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Research Papers: Two-Phase Flow and Heat Transfer

# Thermosolutocapillary Convection in an Open Rectangular Cavity With Dynamic Free Surface

[+] Author and Article Information
Xiaoming Zhou

Institute of Engineering Thermal Physics,
Beijing 100190, China
e-mail: xmzhou@iet.cn

Xiulan Huai

Institute of Engineering Thermal Physics,
Beijing 100190, China
e-mail: hxl@iet.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 13, 2014; final manuscript received October 31, 2014; published online April 16, 2015. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 137(8), 082901 (Aug 01, 2015) (9 pages) Paper No: HT-14-1402; doi: 10.1115/1.4029270 History: Received June 13, 2014; Revised October 31, 2014; Online April 16, 2015

## Abstract

Thermosolutocapillary convection within a rectangular cavity with dynamic free surface is numerically investigated in the absence of gravitational effects. Both the temperature and solute concentration gradients are applied horizontally. The free surface deformation is captured by the level set method. Two cases of the ratio of thermal to solutal Marangoni number $Rσ$ < −1 and $Rσ$ = −1 are considered. For $Rσ$< −1, the free surface bulges out near the left wall and bulges in near the right wall; with the increase of Marangoni number, the free surface deformation decreases and with the increase of capillary number and aspect ratio, it increases. For $Rσ$= −1, the free surface bulges out near the left and right walls and bulges in at the central zone; with the increase of Marangoni number, the free surface deformation mode is changed and with the increase of capillary number and aspect ratio, the free surface deformation increases.

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## References

Bergman, T. L., 1986, “Numerical Simulation of Double-Diffusive Marangoni Convection,” Phys. Fluids, 29(7), pp. 2103–2108.
Chen, Z. W., Li, Y. S., and Zhan, J. M., 2010, “Double-Diffusive Marangoni Convection in a Rectangular Cavity: Onset of Convection,” Phys. Fluids, 22(3), p. 034106.
Li, Y. S., Chen, Z. W., and Zhan, J. M., 2010, “Double-Diffusive Marangoni Convection in a Rectangular Cavity: Transition to Chaos,” Int. J. Heat Mass Transfer, 53(23–24), pp. 5223–5231.
Zhan, J. M., Chen, Z. W., Li, Y. S., and Nie, Y. H., 2010, “Three-Dimensional Double-Diffusive Marangoni Convection in a Cubic Cavity With Horizontal Temperature and Concentration Gradients,” Phys. Rev. E, 82(6), p. 066305.
Chen, C. F., and Chan, C. L., 2010, “Stability of Buoyancy and Surface Tension Driven Convection in a Horizontal Double-Diffusive Fluid Layer,” Int. J. Heat Mass Transfer, 53(7–8), pp. 1563–1569.
Li, Y. R., Gong, Z. X., Wu, C. M., and Wu, S. Y., 2012, “Steady Thermal-Solutal Capillary Convection in a Shallow Annular Pool With the Radial Temperature and Concentration Gradients,” Sci. China Technol. Sci., 55(8), pp. 2176–2183.
Li, Y. R., Zhou, Y. L., Tang, J. W., and Gong, Z. X., 2013, “Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool,” Microgravity Sci. Technol., 25(4), pp. 225–230.
Sim, B. C., Kim, W. S., and Zebib, A., 2004, “Dynamic Free-Surface Deformations in Axisymmetric Liquid Bridges,” Adv. Space Res., 34(7), pp. 1627–1634. [PubMed]
Koster, J. N., 1994, “Early Mission Report on the Four ESA Facilities: Biorack; Bubble, Drop and Particle Unit; Critical Point Facility and Advanced Protein Crystallization Facility Flown on the IML-2 Spacelab Mission,” Microgravity News From ESA Report No.7, pp. 2–7.
Mundrane, M., Xu, J., and Zebib, A., 1995, “Thermocapillary Convection in a Rectangular Cavity With a Deformable Interface,” Adv. Space Res., 16(7), pp. 41–53. [PubMed]
Saghir, M. Z., Abbaschian, R., and Raman, R., 1996, “Numerical Analysis of Thermocapillary Convection in Axisymmetric Liquid Encapsulated InBi,” J. Cryst. Growth, 169(1), pp. 110–117.
Hamed, M., and Floryan, J. M., 2000, “Marangoni Convection. Part 1. A Cavity With Differentially Heated Sidewalls,” J. Fluid Mech., 405(1), pp. 79–110.
Gupta, N. R., Hossein, H. H., and Borhan, A., 2006, “Thermocapillary Flow in Double-Layer Fluid Structures: An Effective Single-Layer Model,” J. Colloid Interface Sci., 293(1), pp. 158–171. [PubMed]
Liang, R. Q., Ji, S. Y., and Li, Z., 2014, “Thermocapillary Convection in Floating Zone With Axial Magnetic Fields,” Microgravity Sci. Technol., 25(5), pp. 285–293.
Brackbill, J. U., Kothe, D. B., and Zemach, C., 1992, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., 100(2), pp. 335–354.
Sussman, M., Smereka, P., and Osher, S., 1994, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,” J. Comput. Phys., 114(1), pp. 146–159.
Liang, R. Q., Liao, Z. Q., Jiang, W., Duan, G. D., Shi, J. Y., and Liu, P., 2011, “Numerical Simulation of Water Droplets Falling Near a Wall: Existence of Wall Repulsion,” Microgravity Sci. Technol., 23(1), pp. 59–65.
Ni, M. J., Komori, S., and Abdou, M., 2010, “A Variable-Density Projection Method for Interfacial Flows,” Numer. Heat Transfer, Part B, 44(6), pp. 553–574.
Zhou, X. M., and Huang, H. L., 2010, “Numerical Simulation of Steady Thermocapillary Convection in a Two-Layer System Using Level Set Method,” Microgravity Sci. Technol., 22(4), pp. 223–232.

## Figures

Fig. 4

Streamlines distribution with Rσ = −8, Ca = 0.1, Le = 100, A = 4, and various Ma ((a) Ma=10, (b) Ma=50, (c) Ma=100, (d) Ma=200)

Fig. 5

Isotherms distribution with Rσ = −8, Ca = 0.1, Le = 100, A = 4, and various Ma ((a) Ma=10, (b) Ma=50, (c) Ma=100, (d) Ma=200)

Fig. 6

Solute concentration distribution with Rσ = −8, Ca = 0.1, Le = 100, A = 4, and various Ma ((a) Ma=10, (b) Ma=50, (c) Ma=100, (d) Ma=200)

Fig. 7

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −8, Ca = 0.1, Le = 100, A = 4, and various Ma

Fig. 1

Physical model

Fig. 2

Comparison of free surface deformation of liquid bridge with Sim’s results

Fig. 3

Contours of (a) temperature and (b) solute concentration with fixed free surface for Rσ = −1, Re = 200, Le = 100, Pr = 5, and A = 2

Fig. 8

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −8, Ma = 10, Le = 10, A = 4, and various Ca

Fig. 9

Streamlines distribution with Rσ = −8, Ma = 10, Le = 10, Ca = 0.1, and various A ((a) A=2, (b) A=4, (c) A=6, (d) A=8)

Fig. 10

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −8, Ma = 10, Le = 10, Ca = 0.1, and various A

Fig. 16

Streamlines distribution with Rσ = −1, Ma = 10, Le = 10, Ca = 0.1, and various A ((a) A=2, (b) A=4, (c) A=6, (d) A=8)

Fig. 17

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −1, Ma = 10, Le = 10, Ca = 0.1, and various A

Fig. 11

Streamlines distribution with Rσ = −1, Ca = 0.1, Le = 10, A = 4, and various Ma ((a) Ma=10, (b) Ma=50, (c) Ma=100, (d) Ma=200)

Fig. 12

Nondimensional surface tension distribution with Rσ = −1, Ca = 0.1, Le = 10, A = 4, and various Ma

Fig. 13

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −1, Ca = 0.1, Le = 10, A = 4, and various Ma

Fig. 14

Streamlines distribution with Rσ = −1, Ma = 10, Le = 10, A = 4, and various Ca ((a) Ca=0.01, (b) Ca=0.05, (c) Ca=0.1, (d) Ca=0.15)

Fig. 15

Free surface (a), surface pressure (b), and surface horizontal velocity (c) distributions with Rσ = −1, Ma = 10, Le = 10, A = 4, and various Ca

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