Prediction and Measurement of the Accelerated Motion of Water Drops in Air

Abstract

The lack of detailed information of the drag forces of cloud droplets during accelerated motion has made it necessary to assume that steady-state drag forces can be used to predict their motion at all times. This assumption is made implicitly in the calculations of collision efficiencies of cloud droplets even though theory and experiment demonstrate that drops accelerate while hydrodynamically interacting. Interaction of droplets in turbulent motion should be particularly sensitive to discrepancies between accelerated drag and steady state. We have observed the motion of small water drops (Reynolds number R?5) accelerating from rest in a still air chamber. The drag coefficients of the accelerated motion of small droplets, obtained in this manner, are compared with observations of steady-state drag coefficients and are found to agree within experimental error. Using the steady-state drag coefficients obtained by Le Clair et al. from wind tunnel studies and numerical solutions to the Navier-Stokes equation of motion, we analytically integrated the equations of motion (R?5) for accelerating and decelerating drops to obtain analytic prediction equations for their velocity and position as functions of time. Calculations from these equations are compared with our observations and found to agree within experimental error, usually much less than 10%.