Attraction and repulsion of solid particles by solidification fronts. II. Dimensional analysis

Abstract

A scheme of dimensional analysis is developed for the description of pushing and engulfing of particles by solidification fronts. The nondimensional groups contain all the properties to be believed relevant, such as the critical velocity of engulfing V_c, the free energy of adhesion of the particle, viscosity, densities, thermal conductivities, temperature, specific heat, diffusion coefficient, and particle diameter. The determination of the parameters of the dimensional analysis is based on a substantial body of experimental critical velocity V_c data as a function of particle diameter. These experiments were performed with naphthalene and biphenyl as matrix materials and a range of polymer particles in the particle size range from 10–200 mm. The final relation obtained is tested for internal consistency and the resulting dependence of the critical velocity of engulfing on particle size is compared with experimental results.