Study of the behavior of a bubble attached to a wall in a uniform electric field

Abstract In order to investigate the effects of a uniform electric field on a bubble attached to a wall, numerical analyses and experiments have been carried out. The orthogonal curvilinear coordinate system generated numerically has been employed for the numerical studies based on a finite-difference solution of the governing equations. The steady bubble shape is obtained under the fixed contact radius condition as part of the solution of the free boundary problem. Along with the shape determination, the Laplace equation for electric potential is solved simultaneously. In experimental studies, an air bubble attached to one plate of a parallel-plate electrode system has been visualized under an applied electric field. The numerical and experimental results show generally good agreements. An air bubble on the lower electrode is found to be extended in the direction parallel to the applied electric field. The elongation increases with an increase of the electric field strength. Consequently, the contact angle also increases with an increase of the electric field strength if the contact radius is fixed. On the other hand, if the contact angle is fixed, the contact radius decreases as the electric field strength increases. It has been observed experimentally that the bubble departure volume remains nearly constant under the uniform electric field. This fact suggests that the downward electric force exerted on the bubble surface is nearly the same as the decrease in the surface tension force due to contact radius decrease under the uniform electric field.