In this study, we experimentally observed the motion of a pair of bubbles initially positioned in line, especially focusing on the intermediate Reynolds number case, i.e., 20 < Re < 60. We observed three types of motion at different Reynolds numbers. At a low Reynolds number (Re < 20), the trailing bubble collided with the leading bubble like a pair of rigid spheres. At a high Reynolds number (100 < Re), the trailing bubble moved out from the original vertical line joining the two bubbles. At intermediate Reynolds numbers (20 < Re < 60), small differences in bubble size affected the motion. When the leading bubble was larger than or equal to the trailing bubble, the trailing bubble first approached the leading bubble and later moved out from the initial vertical line owing to a lift force. When the leading bubble was smaller than the trailing bubble, the trailing bubble first approached the leading bubble, and then a repulsive force acted on both bubbles so that both of them moved out from the vertical line in opposite directions. These motions are attributed to two effects, the first is potential effects at short distance between bubbles, and the second is the wake of the leading bubble.

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The boundary layer of a bubble is an important factor that determines its rising velocity. But it is generally very thin to simulate using typical interface capturing method, such as volume of fluid method. In this study, we numerically investigated the velocity distribution in the boundary layer, and whether a general method for calculation of bubble describes a correct boundary layer. First, we simulated axisymmetric flow around a spherical bubble to calculate the accurate velocity distribution in the boundary layer using boundary fitted coordinate system. The velocity is first increased until a certain distance from the bubble surface and showed maximum value. And then the velocity is decreased with taking a distance from the bubble. Although this tendency is the same as the theoretical analysis, the magnitude is different. In order to guarantee the accuracy of bubble simulation, high spatial resolution in this very thin region where the velocity is increased near the bubble surface is required. Second, we compared the result of deformed bubbles between boundary fitted coordinate system and volume of fluid method. When 4 points are arranged in the velocity increase region, the velocity difference between two methods is approximately 1%. We conclude that the velocity profile by volume of fluid method matches that by boundary fitted coordinate system when the grid resolution is appropriate.

We experimentally investigated the motion of a pair of bubbles initially positioned inline configuration in ultrapure water or an aqueous surfactant solution. The bubble motion was observed by two high speed video cameras. The Reynolds number of bubbles were ranged from 50 to 200, and the bubbles hold a spherical shape in this range. In ultrapure water or small concentration of surfactant solution, initially the trailing bubble deviated from the vertical line on the leading bubble owing to the wake of the leading bubble. And then, the slight difference of the bubble radius changed the relative motion. When the trailing bubble slightly larger than the leading bubble, the trailing bubble approached to the leading bubble due to it's buoyancy difference. The bubbles attracted and collided only when the bubbles rising approximately side by side configuration. On the other hand, the trailing bubble was drafted to the wake region of leading bubble when the bubbles were rising in high concentration of surfactant solution. In this case, the bubbles always collided in line configuration. We consider that these phenomena are caused by the changes of lift force direction in the wake region owing to the surface contamination. In addition, bubble coalescence was inhibited in surfactant solution, even the relative motion was similar to the clean bubble case.