Nemst film

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. 

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

In this presentation we, therefore, investigate the kinetics of ion exchange in such mixtures for the case vdiere diffusion of the ions across a hydrostatic boundary layer (Nemst film) surrounding the particles is the rate controlling step (film diffusion). In well-stirred systems, liquid-phase mass transfer will usually be fevored by a low concentration of the external solution, a high ion-exchange capacity, and a small particle size [I]-... 

Figure 1. Diagrammatic Representation of Nemst Films that Form at Membrane Interfaces, (a) One-, (b) two-, and (c) three-film models are represented. (Reproduced with permission from ref. 31. Copyright 1990 CRC Press.)...

Diffusion. The barriers to transport imposed by the need for diffusion across Nemst films can be minimized by decreasing film thickness or by increasing the mobility of the diffusible species. Rim thickness, up to a certain limiting value (10 to 10 cm) is inversely related to mechanical energy supplied (e.g. by stirring) (30). Viscosity and density of the liquids used as well as equipment geometry also affect film thickness (52), but interfacial films apparently cannot be completely eliminated. 

Mach-Zehnder interferometers allow the monitoring of gas concentrations and even the determination of analytes in liquids. Normally one of the measurement arms is covered with a thin polymer film into which the analyte can sorp. According to Nemst s distribution law, we have an equilibrium between the mobile and the stationary phase if a gas or a liquid pass the measurement window . Figure 12 shows a variety of results. 

Many metal oxides are insulators. In these cases oxidation can only occur if charge neutrality is maintained by way of a significant counterdiffusion of cations and anions (Fig. 5.22e). Once again, mobilities will be equalized by the Nemst field set up when one species moves faster than the other. When counterdiffusion of ions is involved, the oxide film grows at both the inner and outer surfaces. 

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

Since the solid—solid interface and bulk of the mixed conductor remain in chemical and electrical equilibrium, the measured overpotential t] is related directly to the spatially uniform oxidation state of the film through the Nemst equation 4Ft] = RTf d — (3o). Solving for d( and recognizing that the impedance Z = rjU, one obtains... 

When a biocatalyst is immobilized on or within a solid matrix, mass transfer effects may exist because the substrate must diffuse from the bulk solution to the immobilized biocatalyst. If the biocatalyst is attached to non-porous supports there are only external mass transfer effects on the catalytically active outer surface in the reaction solution, the supports are surrounded by a stagnant film and substrate and product are transported across this Nemst layer by diffusion. The driving force for this diffusion is the concentration difference between the surface and the bulk concentration of substrate and product. 

Process models Nemst dielectrics (1894) Warburg diffusion (1901) Finkelstein Solid film (1902) Randles double layer and diffusion impedance (1947) Gerischer two heterogeneous steps with adsorbed intermediate (1955) De Levie porous electrodes (1967) Schuhmann homogeneous reactions and diffusion (1964) Gabrielli generalized impedance (1977) Isaacs LEIS (1992)... 

Within the Nemst hypothesis, the diffusion impedance is assumed to be that for a stagnant film of effective thickness that is related to velocity by... 

In actual ion exchange, the conmerdiffusing ions possess different mobilities, For a quantitative treatment. Pick s Law bes to be replaced by the Nemst-Planck equation which allows both purticle and film diffusion kinetics in exchanging ideal systems to be described ... 

---