Shape and Steady Drag on Single Rising Bubbles

Relations between drag coefficients CD and bubble shapes are investigated by comparing our experimental results with both analytical [Moore, J. Fluid Mech., 23, 749-766 (1965)] and numerical results [Blanco & Magnaudet, Phys. Fluids, 7(6), 1265-1274(1995)] on ellipsoidal bubbles rising in a quiescent clean liquid. We clarify that the analytically obtained CD overestimates the experimental results especially in the case of either high aspect ratio or low Reynolds number, and that numerically obtained results for ellipsoidal bubbles well predict our experimental results. We also show that the effect of the deviation in the shape from the ellipsoid, i.e., fore-aft asymmetry, on CD is negligible; CD for fore-aft asymmetry bubbles is in good agreement with the numerically obtained CD for ellipsoidal bubbles.