0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Boomsma, K., and Poulikakos, D., 2002, “The Effect of Compression and Pore Size Variations on the Liquid Flow Characteristics in Metal Foams,” ASME J. Fluids Eng., 124(1), pp. 263–272. [CrossRef]
Dukhan, N., Picón-Feliciano, R., and Álvarez-Hernández, Á. R., 2006, “Air Flow Through Compressed and Uncompressed Aluminum Foam: Measurements and Correlations,” ASME J. Fluids Eng., 128(5), pp.1004–1012. [CrossRef]
Reidenbach, V. G., Harris, P. C., Lee, Y. N., and Lord, D. L., 1986, “Rheological Study of Foam Fracturing Fluids Using Nitrogen and Carbon Dioxide,” SPE Prod. Eng., 1(1), pp. 31–41. [CrossRef]
Saint-Jalmes, A., and Durian, D., 1999, “Vanishing Elasticity for Wet Foams: Equivalence With Emulsions and Role of Polydispersity,” J. Rheol., 43(6), pp. 1411–1422. [CrossRef]
Bick, A. G., Ristenpart, W. D., van Nierop, E. A., and Stone, H. A., 2011, “Mechanical Inhibition of Foam Formation Via a Rotating Nozzle,” ASME J. Fluids Eng., 133(4), p. 044503. [CrossRef]
Katgert, G., Möbius, M. E., and van Hecke, M., 2008, “Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams,” Phys. Rev. Lett., 101(5), p. 058301. [CrossRef] [PubMed]
Mohammadigoushki, H., and Feng, J. J., 2013, “Size Segregation in Sheared Two-Dimensional Polydisperse Foam,” Langmuir, 29(5), pp. 1370–1378. [CrossRef] [PubMed]
Mohammadigoushki, H., Ghigliotti, G., and Feng, J. J., 2012, “Anomalous Coalescence in Sheared Two-Dimensional Foam,” Phys. Rev. E, 85(6), p. 066301. [CrossRef]
Weaire, D., Coughlan, S., and Fortes, A. M., 1995, “The Modeling of Liquid and Solid Foams,” J. Mater. Process. Technol., 55(3–4), pp. 178–185. [CrossRef]
Jiang, Y., Swart, P. J., Saxena, A., Asipauskas, M., and Glazier, J. A., 1999, “Hysteresis and Avalanches in Two-Dimensional Foam Rheology Simulations,” Phys. Rev. E, 59(5), pp. 5819–5832. [CrossRef]
Kermode, J. P., and Weaire, D., 1990, “2D-FROTH: A Program for the Investigation of 2-Dimensional Froths,” Comput. Phys. Commun., 60(1), pp. 75–109. [CrossRef]
Brakke, K. A., 1992, “The Surface Evolver,” Exp. Math., 1(2), pp. 141–165. [CrossRef]
Durian, D. J., 1995, “Foam Mechanics at the Bubble Scale,” Phys. Rev. Lett., 75(26), pp. 4780–4783. [CrossRef] [PubMed]
Langlois, V. J., Hutzler, S., and Weaire, D., 2008, “Rheological Properties of the Soft-Disk Model of Two-Dimensional Foams,” Phys. Rev. E, 78(2), p. 021401. [CrossRef]
Okuzono, T., and Kawasaki, K., 1995, “Intermittent Flow Behavior of Random Foams: A Computer Experiment on Foam Rheology,” Phys. Rev. E, 51(2), pp. 1246–1253. [CrossRef]
Sun, Q., and Hutzler, S., 2004, “Lattice Gas Simulations of Two-Dimensional Liquid Foams,” Rheol. Acta, 43(5), pp. 567–574. [CrossRef]
Weaire, D., Bolton, F., Herdtle, T., and Aref, H., 1992, “The Effect of Strain Upon the Topology of a Soap Froth,” Phil. Mag. Lett., 66(6), pp. 293–299. [CrossRef]
Weaire, D., and Kermode, J., 1983, “Computer Simulation of a Two-Dimensional Soap Froth: I. Method and Motivation,” Phil. Mag. B, 48(3), pp. 245–259. [CrossRef]
Kern, N., Weaire, D., Martin, A., Hutzler, S., and Cox, S. J., 2004, “Two-Dimensional Viscous Froth Model for Foam Dynamics,” Phys. Rev. E, 70(4), p. 041411. [CrossRef]
Vincent-Bonnieu, S., Hohler, R., and Cohen-Addad, S., 2006, “A Multiscale Model for the Slow Viscoelastic Response of Liquid Foams,” e-print: arXiv preprint cond-mat/0609363.
Kabla, A., Scheibert, J., and Debregeas, G., 2007, “Quasi-Static Rheology of Foams. Part 2. Continuous Shear Flow,” J. Fluid Mech., 587, pp. 45–72. [CrossRef]
Kabla, A., and Debregeas, G., 2007, “Quasi-Static Rheology of Foams. Part 1. Oscillating Strain,” J. Fluid Mech., 587, pp. 23–44. [CrossRef]
Yuan, X., and Edwards, S., 1995, “Flow Behaviour of Two-Dimensional Random Foams,” J. Non-Newtonian Fluid Mech., 60(2), pp. 335–348. [CrossRef]
Gajbhiye, R. N., and Kam, S. I., 2011, “Characterization of Foam Flow in Horizontal Pipes by Using Two-Flow-Regime Concept,” Chem. Eng. Sci., 66(8), pp. 1536–1549. [CrossRef]
Dollet, B., and Graner, F., 2007, “Two-Dimensional Flow of Foam Around a Circular Obstacle: Local Measurements of Elasticity, Plasticity and Flow,” J. Fluid Mech., 585, pp. 181–211. [CrossRef]
Langlois, V. J., 2014, “The Two-Dimensional Flow of a Foam Through a Constriction: Insights From the Bubble Model,” J. Rheol., 58(3), pp. 799–818. [CrossRef]
Ivanov, I. B., Dimitrov, A. S., Nikolov, A. D., and Kralchevsky, P. A., 1992, “Contact Angle, Film, and Line Tension of Foam Films. I. Stationary and Dynamic Contact Angle Measurements,” J. Colloid Interf. Sci., 151(2), pp. 446–461. [CrossRef]
Cox, S. J., and Whittick, E. L., 2006, “Shear Modulus of Two-Dimensional Foams: The Effect of Area Dispersity and Disorder,” Eur. Phys. J. Part E, 21(1), pp. 49–56. [CrossRef]
Marion, G., Sahnoun, S., Mendiboure, B., Dicharry, C., and Lachaise, J., 1992, “Reflectometry Study of Interbubble Gas Transfer in Liquid Foams,” Trends in Colloid and Interface Science VI, Steinkopff, Heidelberg, Germany, pp. 145–148. [CrossRef]
Kabla, A., and Debrégeas, G., 2003, “Local Stress Relaxation and Shear Banding in a Dry Foam Under Shear,” Phys. Rev. Lett., 90(25), pp. 258–303. [CrossRef]
Cox, S., Weaire, D., and Glazier, J. A., 2004, “The Rheology of Two-Dimensional Foams,” Rheol. Acta, 43(5), pp. 442–448. [CrossRef]
Cox, S., 2005, “A Viscous Froth Model for Dry Foams in the Surface Evolver,” Colloid Surf. A, 263(1), pp. 81–89. [CrossRef]
Harris, P. C., 1996, “High-Quality Foam Fracturing Fluids,” GTS: Gas Technology Symposium, Calgary, AB, Canada, Apr. 28–May 1, pp. 265–273.

Figures

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In