NUMERICAL STUDY OF THE BEHAVIOR OF A BUBBLE ATTACHED TO A TIP IN A NONUNIFORM ELECTRIC FIELD

Abstract

In order to investigate the effects of a nonuniform electric field on the behavior of a bubble, a numerical study on the shape of a bubble attached to a conducting tip on a supporting wall is performed. The equilibrium bubble shape is determined by solving the free boundary problem that consists of the governing equation for electric field and the normal stress condition at the bubble surface. A numerically generated composite orthogonal coordinate system is employed to solve the free boundary problem. A bubble on a tip is found to be extended in the direction parallel to the applied electric field. The elongation increases steeply with an increase of the electric field strength and the height of the tip. It is also observed that a highly elongated bubble has a shape with slender waist. The bubble shape obtained from numerical studies are qualitatively similar to the shapes observed in experiments. If the contact radius is maintained during bubble deformation, the contact angle and the aspect ratio increase with the increase of the electric field strength and the tip height. On the other hand, if the contact angle is fixed during bubble deformation, the contact radius decreases as the electric field strength increases. In order to estimate the effect of electric field on the bubble departure volume, the surface tension force and the downward electric force exerted on a bubble are also computed for a bubble of fixed volume under the fixed contact angle condition. The sum of the two forces is found to decrease with increasing strength of nonuniform electric field. This fact suggests that the bubble departure volume decreases in a nonuniform electric field.