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8.6.5 Prescribed Electric Current Density
The electric current density in a mixture is a linear superposition of the ion fluxes, Since only the normal component of ion fluxes may be prescribed at a boundary, it follows that only the normal component of the current density may be prescribed. To prescribe , it is necessary to know the nature of the ion species in the mixture, and how the current is being applied. For example, if the ions in the triphasic mixture consist of Na and Cl , and if the current is being applied using silver/silver chloride (Ag/AgCl) electrodes, a chemical reaction occurs at the anode where Ag combines with Cl to produce AgCl, donating an electron to the electrode to transport the current. At the cathode, the reverse process takes place. Therefore, in this system, there is only flux of Cl and no flux of Na ( at the electrode-mixture interface, so that the prescribed boundary condition should be . Since and in a triphasic mixture, the corresponding effective fluxes are given by and .