Critical Diameter for Lift Reversal of Bubbles in Linear Shear Flows

The lift coeffcient C_L of a bubble in a shear flow is known to change its sign depending on the bubble shape, i.e. C_L of spherical bubbles are positive for any the bubble Reynolds numbers while those of ellipsoidal bubbles can be negative due to the deformation-induced negative lift. The critical bubble diameter, d_C, for the lift reversal was discussed in this study by making use of available CL correlations for clean bubbles in linear shear flows. As a result, the following conclusions were obtained: (1) the C_L correlations well describe the complex characteristics of d_C and the lift reversal criterion in terms of Re_C is well reproduced with the correlations, (2) in the surface tension and inertial force dominant regime, the critical Eötvös and Weber numbers can be used to develop a simple criterion of lift reversal, i.e.they are almost constant, and the Capillary number for d_C can be expressed in terms of the Morton number only, M; these dimensionless groups in the viscous force dominant regime, however, show more complex dependence on M, and (3) the critical Ohnesolge number, Oh_C, monotonically increases with increasing M even in the viscous force dominant regime.