Migration term

The factor B = D/RT is the mobility and contains the diffusion coefficient D, the gas constant R, and the absolute temperature T. The equation includes a diffusion and a migration term. Correspondingly Eq. (2-23) gives the first diffusion law for Zj = 0 and Ohm s Law for grad /i, = 0. For transfer across a phase boundary ... 

Taranenko, N.F. (1964). Fat content of Azov anchovy as an index of reproductive capacity of the fish stock and the migration term (In Russian). Trudy Azovsko-cher-nomorskogo Nauchno-issledovatelnogo Instituta morskogo Rybno Khozyaistva i Oceanografii 22,137-147. 

Again, a lateral transport process of c is neglected because the corresponding term in Eq. (54b) would be by far smaller than the migration term in Eq. (54a) and thus is insignificant for spatiotemporal solutions [14]. 

This is termed a Nernst potential, as the expression is simply the Nernst equation for the one electron redox couple. Again, this driving potential tells us about the combination of the diffusional and migrational terms. 

The particle current, I, can be expressed as the sum of diffusion and migration terms in v space (Chapter 9) ... 

Cyclic enones, such as substituted cyclohex-2-enones or cyclohexa-2,5-diones, also undergo sigmatropic photorearrangement to form bicyclo[3.1.0]hexanones (lumiketones) or bicyclo[3.1.0]hex-3-en-2-ones, respectively, for which both concerted and stepwise (biradical) reaction mechanisms have been proposed.640,641,770 For example, a [l,2]-shift concurrently with the ring contraction (termed the type A reaction) is observed upon irradiation of the methylphenyl derivative 159 in polar solvents, whereas phenyl migration (termed the type B reaction) predominates in nonpolar solvents (Scheme 6.70).771,772 The reactions are believed to proceed via both the n,n and n,Tt triplet ketone states. In the presence of alkenes, cyclic enones may readily undergo a competitive photocycloaddition reaction (Section 6.1.5). 

For the case of a binary electrolyte (i.e., a single salt that dissociates in solution into one cation and one anion species), we can rewrite the molar flux equations for positive and negative ions in terms of a salt concentration gradient diffusion term, a migration term explicit in the current density (as opposed to the VO driving force term in Equation (26.54)), and a bulk convection term ... 

First models have been derived by Dukhin et al. [27, 28, 30, 101], and Borwankar and Wasan [102]. They used a quasi-equilibrium model by assuming that the characteristic diffusion time is much greater than the relaxation time of the electrical double layer, and thus, the complicated electro-diffusion problem is reduced to a simply transport problem. Datwani and Stebe [103] analysed this model and performed extensive numerical calculations, however, they did not include the electro-migration term into the diffusion equation so that the results are not relevant for further discussions. 

U in Eq. (81) represents the difference between the migration term and the convective term. Hence, with thick separators, U is greater than zero since the convective flow is very small and the COH versus x behavior is convex. When U < O, the COh versus x curve is concave as shown in Fig. 17, which is the pattern observed in... 

When convection occurs, the overall convection current density is zero (see section 4.2.1.5). Therefore, when expressing the overall current density in a zone where diffusion can be disregarded, only the migration terms are to be taken into consideration. 

Refer to section 4.2.1 which describes the macroscopic laws of conduction, and in particular, migration terms. 

The migration term, once extracted from the first equation, then replaced in the second equation, is therefore removed to obtain the following simple equation ... 

As for the migration terms, a link Is also made between the migration molar flux densities of the two Ions at all points, since the electric field Is the same for both ions ... 

The mathematical difficulty of the elec-trodiffusion equations, Eq. (7), arises from the nonlinear migration term, which couples the Nemst-Planck equations of the different ionic species. By assuming that the electric field is constant (GCF assumption), this difficulty is removed and analytical solutions are easy to find. Unfortunately, the validity conditions for this approximation are not always satisfied in electrochemical systems [12, 49], and it... 

As the field is increased, considering first the macroscopic case with Nq > Hq ( Ohmic contact-virtual cathode ), the diffusion component eD dn/dx of the current (/ = ne/xE + eD dn/dx) eventually becomes negligible in comparison with the migration term. Assuming that no traps are present and that the space charge is due... 

A fundamental feature of all these analyses is that electron hopping is not only driven by a concentration gradient, it is also field-assisted. AVe therefore have a diffusional term and a migrational term. Hence the potential difference between sites is taken into account, and the electronhopping flux /x must contain a migrational contribution. In the following discussion, we adopt the analysis presented by Albery and coworkers. ... 

This complicated set of nonlinear equations (due to the migration term in Eqn. 48) was solved for cases where a system has a predominance of ionic concentrations and for the opposite limiting case of strong coion exclusion from the In the former case... 

Here we see that the diffusion and migration terms in the flux equations combine into the gradient of electrochemical potential of each species. We now need to see how to modify these fluxes when a gradient in water electrochemical potential exists. 

To model the system frequency response, we rewrite the PDEs, represented by equation (8.43), by replacing u(x,t) with u<,(x)+u (x,f), the steady state solution plus a small time varying perturbation u. The steady state and the perturbation were set by the input current density j t)= Jo + / (0- Note we could have perturbed the other inputs and Xq, but this is not experimentally practical. We substitute u +u into equation (8.43) and express the c matrix as C1U+C2. This is to cover the nonlinear situation in the migration terms containing y j d /dx and y dX/dx in equation (8.45). 

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