Lattice-Boltzmann simulation of finite Reynolds number buoyancy-driven bubbly flows in periodic and wall-bounded domains

A lattice-Boltzmann method is used to probe the structure and average properties of suspensions of monodisperse, spherical, noncoalescing bubbles rising due to buoyancy with Reynolds numbers based on the bubble terminal velocities of 5.4 and 20. Unbounded suspensions subject to periodic boundary conditions exhibit a microstructure with a strong tendency toward horizontal alignment of bubble pairs even at volume fractions of as high as 0.2. This microstructure leads to a mean rise velocity whose dependence on the bubble volume fraction is not well fitted by a standard power-law function. Simulations with bounding vertical walls exhibit a deficit of bubbles near each wall and a peak of volume fraction approximately one bubble diameter from the wall. We attribute this structure to the effects of a repulsive wall-induced force and a lift force associated with the liquid flow driven by the variation in the buoyancy force with horizontal position. Weaker peaks of bubble volume fraction extend into the bulk of the suspension and these peaks are separated by a distance equal to the peak in the pair distribution function for bubble pairs in an unbounded fluid. This suggests that the layering is a result of hydrodynamic bubble-bubble interactions.