Effect of the history term on the motion of rigid spheres in a viscous fluid

Abstract

The inclusion of the history term (often called “the Basset term”) in the equation of motion of a sphere makes this equation non-explicit in the velocity or acceleration. For this reason, the numerical solution of the equation becomes cumbersome and computationally time-consuming. By the use of an integrodifferential operator, the equation of motion of a sphere is transformed to a second-order ordinary differential equation, which is explicit in the velocity. This equation is solved numerically to determine the effect of the history term on the calculations of particle velocity and trajectories in unsteady flows. The numerical calculations make use of empirical correction factors to account for the effects of finite Reynolds number. Computations are made with the fluid velocity being sinusoidal, random and monotonically increasing. It was observed that the effect of the history term was more pronounced at higher frequencies of the fluid velocity and for fluid-to-particle density ratios higher than 0.002.