RHEOLOGY OF DENSE BUBBLE SUSPENSIONS

The rheological behavior of rapidly sheared bubble suspensions is exam ined through numerical simulations and kinetic theory. The limiting ca se of spherical bubbles at large Reynolds number Re and small Weber nu mber We is examined in detail. Here, Re=rho gamma alpha(2)/mu and We=r ho gamma(2) alpha(3)/s, a being the bubble radius, gamma the imposed s hear, s the interfacial tension, and mu and rho, respectively, the vis cosity and density of the liquid. The bubbles are assumed to undergo e lastic bounces when they come into contact; coalescence can be prevent ed in practice by addition of salt or surface-active impurities. The n umerical 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 b ubbles. A kinetic theory based on Grad's moment method is used to pred ict the distribution function for the bubble velocities and the stress in the suspension. The hydrodynamic interactions are incorporated in this theory only through their influence on the virtual mass and visco us dissipation in the suspension. It is shown that this theory provide s reasonable predictions for the bubble-phase pressure and viscosity d etermined from simulations including the detailed potential flow inter actions. A striking result of this study is that the variance of the b ubble velocity can become large compared with (gamma alpha)(2) in the limit of large Reynolds number. This implies that the disperse-phase p ressure and viscosity associated with the fluctuating motion of the bu bbles is quite significant. To determine whether this prediction is re asonable even in the presence of nonlinear drag forces induced by bubb le deformation, we perform simulations in which the bubbles are subjec t to an empirical drag law and show that the bubble velocity variance can be as large as 15 gamma(2) alpha(2). (C) 1997 American Institute o f Physics.