Three-dimensional numerical simulation of sedimenting drops inside a vertical channel

Numerical simulation of sedimenting deformable drops inside a vertical channel has been performed at finite Reynolds numbers. The channel is confined by two vertical walls in x-direction and is periodic in y- and z-directions. Results are obtained using a finite difference/front-tracking method. The main dimensionless parameters are the Reynolds number, the Bond number and ratio of the length of channel to the diameter of drops. The effect of these parameters on lateral migration of drops is investigated. It is found that the wall repulsion is the main mechanism of the lateral migration of the drop, and drop migrates toward the channel axis. When the Reynolds number is relatively low, two different lateral migration regimes are observed: migration with monotonic approach and migration with damped oscillations. These regimes are affected by the dimensionless parameters. When the Bond number increases, the oscillations of drop around the centerline of channel are stronger and drop reaches the channel centerline in a larger period. Results of lateral migration of one drop are consistent with perturbation theory, and two-dimensional numerical simulations performed by Feng et al. (1994). The drag coefficient has also been calculated, and effect of various parameters has been discussed. Two drops interaction is similar to that observed by Feng et al. (1994) for two-dimensional circular cylinders. Results are consistent with experiments performed by Wu and Manasseh (1998). Simulations of four sedimenting drops show that depending on the relative size of drops, they either fall in two rows or they form a single horizontal layer and settle with a unique velocity.