New model to predict the velocity and acceleration of accelerating spherical particles

The equation of motion for an accelerating particle is complicated to solve, primarily because of the Basset-history term. Therefore, most solutions found in the literature are numerical. Various experiments conducted with different particles and fluids have been presented and analyzed in this study. A simple exponential function for the particle velocity was found to fit all the experiments, describing the acceleration as a function of distance. Consequently, a simple exponential equation was developed for velocity. These functions depend on the initial acceleration and terminal velocity. While the terminal velocity can be predicted by several known equations, the initial acceleration was defined without any empirical parameter for cases of negligible history forces. In addition, the effect of history forces was correlated. Consequently, the velocity during the acceleration of 51 experiments was predicted to be ±10%.