TITLE:
Review of the Dynamics of Falling, Accreting, Spherical Drops Acted Upon by Air Resistance
AUTHORS:
Øyvind G. Grøn
KEYWORDS:
Accreting Raindrop, Gravity, Air Resistance, Dynamics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.7,
July
31,
2025
ABSTRACT: In this review a detailed treatment of the dynamics of an accreting raindrop falling through stationary mist under the action of gravity and air resistance, is presented. There are two contributions to the air resistance: one term proportional to the velocity and one proportional to the square of the velocity. It is discussed when it is a good approximation to neglect one of these terms. Also, a new form of the solution of the equation of motion is presented when accretion is neglected, but both the linear and quadratic contributions to the air resistance are present. The paper is written in a style making it useful in the teaching of classical dynamics, including in between calculations and providing several examples where the equation of motion of the drop, and the equation for the change of the droplet’s mass due to accretion, can be solved analytically in terms of elementary functions.