A test of the Tate equation to predict bubble size at an orifice in the presence of frother

Abstract

Air bubbles of uniform size (ca. 1 mm diameter) were generated at a submerged orifice (glass capillary) under controlled frequency (down to ca. 0.06 s − 1 ) in aqueous solutions of frother (Dowfroth 250). The bubbles were sized with an imaging technique. One objective was to establish whether the Tate equation (static balance between buoyancy and capillary forces) could be used as a standard sizing calibration method. Another aim was to verify whether with decreasing surface tension (due to increasing frother concentration) the anticipated decrease in bubble size agreed with the equation prediction. An effect of frother was detected compatible with the role of surface tension but divided into two concentration regions, seemingly the result of a gradual change in bubble shape and wetting: > 6 ppm the bubble holds a spherical shape and the capillary appeared to be completely wetted while at ≤ 6 ppm a degree of non-wetting and bubble distortion (neck formation just prior to detachment) were apparent, supported by qualitative observations. In addition, at > 6 ppm the Tate value was only approached by decreasing the bubble frequency but not attained. Plausible causes for the failure to reach the predicted size are discussed.