Critical Diameter for Lift Reversal of Bubbles in Linear Shear Flows

Abstract

The lift coefficient 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 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 C L 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 Ohnesorge number, Oh C , monotonically increases with increasing M even in the viscous force dominant regime. Therefore a tentative d C correlation based on Oh C was developed.