In this paper, the spherical particles growth during lithium electrodeposition was investigated by directly solving the governing equations based on the Landau transformation method. The basic growth kinetic characteristics of a spherical particle during electrodeposition was studied. Predicted results show that the dynamic oscillation of the growth velocity occurs during the spherical particle growth. It was found from numerical simulations that applied electrical potential difference, electrolyte concentration, and diffusion coefficient are 3 main factors influencing the spherical growth and the existence of the dynamic oscillation state of the growth velocity during electrodeposition. The increase in both the applied electrical potential difference and the electrolyte concentration can lead to the increase of the growth velocity of the spherical particle, while the growth velocity is independent of the diffusion coefficient. Moreover, it was found that the wavelength and the amplitude of the dynamic oscillation of the growth velocity can be influenced by the applied electrical potential difference, the electrolyte concentration, and the diffusion coefficient. We determined that the dynamic competition between electrochemical reactions and ion transport in the electrodeposition is the reason for the existence of the oscillation of the growth velocity.

The characteristic boundary layer evolution in globulitic solidification of alloys was investigated by using the Landau transformation method that takes into account attachment kinetics and interface curvature. The accuracy of the numerical solution was verified by comparing numerical results with an analytical solution without curvature and kinetic effects. Numerical results show that the increase of the kinetic coefficient results in the decrease of the value of the equilibrium interface liquid concentration, and the normal velocity of the interface was negatively correlated with the kinetic coefficient. We found that the thickness of the quasi-steady characteristic boundary layer is close to that of the unsteady one during globulitic solidification when the supersaturation is small. With the supersaturation increasing, it deviates from the unsteady one. This indicates that the kinetic effect cannot be ignored in the numerical simulations of rapid solidification. It is of practical significance to study the rapid solidification process and predict the microstructure.

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