An Electrostatic Theory for Instruments which Measure the Radii of Water Drops by Detecting a Change in Capacity Due to the Presence of a Drop

Abstract

A very abrupt rise in capacity occurs as a water drop approaches and comes in contact with one of the electrodes of a capacitor. This capacity change can be used to measure drop sizes and thus to determine dropsize distributions in clouds since the maximum amplitude of the change increases with the radius of the drop. The main result of this paper is a formula for the change in capacity as a function of the distance between the electrode and the drop. The maximum value of the capacity occurs just when the drop touches the electrode, and is approximately E2R23/V2[cm], where E is the electric field at the location of the drop, V the voltage across the capacitor plates, and R2 the radius of the drop (in cgs-Gaussian units). The theory agrees very well with an experiment in which the capacity was measured by placing a fixed charge on the capacitor and measuring the change in voltage as a steel ball (in place of a water drop) approached one of the electrodes. The fragments resulting from the break-up of the drop after hitting an electrode will also cause a voltage change. A formula based on a simple model of drop break-up predicts that the maximum amplitude due to the break-up would be proportional to the square of the radius of the drop (instead of the cube, as the above formula predicts). This agrees with what Keily observed during his investigations of a dropsize device based on this principle.