Radial bubble crossflow to reduce drag in vertical circular Couette flow

This Letter studies the effect of radial bubble crossflow on drag reduction of the vertical Couette flow between an upward moving cylinder and a fixed outer coaxial cylinder. A simple formula is given for the reduced drag under the condition that the lift force coefficient equates to the added mass coefficient, which predicts that the effect of radial bubble crossflow on drag reduction increases with decreasing bubble size but decreases with increasing speed of the moving cylinder, in qualitative agreement with some known results. The practical applicability of the derived formula is illustrated with specific numerical examples.