Experimental study on the drag coefficient for an ellipsoidal bubble with fore-aft asymmetry

We experimentally evaluate the drag coefficient for spherical and ellipsoidal clean bubbles rising steadily in liquids of low Morton number ranging from 10$^{-11}$ to 10$^{-8}$. Four different silicone oils and super purified water are used as liquids. The shapes and rising motion of bubbles are captured by using a still camera and a high-speed video camera, respectively. The degree of fore-aft asymmetric bubble shape is quantitatively evaluated using image processing. The experimentally obtained drag coefficients are compared with those for symmetric ellipsoidal bubbles obtained analytically by Moore [J. Fluid Mech. \textbf{23}, 749 (1965)], and via numerical simulation by Blanco {\&} Magnaudet [Phys. Fluids \textbf{7}, 1265 (1995)]. The main conclusions are summarized as follows; (1) Moore's drag coefficient overestimates the experimentally obtained drag coefficient especially when bubble aspect ratio increases, (2) Blanco {\&} Magnaudet's prediction of drag coefficients for bubbles with ellipsoidal shape are also valid for those with fore-aft asymmetric shape of corresponding aspect ratio.