Migration mass-transfer-controlled reactions

Since electrowinning requires current flow, assume a coupled diffusion and migration mass transfer and neglect any reaction rate controlling the chemical process. The coupled current density has been derived in Chapter 4. Letting D = Di=D2 due to the assumed symmetry in section 7.7 gives... 

Let us assume that the reaction rate for the reduction of an oxidant is partly mass transfer controlled. If one neglects migration, the flux at the electrode surface is given by Eq. (64). 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

With very slow reactions (such as between carbon dioxide and water) the dissolved molecules migrate well into the body of the liquid before reaction occurs so that the overall absorption rate is not appreciably increased by the occurrence of the chemical reaction. In this case, the liquid film resistance is the controlling factor, the liquid at the interface can be assumed to be in equilibrium with the gas, and the rate of mass transfer is governed by the molecular CO2 concentration-gradient between the interface and the body of the liquid. At the other extreme are very rapid reactions (such as those of ammonia with strong acids) where the dissolved molecules migrate only a very short distance before reaction occurs. The... 

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