| This work focuses on the morphological instability of moving fronts. The stability of electrode surfaces during an electrodeposition process has been considered as an example. We have shown that the physics of the instability is due to reinforced concentration and electrical potential gradients at the cathode generating the instability there. The anode, on the other hand, retains a stable planar morphology.; It has been found that increasing the voltage drop between the electrodes or the average ionic concentration will shift the electrolytic cell more towards the instability. Conversely, increasing the distance between the electrodes will work in favor of stabilizing the electrodeposition process.; We have also shown theoretically that once the electrodes lose their planar shape, the velocity of the surfaces and consequently the measured current will drop in relation to the predicted base value. It should not have been possible to obtain this conclusion without the application of two important restrictions, namely constant volume and constant average concentration of electrolytic solution.; Through this dissertation three main approximations were introduced. The first approximation is one of chemical reaction equilibrium which implies that reactions are assumed to take place fast compared to the transport processes of diffusion and migration. The second important approximation was to assume that the concentration is the same as the average ionic concentration as far as the migration is concerned. The last approximation was that the dynamic change of concentration is subservient to the dynamic change due to transport arising from the movement of the boundary. These approximations simplify the model greatly and proved to be valid under reasonable conditions.; The design parameters of an electrodeposition cell are also calculated where the dimensions of the cell are suggested in addition to the predicted values of the voltage drop and the current at which the instability might take place.; It is recommended that the findings of this work be linked to other moving front instabilities such as those that take place in solidification, precipitation and viscous fingering and to see what these instabilities have in common and in what aspects they might differ. |
