The hydrodynamic instability of water drops falling at terminal velocity in vertical electric fields

Abstract

A study has been made of the onset of instability and corona in water drops of raindrop size falling at their terminal velocity in a vertical wind tunnel at atmospheric pressure and exposed to vertical electric fields. The overall behavior at initial instability is similar for charged and uncharged water drops of all sizes in fields of both polarities, either pulsed or slowly varying, and even for uncharged drops of the low-surface-tension liquids, acetone and ethyl alcohol. Instability proceeds by the formation of a ‘point’ at the upper surface of the drop from which electrical corona is emitted, changing the net charge on the drop. Contrary to the findings of previous investigators, no mass-loss is observed at instability; charge-loss is by corona even at atmospheric pressure. Typical charging of an initially uncharged 2-mm-radius water drop at instability is 5×10−10 coul; the charge-loss of an initially charged ( ≈1.5×10−9 coul) drop is typically 2×10−9 coul. For large uncharged water drops (radii >2 mm) the field necessary for instability is higher than that given by the criterion of Taylor (1964) and is essentially independent of radius at about 9.5 kv cm−1. For large highly charged drops the instability field is typically 5.5 kv cm−1. It is suggested that some of the more unexpected results are a consequence of the aerodynamic pressures on the drops.