Nonlinear stability analysis of the diffusional spheroidization of rods

Experimental observations have revealed a significant scatter in the spheroidization wavelength in solid rods and rod-shaped inclusions. Using a finite difference method, the role of multiharmonic initial conditions, where the wavelength and amplitude vary with position, is investigated as a cause of the scatter. When the initial amplitude of the radius perturbation is small relative to the radius of the perturbation, the waves with their wavelengths at the maximum growth rate are shown to evolve with little scatter. As the initial amplitude increases, however, a large magnitude of scatter in the growing wavelength is observed due to wave/wave interactions. A simplified, analytical model is also proposed to describe the nonlinear wave/wave interaction between two waves. Based on this model, it is found that the stability of one wave can be affected by the other, and that a new wave can be generated. A wave stability diagram is constructed to predict the stability of a given wave