The disintegration and electrification of charged water drops falling in an electric field

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Abstract
The spheroidal assumption employed by Taylor (1964) has been applied to a theoretical treatment of the deformation and disintegration of charged water drops falling through an electric field of strength F. Aerodynamic and hydrostatic pressure‐difference terms were incorporated into equilibrium equations from which the fields required to produce instability were determined. Values of F (Ro/T)1/2 required for disintegration were computed as a function of the applied charge Q, undistorted drop radius Ro and surface tension T. The predicted values of F (Ro/T)1/2 have been tested experimentally for positively or negatively charged water drops of Ro ranging from 0·10 to 0·17 cm falling through horizontal or vertical fields at temperatures varying from + 20 to −18°C. The agreement between theory and experiment was found to be good; the maximum discrepancy of about 3 per cent was obtained with the largest drops utilized and is probably a consequence of the oscillation factor discussed by Ausman and Brook (1967). As predicted, the field required to disintegrate a falling drop was found to be markedly dependent upon the magnitude of the charge that it carried. It is shown that the field, F, required to effect the disintegration of the great majority of charged raindrops falling through the intense electric fields of a thunderstorm can be expressed in electrostatic units to within an accuracy of 2 per cent by the equation F (Ro)1/2 = 13·6 – 8Q.The mass loss accompanying the disintegration of falling drops was found to bear a similar relationship to the field strength as was previously observed by Latham (1965) and Matthews (1967). Measurements on suspended drops of water showed that the valués of charge and mass loss, q and δM respectively, accompanying the disintegration are close to the theoretical maxima. The close parallelism between the experimental curves of q against Q and δM against Q suggests that instability occurs over a large fraction of the surface area of the lower hemispheroid.

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