Creeping motion of a bubble with fixed surface charge in a uniform electric field

Abstract

Approximate solutions of the shape junction and the electrophoretic movement of a bubble in an aqueous medium with ionized detergent and a small number of electrolytes under the influence of uniform electric field are derived Specifically, a bubble that has the interface saturated and densely packed with detergent molecules is considered and the charges were deemed to be fixed provided the position change among the detergent molecules is hindered relative to the free molecule. The surface tension at the interface is weakened with the addition of the detergent, and the deformation can be significant. The variation of the shape of the bubble was represented by the Legendre polynomial and the perturbed velocity profile was used to derive the drag force for the deformed bubble. The speed and size of the bubble was assumed to be very small so that the flow around it is in the creeping flow regime. The shape of the bubble with fixed surface charge undergoes a prolate deformation with axial symmetry around the axis parallel to the direction of the electric field and exhibits asymmetry with respect to the plane that goes through the center of the bubble and is perpendicular to the axis. But this asymmetry is not significant unless the surface charge density and the electric field are very large. Only symmetric deformation governs the movement, and, consequently, the drag force is not dependent on the sign of surface charge. As the bubble becomes more slender with deformation, the movement is enhanced.