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Research Papers: Multiphase Flows

Modeling and Experimental Investigation of Bubble Formation in Shear-Thinning Liquids

[+] Author and Article Information
Mohamad Taghi Esfidani

School of Mechanical Engineering,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: mtesfidani@gmail.com

Mohammad Reza Oshaghi

School of Mechanical Engineering,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: mreza.oshaghi@gmail.com

Hossein Afshin

Associate Professor
School of Mechanical Engineering,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: afshin@sharif.edu

Bahar Firoozabadi

Professor
School of Mechanical Engineering,
Sharif University of Technology,
Tehran 1458889694, Iran
e-mail: firoozabadi@sharif.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 14, 2016; final manuscript received February 5, 2017; published online April 24, 2017. Assoc. Editor: Kausik Sarkar.

J. Fluids Eng 139(7), 071302 (Apr 24, 2017) (9 pages) Paper No: FE-16-1306; doi: 10.1115/1.4036158 History: Received May 14, 2016; Revised February 05, 2017

This investigation presents both theoretical and experimental studies on the size of a growing bubble in power-law non-Newtonian liquids. At first, some previous works on the prediction of bubble size in Newtonian liquids have been extended by considering the balance of forces acting on the bubble at the moment of separation. Predicted bubble sizes were validated against the experimental results for a wide range of operating conditions, including different gas flow rates and needle diameters as well as a wide range of physical properties of the Newtonian liquids. Furthermore, in order to determine the size of the bubbles formed in power-law non-Newtonian liquids with a similar analysis, the effective shear rate of bubble growth was calculated in which the rheological properties of fluid were taken into account and subsequently the viscosity of the fluid was modified. Theoretically obtained bubble sizes for non-Newtonian liquids are in a good agreement with our experimental high-speed video observations of three carboxyl methyl cellulose (CMC) solutions.

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Figures

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Fig. 1

Schematic of forces acting on the bubble

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Fig. 2

Comparison of drag coefficient calculated by Eqs. (6) and (7)

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Fig. 3

Experimental setup: 1, Syringe pump; 2, valve; 3, needle; 4, fluid container; 5, light-emitting diode (LED) projector; 6, high-speed camera; and 7, computer

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Fig. 4

Calibration of experiments. The bubble diameter as a function of time: (a) water and (b) glycerin (needle internal diameter = 2.0 mm).

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Fig. 5

The shape of the growing bubble in water at four different times: (a) t = 9 ms, (b) t = 18 ms, (c) t = 27 ms, and (d) t = 37 ms

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Fig. 6

Viscosity as a function of shear rate for aqueous solutions of CMC

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Fig. 7

Comparison of theoretical (line) and experimental (point) bubble diameter formed in Newtonian liquids (needle internal diameter = 1.4 mm)

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Fig. 8

Comparison of theoretical (line) and experimental (point) bubble diameter formed in Newtonian liquids (needle internal diameter = 2.0 mm)

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Fig. 9

Comparison of the predictions from the present model and experimental results of Jamialahmadi et al. [3] and Davidson and Schüler [28] in water (ρ = 1000 kg/m3, μ = 0.001 Pa·s, and σ = 72 mN/m) and aqueous solution of glycerol (ρ = 1256 kg/m3, μ = 0.929 Pa⋅s, and σ = 63.9 mN/m), respectively

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Fig. 10

The magnitude of forces acting on the bubble formed in a Newtonian fluid: (a) water and (b) glycerin (needle internal diameter = 2.0 mm)

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Fig. 11

Bubble diameter as a function of viscosity for various gas flow rates (needle internal diameter = 2.0 mm)

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Fig. 12

Bubble shape at the moment of separation for various gas flow rates (needle internal diameter = 2 mm). The concentration of CMC solution is (a) 1% w/w, (b) 1.5% w/w, and (c) 2% w/w.

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Fig. 13

Variation of the dimensionless rupture height in CMC solutions (the dashed line shows the average value)

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Fig. 14

Size of the bubbles in CMC solutions. The lines indicate predicted values, and the points show experimental values (needle internal diameter = 1.4 mm).

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Fig. 15

Size of the bubbles in CMC solutions. The lines indicate predicted values, and the points show experimental values (needle internal diameter = 2.0 mm).

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Fig. 16

Comparison between predicted bubble diameter by present model and experimental data from Martín et al. [33] innon-Newtonian aqueous solutions of CMC (1.2, 1.4, and 1.6% w/w) at flow rates of 1, 5, and 10 cm3/s

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Fig. 17

Variation of Reynolds number with gas flow rate in CMC solutions

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Fig. 18

Variations of effective shear rate with gas flow rate for CMC solutions of different concentrations (needle internal diameter = 2.0 mm)

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