Dispersed-phase stress tensor in flows of bubbly liquids at large Reynolds numbers
Copyright 1993 Journal of Fluid Mechanics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and Journal of Fluid Mechanics. The article may be found at http://dx.doi.org/10.1017/S0022112093000679
We derive averaged equations for large Reynolds number laminar flows of gas–liquid dispersions accounting for slowly varying spatial and temporal fields. In particular, we obtain an exact expression for the dispersed-phase stress tensor to be used in the force balance equation for gas bubbles and illustrate its application by evaluating the stress tensor for a few special cases. It is shown that the dispersed-phase stress tensor gradient with respect to the mean relative motion or the void fraction for the uniformly random bubbly liquids under conditions of large Reynolds number laminar flows is negative and thus has a destabilizing influence on the dynamics of void fraction waves in bubbly liquids.
Ashok S. Sangani and A. K. Didwania. "Dispersed-phase stress tensor in flows of bubbly liquids at large Reynolds numbers" Journal of Fluid Mechanics 248 (1993): 27-54.
Available at: http://works.bepress.com/ashok_sangani/26