On the spheroidization of rod-shaped particles of finite length

The governing equation for the capillarity-induced shape changes of a surface of revolution by surface diffusion, $$\frac{{\partial n}}{{\partial t}} = \frac{B}{y}\frac{\partial }{{\partial s}}\left( {y\frac{{\partial K}}{{\partial s}}} \right)$$ where∂n/∂t is the normal velocity of the surface,y is measured normal to the axis of revolution,s is arc length,K is the total surface curvature andB is a kinetic parameter which is constant for a given temperature and material, is presented. A numerical solution to this equation is used to analyse finite cylinders with hemispherical ends. A critical length-to-diameter ratio (L/D) of 7.2 is predicted, below which only one spheroidal particle results and above which two or more are formed, and is shown to have experimental support in several systems.