Rheology of dense bubble suspensions

The rheological behavior of rapidly sheared bubble suspensions is examined through numerical simulations and kinetic theory. The limiting case of spherical bubbles at large Reynolds number Re and small Weber number We is examined in detail. Here, Re=ργa2/μ and We=ργ2a3/s, a being the bubble radius, γ the imposed shear, s the interfacial tension, and μ and ρ, respectively, the viscosity and density of the liquid. The bubbles are assumed to undergo elastic bounces when they come into contact; coalescence can be prevented in practice by addition of salt or surface-active impurities. The numerical simulations account for the interactions among bubbles which are assumed to be dominated by the potential flow of the liquid caused by the motion of the bubbles and the shear-induced collision of the bubbles. A kinetic theory based on Grad’s moment method is used to predict the distribution function for the bubble velocities and the stress in the suspension. The hydrodynamic interactions are incorporated in this the...