Studies on chains of bubbles rising through quiescent liquid

Abstract

The liquid velocity profile induced by a chain of bubbles is studied theoretically and a comparison with measurements is made. The wake velocity and the bubble shape involved in the theoretical development are considered based on the wake theory and the previous empirical relation for single bubbles, respectively. The shape and wake volume of chain bubbles can be treated in the same manner as those of single bubbles by using relative velocity. As a result, using the previous results of the drag coefficient and shape of single bubbles enables the prediction of the rising velocity of chain bubbles.

Generalized correlation for bubble motion

“…His set of equations is found to be difficult to use since the transitions between each section of the curve are not well defined. Miyahara and Takahashi (1985), using a limited amount of experimental data taken from the literature, also observed a different behavior for liquids having Morton number values greater or less than lo-'. They used the deformation parameter developed by Tadaki and Maeda (19611, where the ratio of the bubble spherical equivalent diameter ( d ) over its major axis ( A ) was related to the Tadaki number (Tu).…”

“…They used the deformation parameter developed by Tadaki and Maeda (19611, where the ratio of the bubble spherical equivalent diameter ( d ) over its major axis ( A ) was related to the Tadaki number (Tu). With these definitions, Miyahara and Takahashi (1985) found that for a modified Reynolds number (Re') greater than 10, the modified drag coefficient (C; ) lies between two given limiting curves.…”

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions

“…According to Miyahara and Takahashi (1985) in the case of a nonspherical particle with a vertical axis of symmetry, the force balance showed that the Reynolds number should be expressed as:…”

“…The drag coefficient of a nonspherical particle with a vertical axial symmetry moving in either Newtonian or nonNewtonian fluid can be calculated on the basis of the force balance and is defined (Karamanev, 1994;Miyahara and Takahashi, 1985) as…”

Simulation of Rising Bubbles Dynamics Using the Lattice Boltzmann Method

“…Olsson and Kreiss [20] presented a conservative method of level set type for moving interfaces in divergence-free velocity fields and applied this approach to single rising bubbles. The wake velocity and the bubble shapes of single and a chain of bubbles were studied by Miyahara et al [23] for various Tadaki numbers (Re×M 0.23 ). Hoffmann et al [24] investigated bubbles rising at intermediate…”