Steady state migration fluxes

The anions, which are not involved in the reaction v = 0, should not move in the steady state [i.e., in Eq. (4.17), J = 0]. This implies that the diffusional component of their flux to the surface should be fully compensated by a migration component away from the surface (Fig. 4.3). 

Assuming that the subsurface conditions are isothermal and isochemical and the migration system is in steady state, the flux of separate phase hydrocarbon migration at a certain location may be estimated from Equation 4.18. For hydrostatic conditions, the generalized Darcy equation 4.18,... 

Equation (8) indicates that the current measured at the SECM tip, it(z = 0), is directly proportional to ft. At steady state, mass continuity requires that the rate of transport from the pore into the receptor compartment be equal to the rate of transport within the pore. Thus, it(z = 0) is also proportional to the rate of transport at any point within the pore. The molecular flux in the pore, N, is obtained by simply dividing ft by the cross-sectional area of the pore. Note that in deriving Eq. (8), no restrictions have been placed on the mechanism of transport within the pore. Thus, it(z = 0) is proportional to the flux in the pore, independent of whether the flux is due to diffusion, migration, or convection. It can be shown that the tip current at any arbitrary separation distance, z, is also proportional to the flux in the pore. 

Steady State Migration Fluxes in Multicomponent Electrolytes and the Central Problem with Closed Circuit Theory... 

Here, is the mobility, that is, the steady state velocity under unit force per particle, corresponding to a change of chemical potential per particle by unit energy for a displacement of unit length. Further Np is Avogadro s number, e is the electronic charge, and Zi the electrical valence of a particle of type i. It follows that the flux in moles migrating per unit cross-section A per unit time equals ... 

The steady-state flux of hydrated protons in the agglomerate is due to diffusion and migration in the internal electric field. It is dictated by the Nernst-Planck equation, with a sink term, ip, due to electrochemical reactions at the dispersed Pt water interfaces. 

Relative contributions of the migration and diffusion molar flux densities at steady state... 

The transient period also denotes a change in the distribution between the migration and diffusion processes. At steady state, an equal distribution has been achieved, as already demonstrated above based on the assumption that the Nernst-Einstein equation applies. Figure A.20 illustrates this phenomenon by showing the changing curves for the diffusion and migration molar flux densities ratio for Ag", throughout the electrolyte. 

Advection and diffusion in the cap materials are subject to retardation by transient sorption as is contaminant migration in groundwater. Under steady conditions, sorption does not influence the flux of contaminants through the cap materials. Thus, the steady-state fluxes (rates per unit area) of diffusion and advection in the cap are given simply by... 

When the solution contains supporting electrolyte, the contribution of migration to mass transfer is small. Hence, the flux, v, or the current density, /, is a result of diffusion, since the charge-transfer step is considered to be fast. The concentration at the cathode surface. Cs, decreases under the.se conditions as shown in Fig. 4.2.5. Assuming a linear distribution of concentration in the diffusion layer thickness 5. we have, at steady. state ... 

This equation has been seen previously, it bears a marked similarity to Eqn 68, which described the steady-state diffusion/migration flux. Now the average energy change per unit displacement of the electron... 

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