of cell can be achieved by miniaturization process for obtaining a very high Area/Volume ratio, i.e., a maximum distance between the working and counter electrodes that is even smaller than the diffusion layer [31], In these cells it is easy to carry out a bulk electrolysis of the electroactive species even with no convection. Two different cell configurations can be described a cell with two working electrodes or a working electrode versus an electro-inactive wall separated at distance / (see Fig. 2.23). 

Equation (13.19) also makes another aspect clear, the parameters that one has to attempt to optimize in electrochemical energy converters. Inspection of Eq. (13.19) and Figs. 13.5 and 13.8 shows that ideal reversible behavior will be approached when iQ and iL are very large and the internal electrolyte resistance of the cell is small. The maximization of iL is a matter of designing and engineering cells to which the diffusion and convection of ions most easily occurs (see Section 13.5.1). To reduce Rt, electro-... 

Norden, A., and A. Lodding Self-Transport, Electro Convection and Effective Self-Diffusion in Liquid Rubidium Metal. Z. Naturforsch. 22 a, 215 (1967). 

A similar development was provided by Tribollet and Newman for electro-hydrodynamic impedance. The use of look-up tables facilitates regression of models to experimental data that take full accoimt of the influence of a finite Schmidt number on the convective-diffusion impedance. Use of only the first term in equation (11.97) yields a numerical solution for an infinite Schmidt number. Tribollet and Newman report use of the first two terms in equation (11.97) The low level of stocheistic noise in experimental data justifies use of the three-term expansion reported here. 

Proteins may be eluted from gels by diffusion, solvent convection or electro-elution. 

To explain these phenomena, it is necessary to consider the transient solutions of the ion flux equations for constant current. For simplicity we assume perfect solution laws (ion activity coefficients unity), a completely anion-selective membrane (transport number of anions in the membrane unity), and constant temperature, and neglect electro-osmotic water transport. We also assume linear geometry and a stationary diffusion layer of thickness 8 close to the membrane, beyond which the concentration remains essentially constant. Convection in the diffusion layer (2-4) is assumed to be negligible. 

Kim and Pivovar [4] remarked that, at constant current density, 5 is the parameter that determines the relative contribution of diffusion and electroosmotic to alcohol crossover because diffusion flux is depending of the membrane thickness, while electro-osmotic drag is not. Therefore, the thinner the membrane, the lower the electro-osmotic contribution, and the current density for having roughly equal diffusion and convection contribution to crossover is 4 times higher in Nalion 112 (8 = 50 pm) as compared to Nafion 1 (5 = 178 pm). 

---