Concentration diffusion

Pick s Second Law relates the change in diffusant concentration with time, dC/dt, to the change in concentration gradient at a given point in the membrane ... 

The ability of any experimental method to produce accurate and reproducible results and provide the sensitivity needed to discern differences between transport mechanisms depends on minimizing variability intrinsic to the method. However, formal error analysis is rarely undertaken, even for commonly used methods. Fawcett and Caton [45] performed an error analysis of the capillary method for determining diffusion coefficients more than 25 years after the method was introduced. The value of the analysis is that it reveals which factors contribute the greatest variability to the dependent variable of interest. In the case of transport studies, the dependent variable of primary interest is diffusant concentration, C(t), where... 

FIGURE 10.8 Profiles of the relative oxygen diffusion-concentration product across the DMPC bilayer containing 0 (O) and 10mol% zeaxanthin ( ) at 25°C. The approximate locations of nitroxide moieties of spin labels are indicated by arrows. The value of the oxygen diffusion-concentration product in water can be obtained from the oxygen diffusion coefficient and oxygen concentration in water equilibrated with air at 25°C. (From Subczynski, W.K. et al., Biochim. Biophys. Acta, 1068, 68, 1991. With permission.)... 

Subczynski, W. K., E. Markowska, and J. Sielewiesiuk. 1991. Effect of polar carotenoids on the oxygen diffusion-concentration product in lipid bilayers. An EPR spin label study. Biochim. Biophys. Acta 1068 68-72. 

It is useful to point out here that we frequently encounter partial steady-states. An important example is the case where the diffusion process is much faster than a surface process, and thus a quasi-steady-state is reached for the diffusion concentration profile at each changing concentration of the surface. This distinction between different timescales of the processes can lead to a significant simplification of complex problems, see end of Section 4.3 or Chapter 4 in this volume. 

Fig. 7.35. Development of diffusion concentration profiles in ensembles of microelectrodes. Concentration distortions at very short times during chronoamperometry or fast sweep rates during (a) cyclic voltammetry, (b) intermediate times or sweep rates, and (c) long times or slow sweep rates. Voltam-metric responses are shown schematically. (Reprinted from B. R. Scharifker, Microelectrode Techniques in Electrochemistry, in Modem Aspects of Electrochemistry, Vd. 22, J. O M. Bockris, B. E. Conway, and R. E. White, eds., Plenum, 1992, p. 505.)...

Equation (1.57a) implies that in the locally electro-neutral ambipolar diffusion concentration of both ions evolves according to a single linear diffusion equation with an effective diffusivity given by (1.57b). Physically, the role of the electric field, determined from the elliptic current continuity equation... 

The serum-protein binding ability, which varies between animals and is also influenced by the disease state of the animal, will also determine the free diffusible concentration. This, in turn, will have an effect on the elimination of drug residues as well as on their penetration in eggs or milk. This effect will be more pronounced for drugs with a higher tendency for protein binding such as sulfonamides, doxycycline, and cloxacillin (47). 

Figure 9.8 Isolated-boundary (Type-B) self-diffusion associated with a stationary grain boundary, (a) Grain boundary of width 6 extending downward from the free surface at y = 0. The surface feeds tracer atoms into the grain boundary and maintains the diffusant concentration at the grain boundary s intersection with the surface at the value cB(y = 0, t) = 1. Diffusant penetrates the boundary along y and simultaneously diffuses transversely into the grain interiors along x. (b) Diffusant distribution as a function of scaled transverse distance, xi, from the boundary at scaled depth, yx, from the surface. Penetration distance in grains is assumed large relative to 5.

Here, d is the average grain size of the columnar grains, JB is the diffusional flux along the grain boundaries, dcB/dx = [cs(0) —cB(l)] /l, where cs(0) and cB(l) are the diffusant concentrations in the boundaries at the source surface and accumulation surface, respectively, and l is the specimen thickness. In the early stages, cB(l) 0 and, therefore, to a good approximation,... 

D concentration independent average diffusion coefficient Dc o diffusion coefficient at zero diffusant concentration... 

If C and Co are the ionic concentrations of metal in the solution of the element-collector and in the surrounding environment respectively, then metal ions pass through the membrane as a result of (1) diffusion (concentration difference C-Co), (2) migration in the external electric field with strength E and (3) migration in the internal electric field with strength Edi. Putikov (1993) shows that the differential equation for the metal concentration C in the element-collector is. 

In the interruption test (Kressman and Kitchener, 1949), the ion exchanger is temporarily separated from the liquid. If the rate is controlled by mass transfer in the liquid, the rate upon reimmersion is the same as at the time of separation, the quasi-stationary state in the film is very quickly re-established. If the rate is controlled by intraparticle diffusion, concentration gradients within the particle have time to relax, and the rate is faster upon reimmersion. This comparison is independent of specific mechanisms and algebraic forms of rate laws. 

Xsn is the solvent-polymer interaction parameter for a solvent concentration of s. We will assume that the concentrations 4>s and < )p are much larger than the diffusant concentration (i so that Xs and Xp can be replaced by Xs and Xp. In this limit... 

Philip, J.R. 1955. Numerical solution of equations of the diffusion type with diffusivity concentration-dependent. Trans. Faraday Soc. 51 885-892. 

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