THE ROLE OF COHERENT STRUCTURES IN BUBBLE TRANSPORT BY TURBULENT SHEAR FLOWS

Using Auton's force law for the unsteady motion of a spherical bubble in inhomogeneous unsteady flow, two key dimensionless groups are deduc ed which determine whether isolated vortices or shear-layer vortices c an trap bubbles. These groups represent the ratio of inertial to buoya ncy forces as a relaxation parameter PI = DELTAU2/2gx and a trapping p arameter GAMMA = DELTAU/V(T) where DELTAU is the velocity difference a cross the vortex or the shear layer, x is streamwise distance measured from the effective origin of the mixing layer and V(T) is the termina l slip speed of the bubble or particle. It is shown here that whilst b uoyancy and drag forces can lead to bubbles moving in closed orbits in the vortex flows (either free or forced), only inertial forces result in convergent trajectories. Bubbles converge on the downflow side of the vortex at a location that depends on the inertial and lift forces. It is important to note that the latter have been omitted from many e arlier studies. A discrete-vortex model is used to simulate the large- scale unsteady flows within horizontal and vertical mixing layers betw een streams with velocity difference DELTAU. Trajectories of non-inter acting small bubbles are computed using the general force law. In the horizontal mixing layer it is found that GAMMA needs to have a value o f about 3 to trap about 50% of the bubbles if PI is about 0. 5 and gre ater if PI is less. The pairing of vortices actually enhances their tr apping of bubbles. In the vertical mixing layer bubbles are trapped ma inly within the growing vortices but bubbles are concentrated on the d ownflow side of the vortices as GAMMA and PI increase. In a companion paper we show that lateral dispersion of bubbles can be approximately described by an advective diffusion equation with the diffusivity abou t equal to the eddy viscosity, i.e. rather less than the diffusivity o f heat or other passive scalars.