A Numerical Model for the Equilibrium Shape of Electrified Raindrops

Abstract The model Beard Chuang, using the differential form of Laplace's formula, has been extended to raindrop shapes under the influence of vertical electric fields and drop charges. A finite volume method was used with a boundary-fitted coordinate system to calculate the shape-dependent electric field. The distorted shape was obtained by numerical integration from the upper to lower pole by iteration to achieve the appropriate drop volume and force balance using shape-dependent stresses. The model prediction of the critical electric field for instability is within a few percent of previous models for a stationary drop, but stability was found to be considerably enhanced for raindrops because of the counteracting aerodynamic distortion. The predicted critical fields for larger raindrops, however, are about 2 kV cm−1 higher than found in the wind tunnel measurements of Richards and Dawson. Model raindrop shapes in a strong, electric field show a pronounced extension of the upper pole, and a flattened ba...