A Single Bubble 3D Motion in Dilute Surfactant Solution (2nd Report, Forces and Slip Conditions on a Bubble in Quasi-Steady Motion)

Abstract

The surfactant effect on the three-dimensional motion of a single bubble rising in stationary liquid is recently reported by Tagawa et al. (2010) as a first report. In this paper we investigate the forces acting on the single bubble under various surface slip conditions. Using our three-dimensional measurement system, velocities, trajectories and shapes of a bubble of 2.0± 0.1mm diameter in 1-Pentanol solution are obtained. We observe the quasi-steady helical motions without shape oscillations. These motions enable us to apply the generalized-Kirchhoff equation proposed by Mougin et al. (2002) for the calculation of the drag and lift forces. The slip condition is quantified as the normalized drag coefficient CD* which is the experimental drag coefficient normalized by drag coefficients of free-slip and no-slip conditions; CD* = 0 for free-slip, CD* = 1 for no-slip condition. It is found that maximum magnitude of lift force FL is in CD* = 0.12 where the minimum frequencies f and maximum amplitudes A of the bubble horizontal path are seen. We show that the non-monotonic behavior of the frequency f on the slip condition can be explained by the direction of the lift force. Remarkably, for the non-zero CD* in surfactant solution the direction of the lift force is almost constant and lower than that at CD* = 0. It implies that the double-threaded wake keeps almost same alignment in the reference frame due to the constant slip condition along the azimuthal direction.