Statistical analysis of small bubble dynamics in isotropic turbulence

The dynamics and dispersion of small air bubbles in isotropic turbulence are analyzed computationally. The flow field is simulated using a pseudospectral code, while the bubble dynamics are analyzed by integration of a Lagrangian equation of motion that accounts for buoyancy, added mass, pressure, drag, and lift forces. Probability density functions (pdfs) of bubble velocities, lift and drag forces, and of field velocities and vorticities along bubble trajectories are used to analyze bubble dynamics. Lagrangian bubble trajectories are also employed to determine dispersion characteristics, following the theoretical development of Cushman and Moroni [Phys. Fluids 13, 75 (2001)]. Consistent with available experimental data, bubble rise velocities are increasingly suppressed with increasing turbulence intensity. The analysis also reveals that the vertical bubble velocities are characterized by asymmetric pdfs that are positive or negative-skewed dependent upon the nondimensional turbulence intensity and the Taylor length scale. The role of the lift force in moving the bubbles to the down-flow side of turbulent eddies, and consequently retarding their rise, is consistently observed in all analyses. The dispersion of 40μm bubbles and transition to Fickian behavior is shown to be weakly affected by the turbulence level. Larger, 400μm bubbles are shown to be more sensitive to turbulence level with transition to Fickian behavior delayed in low turbulence fields.