Eliminated diffusion boundary layer

When van der Waals and double-layer forces are effective over a distance which is short compared to the diffusion boundary-layer thickness, the rate of deposition may be calculated by lumping the effect of the particle-collector interactions into a boundary condition on the usual convective-diffusion equation. This condition takes the form of a first-order irreversible reaction (10, 11). Using this boundary condition to eliminate the solute concentration next to the disk from Levich s (12) boundaiy-kyersolution of the convective-diffusion equation for a rotating disk, one obtains... 

For many systems, the diffusion steps are rate determining. The barriers to transport imposed by the need for diffusion across boundary layers can be minimized by decreasing film thickness, or by increasing the mobihty of the diffusible species. Film thickness, up to a certain hmiting value, is inversely related to mechanical energy supphed (e.g., by stirring) [45]. Viscosity and density of the liquids used as well as equipment geometry also affect film thickness [46] but interfacial films apparently cannot be completely eliminated. 

External mass transfer, such as diffusion to particles or to the outside of pipes or cylinders, requires different correlations from those for internal mass transfer, because there is boundary-layer flow over part of the surface, and boundary-layer separation is common. The mass-transfer coefficients can be determined by studying evaporation of liquid from porous wet solids. However, it is not easy to ensure that there is no effect of internal mass-transfer resistance. Complications from diffusion in the solid are eliminated if the solid is made from a slightly soluble substance that dissolves in the liquid or sublimes into a gas. This method also permits measurement of local mass-transfer coefficients for different points on the solid particle or cylinder. 

This is a product of the ratio of the mobility of ion A to that of ion B in the membrane phase and the selectivity coefficient of ion A to ion B. In electrodialysis, diffusion boundary layers are formed at membrane surfaces, where the concentration at the membrane surfaces is not the same as that of the bulk solution. To obtain the real PAB of the ion exchange membrane, the diffusion boundary layer should be eliminated by vigorous agitation of the solution, which corresponds to the limiting value at zero current density,... 

Because there is a concentration difference across the ion exchange membrane in practical electrodialysis, the transport number (current efficiency) in the presence of the concentration difference is required. When the current efficiency (dynamic state transport number) is measured in the presence of a concentration difference, the current efficiency in the absence of the concentration difference may be basically obtained by subtracting the amount of electrolyte diffusing through membrane from the measured current efficiency. In all cases, when the transport number is measured, the solutions in both compartments should be vigorously agitated to eliminate the effect of diffusion boundary layers on the transport number. 

For dense and highly dense membranes, the measuring apparatus and method should be improved.56 A plastic support for the membrane may be used to prevent it bending. Solutions at both sides are agitated to eliminate the effect of diffusion boundary layers on the potential. The generated potential is measured with a potentiometer or high impedance voltmeter. 

If the mixing is so vigorous that the diffusion boundary layer can be eliminated, Eq. 

Thin-layer chromatography (TLC) is another liquid-liquid partition technique applicable to polysaccharides, but in two dimensions. In TLC, the M cutoff boundaries between separated molecules are sharpened, because diffusion is minimized or eliminated in favor of capillary transport. The sample capacity of a TLC plate is in microliters. Resolution is enhanced further at high solvent pressure (Rombouts and Thibault, 1986). 

Instantaneous diffusion oo-approach) model assumes that the catalyst is virtually distributed at the gas/washcoat interface so that there is infinitely fast mass transport within the washcoat. This model eliminates the washcoat parameters, such as its thickness and porosity, and the diameters of the inner pores. Therefore, oo-approach does not account for internal mass transport limitations that are due to a porous layer. It means that mass fractions of gas-phase species on the surface are obtained by the balance of production or depletion rate with diffusive and convective processes (Deutschmann, 2008 Kee et al., 2001 Wamatz, 1992). Thus, the net production rate of each chemical species due to surface reactions can be balanced with the diffusive flux of that species at the gas-surface boundary, assuming that no deposition or ablation of chemical species occurs on/from the catalyst surface ... 

The authors also studied both the diffuse reflection spectrum and the photochemical behavior of the deposited films. The efficiency of cathodic photocurrent production was dependent on the deposition potential. The efficiency peaked at a deposition potential of -0.40 volts. The authors attributed this to the presence of excess Te at potentials more positive than -0.40 volts and to the n-type character of the CdTe at potentials more negative than -0.40 volts. The effects of heat treatment and etching were also studied. Heat treatment improved the photocurrent due to the increased grain size which eliminated grain boundaries. Etching had the effect of removing the surface layer of Te and improving photocurrents. 

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