As a bubble traverses an inviscid flow field possessing vorticity it experiences a lift force in proportion to the cross-product of the relative velocity difference and the Row field vorticity. The proper derivation of this force construct is important in the formulation of bubble trajectory models applied to high vorticity regions such as a shear flow, but is hampered by three aspects. First, there is disagreement as to the evolutionary basis of the lift force. Second, the models of lift force are derived for a nominal one-dimensional flow case, i.e., collinear bubble velocity and flow field velocity vectors, but are applied to general three-dimensional simulations where the two velocities are not necessarily co-planar. This vectorial generalization of dynamic lift has not been validated, Third, the mathematical model to predict lift force is awkward to apply in a numerical trajectory simulations. In the present study, we argue that the lift force derives from a contouring of the kinetic energy and convective potential-rate fields. This forms the basis for a simple predictive tool which is termed a split lamina model, which is capable of extracting an analytical validation of the vectorial generalization. Conceptually, the split lamina model artificially cleaves a bubble into two separate halves along the plane of the impinging Row field velocity. As each half-bubble resides a flow: field of a slightly different velocity, the force acting on respective halves is calculated by integrating the defect in kinetic energy and convective potential-rate. Upon mathematical reassembly of the halves the registered force imbalance is assigned to be the lift ford. For a simple shear flow, the split lamina technique predicts the analytical lift coefficients for a sphere to within three percent of the accepted value C-L = 1/2. Hence, promoting a study of the off-nominal flow conditions, the 3D vectorial generalization of Auton (1987. Journal of Fluid Mechanics, 183, 199-218) is subsequently validated by applying the velocity potential derived in Schrage (1998. Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, May). For moderate three dimensionality, the split lamina model emulates the vectorial generalized lift force to within 10 percent. To simplify the conventional cross-product format, the lift force is compacted as an adjunct force tenser K which operates on the bubble relative velocity difference vector to describe the force in accordance with F-L = pV(a)K(u - v). (C) 2001 Elsevier Science Ltd. All rights reserved.
