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Research Papers: Fundamental Issues and Canonical Flows

Flow Behavior of Two-Dimensional Wet Foam: Effect of Foam Quality

[+] Author and Article Information
Zefeng Jing

Key Laboratory of Thermo-Fluid Science
and Engineering of MOE,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an Shaanxi 710049, China
e-mail: nyg201@foxmail.com

Shuzhong Wang

Key Laboratory of Thermo-Fluid Science
and Engineering of MOE,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an Shaanxi 710049, China
e-mail: SZWang@aliyun.com

Mingming Lv

Key Laboratory of Thermo-Fluid Science
and Engineering of MOE,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an Shaanxi 710049, China
e-mail: y.fzhang@gmail.com

Zhiguo Wang

Key Laboratory of Thermo-Fluid Science
and Engineering of MOE,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an Shaanxi 710049, China
e-mail: 719137427@qq.com

Xiangrong Luo

Key Laboratory of Thermo-Fluid Science
and Engineering of MOE,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an Shaanxi 710049, China
e-mail: wsjing@stu.xjtu.edu.cn

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 4, 2014; final manuscript received October 16, 2014; published online January 27, 2015. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 137(4), 041206 (Apr 01, 2015) (9 pages) Paper No: FE-14-1285; doi: 10.1115/1.4028892 History: Received June 04, 2014; Online January 27, 2015

The flow behaviors of two-dimensional (2D) wet monodisperse and polydisperse foams are investigated by the quasi-static simulation. We set the same inlet velocity on the cross section of the foam channel and then focus on the elastic–plastic deformation of the 2D wet foam according to the strain caused by the foam flow. The gas fraction in foam is referred to as foam quality and the effects of foam quality on the shear modulus, bubble dynamics, and stress–strain properties are obtained by the simulation. In the elastic domain, the shear modulus of monodisperse foam decreases exponentially with foam quality, but for the polydisperse foam, the shear modulus tends to increase. The shear banding of the polydisperse foam appears in the low strain and disappears gradually as the strain and foam quality increase. We adopt shear rate to represent the change rate of average bubbles displacements versus y-coordinates and find that the distribution of shear rate in the y-direction changes with iteration. Additionally, energy of the foam is stored and dissipated with the elastic–plastic deformation of the foam. The average shear stress generated by the foam structure and the initial increment of normal stress difference caused by the elastic deformation increase with the increase of foam quality.

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Figures

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Fig. 1

The T1 event for a 2D wet foam. This topological rearrangement results in neighbor swapping between two pairs of bubbles. Bubbles 2 and 3 were initially adjacent to each other. Subsequently, bubbles 1 and 4 become neighbors after the T1 event.

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Fig. 2

A contact angle α is determined by the tension of air–liquid–air interface γ1 and the tension of air–liquid interface γ2

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Fig. 3

Examples of 2D wet foam with Φg = 0.90 between parallel walls for different area-disorders

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Fig. 4

Half of the foam channel. The vertices of films on the centerline move a distance δx in the x direction. W represents the half-width of the whole flow channel.

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Fig. 5

The shear modulus G of the foam as a function of foam quality Φg for different area-disorders

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Fig. 6

The equilibrium configurations of the foam with Φg = 0.92 and μ2(A)= 0 at different strains. For the ordered foam, the T1s localize between the first and second layer of bubbles in the strain increment.

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Fig. 7

The equilibrium configurations of the foam with Φg = 0.92 and μ2(A)= 0.0381 at different strains

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Fig. 8

The y-position of each T1 event versus increasing strains for different foam qualities: μ2(A) of the foam is 0.0381

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Fig. 9

Displacement fields and displacement size of each bubble corresponding to the left displacement fields for: (a) 0–8 iterations, (b) 12–20 iterations, and (c) 24–32 iterations for the foam with Φg = 0.92 and μ2(A)= 0.0381. The plus signs show the coordinates of T1s during the iteration intervals. And the y-positions of T1s versus applied strains are shown in Fig. 8(c). The curves display average displacements of the bubbles at approximate y-coordinates versus y-positions in these iteration intervals.

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Fig. 10

Displacement fields and displacement size of each bubble corresponding to the left displacement fields for 0–8 iterations for the foam with Φg = 0.92 and μ2(A)= 0. There is not T1 event in this iteration interval.

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Fig. 11

Evolutions of (a) the shear stress, (b) normal stress difference, and (c) the energy of the foam with respect to the strain for different area-disorders with Φg = 0.92. The straight lines “a” and “b” represent the average shear stress of monodisperse (μ2(A)= 0) foam and polydisperse (μ2(A)= 0.0381) foam during the strain increment, respectively.

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Fig. 12

Evolutions of (a) the shear stress and (b) normal stress difference of the foam with different foam qualities versus the strain. The area-disorder μ2(A)= 0.0381. The straight lines “a,” “b,” and “c” represent the average shear stress of the foam with Φg = 0.9, 0.92, and 0.94, respectively.

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