Electro-migration 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. 

According to (1.3b), the nonconvectional electro-diffusion flux component j. is a superposition of the following two terms. The first is the diffusional Fick s component proportional to the concentration gradient VC. The second is the migrational component, proportional to the product of the ionic concentration Cj and the electric force —ZiFV

proportionality factor. Einstein s equality (1.3c) relates ionic mobility to diffusivity >. ... 

Under the influence of a fall of potential almost all colloids migrate either to the cathode or to the anode. The phenomenon of electrical migration of colloids is closely associated with that of electro-osmosis. This latter phenomenon may be defined as the passage of liquids through membranes under the influence of a fall of electrical potential. When the particles move through the solution the phenomenon is called cata-phoresis. When the particles remain stationary and the liquid moves, the term endosmosis is applied. The earliest observations on these phenomena were made by Picton and Linder, Coehn,f Lottermoser, and Wiedemann. ... 

The first, second, and third terms on the right-hand side of Equation (12.12) respectively, represent the three governing transport mechanisms of species diffusion, migration, and eonvection. Combining Equations (12.11) and (12.12) with the condition of electro-neutrality (E ZhCh =0) gives ... 

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