Review—The Transient Equation of Motion for Particles, Bubbles, and Droplets

Abstract

The development, form, and engineering applications of the transient equation of motion of rigid particles, bubbles, and droplets are presented. Some of the early work on the equation of motion, as well as recent advances, are exposed. Particular emphasis is placed on the semiempirical forms of the equation, which are widely used in engineering practice. The creeping flow assumption, on which most of the known applications are based, is critically examined and its limitations are pointed out. Recent results on particle flow, which include the effect of the advection of a downstream wake and are applicable to finite (but small) Reynolds numbers are also presented. The form of the history (Basset) term is discussed, in the light of recent work and its effect on the integrated results of the equation of motion is examined. Recommendations are given on the appearance, importance, and significance of the history and added mass terms for those who may use the semiempirical form of the transient equation of spheres in a differential or integrated form.