Document Type




Embargo Period



bubbles, suspensions, rheology, kinetic theory, flow simulation, surface tension, viscosity, drag, method of moments


Chemical Engineering


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 = p y a^2 / u and We = p y^2 a^3 / s, a being the bubble radius, g the imposed shear, s the interfacial tension, and m and r , 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 theory only through their influence on the virtual mass and viscous dissipation in the suspension. It is shown that this theory provides reasonable predictions for the bubble-phase pressure and viscosity determined from simulations including the detailed potential flow interactions. A striking result of this study is that the variance of the bubble velocity can become large compared with (y a)^2 in the limit of large Reynolds number. This implies that the disperse-phase pressure and viscosity associated with the fluctuating motion of the bubbles is quite significant. To determine whether this prediction is reasonable even in the presence of nonlinear drag forces induced by bubble deformation, we perform simulations in which the bubbles are subject to an empirical drag law and show that the bubble velocity variance can be as large as 15 y^2 a^2.

Additional Information

Copyright 1997 Physics of Fluids. This article may be downloaded for personal use only. Any other use requires prior permission of the author and Physics of Fluids. The article may be found at



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.