Research Papers: Multiphase Flows

An Experimental Investigation for Bubble Rising in Non-Newtonian Fluids and Empirical Correlation of Drag Coefficient

[+] Author and Article Information
Fan Wenyuan, Ma Youguang, Jiang Shaokun, Yang Ke

State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China

Li Huaizhi

 Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC-INPL, 1 rue Grandville, BP 451 54001 Nancy Cedex, France

J. Fluids Eng 132(2), 021305 (Feb 17, 2010) (7 pages) doi:10.1115/1.4000739 History: Received April 22, 2009; Revised November 08, 2009; Published February 17, 2010; Online February 17, 2010

The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eötvös number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of the experiment system: 1—compressed nitrogen cylinder; 2—manometer; 3—valves; 4—pressure maintaining valve; 5—rotameter; 6—Plexiglass square tank; 7—tripod; 8—lasers; 9—photodiodes; 10—sampling detector; 11—computer; and 12—CCD camera

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Figure 2

Calibration curve of bubble terminal velocity in 93% Glycerin solution (uncertainty of data: ±2.1%)

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Figure 3

Master curve of shifted CD based on 1.0% PAM (uncertainty of data: ±8.6%)

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Figure 4

Bubble shape in different non-Newtonian fluids in the diagram of Grace (27): (a) 0.70%CMC, (b) 1.0%PAM, (c) 0.8%PAM, (d) 0.6%PAM, (e) 0.50%CMC, and (f) 0.35%CMC

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Figure 5

Master curve with shifted E based on 1.0% PAM (uncertainty of data:±6.9%)

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Figure 6

Instantaneous images of bubble rising: (a) 0.8%PAM, Re=43, Eo=5.0; (b) 0.8%PAM, Re=52, Eo=5.5; (c) 0.8%PAM, Re=61, Eo=5.8; and (d) 0.35%CMC, Re=172, Eo=4.5

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Figure 7

Effect of gas flow rate on bubble terminal velocity: (a) 0.6%PAM, d=1.6 mm (uncertainty of data: ±5.4%); and (b) 0.5%CMC d=1 m (uncertainty of data: ±4.0%)

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Figure 8

Effect of bubble volume on bubble terminal velocity (uncertainty of data: ±7.8%)

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Figure 9

Effect of solution concentration on bubble terminal velocity (uncertainty of data: (a) ±4.6% and (b) ±6.5%)

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Figure 10

Relationship between CD/Ar0.683 Eo−0.0931 and Re

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Figure 11

Comparison between measured and predicted CD

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Figure 12

Validity on present model in 93% glycerin solution




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