Back diffusion, quantitative

In an early study by Schery and Gaeddert (1982), an accumulator device was used to measure the effect of atmospheric pressure variations on the flux of Radon (222Rn), an inert radioactive element with a half-life of 3.8 days, from the soil. Fluxes measured by the accumulator were compared with predictions for flow-free diffusion from a model developed by Clements and Wilkening (1974), which applies Fick s law. A mean 222Rn-flux enhancement of about 10%, with a high value of 20%, due to cyclic atmospheric pressure variations was observed. However, the device s effectiveness was limited by back diffusion from the accumulator to the subsurface, leading the authors to view the flux values as semi-quantitative. 

Most of the charge is distributed between the two back-to-back, diffuse layers, hence the relatively good agreement with the Gouy-Chapman theory which when examined closely appears more qualitative than quantitative. 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

Divisek et al. presented a similar two-phase, two-dimensional model of DMFC. Two-phase flow and capillary effects in backing layers were considered using a quantitatively different but qualitatively similar function of capillary pressure vs liquid saturation. In practice, this capillary pressure function must be experimentally obtained for realistic DMFC backing materials in a methanol solution. Note that methanol in the anode solution significantly alters the interfacial tension characteristics. In addition, Divisek et al. developed detailed, multistep reaction models for both ORR and methanol oxidation as well as used the Stefan—Maxwell formulation for gas diffusion. Murgia et al. described a one-dimensional, two-phase, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymer membrane for a liquid-feed DMFC. 

We, therefore, obtain the important conclusion that the increase in interfacial area is directly proportional to total strain. Hence, total strain becomes the critical variable for the quantitative characterization of the mixing process. We further conclude from Eq. E7.1-15 that at low strains, depending on the initial orientation, the interfacial area may increase or decrease with imposed strain. This implies clearly that strain may demix as well as mix two components. Indeed if the fluid is sheared in one direction a certain number of shear units, an equal and opposite shear will take the fluid back to its original state (no diffusion). 

The first qualitative observation of vacancy-induced motion of embedded atoms was published in 1997 by Flores et al. [20], Using STM, an unusual, low mobility of embedded Mn atoms in Cu(0 0 1) was observed. Flores et al. argued that this could only be consistent with a vacancy-mediated diffusion mechanism. Upper and lower limits for the jump rate were established in the low-coverage limit and reasonable agreement was obtained between the experimentally observed diffusion coefficient and a theoretical estimate based on vacancy-mediated diffusion. That same year it was proposed that the diffusion of vacancies is the dominant mechanism in the decay of adatom islands on Cu(00 1) [36], which was also backed up by ab initio calculations [37]. After that, studies were performed on the vacancy-mediated diffusion of embedded In atoms [21-23] and Pd atoms [24] in the same surface. The deployment of a high-speed variable temperature STM in the case of embedded In and an atom-tracker STM in the case of Pd, allowed for a detailed quantitative investigation of the vacancy-mediated diffusion process by examining in detail both the jump frequency as well as the displacement statistics. Experimental details of both setups have been published elsewhere [34,35]. A review of the quantitative results from these studies is presented in the next subsections. 

A quantitative description for the diffuse layer dates back to Gouy [40] and Chapman [41]. This model is fully described elsewhere [42], and we shall here only outline basic features of the theory. The first stage in this approach is to use the Poisson equation. Eq. (I), to describe the relationship between the electrical potential 4>(.v) and the charge density p of ions of charge at a distance v from a flat charged surface, with a regional permittivity f ... 

A major breakthrough in the study of gas and v or transport in polymer membranes was achieved by Daynes in 1920 He pointed out that steady-state permeability measurements could only lead to the determination of the product EMcd and not their separate values. He showed that, under boundary conditions which were easy to achieve experimentally, D is related to the time retired to achieve steady state permeation throu an initially degassed membrane. The so-called diffusion time lag , 6, is obtained by back-extrapolation to the time axis of the pseudo-steady-state portion of the pressure buildup in a low pressure downstream receiving vdume for a transient permeation experiment. As shown in Eq. (6), the time lag is quantitatively related to the diffusion coefficient and the membrane thickness, , for the simple case where both ko and D are constants. 

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