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Viscous effect on stagnation depth of bubbles in a vertically oscillating liquid column
Author(s) -
Marmur Abraham,
Rubin Eliezer
Publication year - 1976
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450540605
Subject(s) - dimensionless quantity , drag coefficient , drag , mechanics , stagnation point , stagnation temperature , bubble , viscous liquid , stagnation pressure , acceleration , parasitic drag , physics , classical mechanics , heat transfer , mach number
Previous theories which evaluated the stagnation depth of bubbles in a vertically oscillating liquid column are reviewed, and it is pointed out that they used an insufficient criterion for determining stagnation. The correct condition, which states that stagnation means zero mean velocity rather than acceleration, necessitates the solution of the equation of motion of the bubble, and thus viscous drag has to be included. It is shown, in accordance with available experimental data, that the value of the dimensionless group M = ω 4 A 2 ρh/2gP o (which gives the stagnation depth h) is not in general a constant, but is dependent on four other dimensionless groups. Although there is no reliable information concerning the drag coefficient curve for such a situation, it is suggested, on the basis of comparison between different drag coefficient curves, that the high values of M reported in the literature and not accounted for by theory are due to bubble shape deviations from sphericity in viscous flow.