Velocity and Displacement of Spherical Particles Subjected Only to Drag

Abstract

The problem regards the velocity and displacement of spherical particles (e.g. droplets) subjected only to drag forces by a surrounding fluid medium (e.g. air). Expressing the drag coefficient as CD = (24/Re)(1 + 0.16 · Re0.67) (Re ≤ 103) and assuming that no other force but drag (e.g. gravity) acts on the particles, the exact solution of the relevant equation of motion shows that, for t → ∞, the velocity of a particle tends to zero while its displacement tends to a finite value which depends on the particle’s diameter and initial velocity. Thus, for example, in zero gravity identical particles emitted from the same point with the same initial speed but along different directions will eventually accumulate on a spherical surface surrounding the emission point.