FLUID DYNAMICS OF BUBBLY LIQUIDS

Abstract

Experiments have been performed to elucidate the average flow properties of bubbly liquids. The experiments examine a particular class of inertially dominated multiphase flows that are particularly amenable to theoretical analysis. High-Reynolds-number, low-Weber-number bubbles produce a fluid velocity disturbance that may be approximated as a potential flow and extensive theoretical and numerical simulation work has been performed based on this approximation. We studied the behavior of monodisperse suspensions of bubbles with diameter of about 1.4 mm rising in water in vertical and inclined channels. Measurements of the liquid phase velocity fluctuations were obtained with a hot wire anemometer. The shear stress at the wall was measured using a hot film probe flush mounted on the wall. The gas volume fraction, bubble velocity, and bubble velocity fluctuations were measured using a dual impedance probe. Digital image analysis was performed to quantify the small polydispersity of the bubbles as well as the bubble shape.

A rapid decrease in the average bubble velocity in vertical channels with bubble concentration in very dilute suspensions is attributed to the effects of bubble-wall collisions. The more gradual subsequent hindering of bubble motion is in qualitative agreement with the predictions of Spelt and Sangani (1998) for the effects of potential-flow bubble-bubble interactions on the mean velocity. The ratio of the bubble velocity variance to the square of the mean is O(0.1). For these conditions Spelt and Sangani predict that the homogeneous suspension will be unstable and clustering into horizontal rafts will take place. Evidence for bubble clustering is obtained by image analysis of video images. The fluid velocity variance is larger than would be expected for a homogeneous suspension and the fluid velocity frequency spectrum indicates the presence of velocity fluctuations that are slow compared with the time for the passage of an individual bubble. These observations provide further evidence for bubble clustering.

Inclination of the channel at angles of 2 to 10 degrees to gravity, produces a variation in bubble volume fraction across the channel. The resulting buoyancy variation drives a shear flow in the channel and provides a convenient means of observing the effects of weak shear on a bubbly liquid. The tendency of buoyancy driven motion to cause the bubbles to accumulate on the upper wall is balanced by lift forces and by an effective hydrodynamic diffusion of bubbles, leading to a modest bubble volume fraction variation across the gap. The magnitude of the shear flow produced by the bubbles can be interpreted in terms of a balance between buoyancy forces and an effective viscous stress. The effective viscosity is more than 100 times larger than the viscosity of the suspending water. The effective viscosity is large because it arises from Reynolds stresses in the liquid which are much larger than the stress due to fluid viscosity at high Reynolds numbers. The Reynolds stress is further enhanced by the presence of bubble clusters.

Koch, D.L., Tsang, Y., Zenit, R., Sangani, A., Fluid Dynamics of Bubbly Liquids, Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena Conference, NASA Glenn Research Center, Cleveland, OH, CP-2000-210470, pp. 1608-1609, August 9, 2000.