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The lattice Boltzmann method is used to simulate numerically the droplet motion driven by Marangoni effect, which is induced by surface tension gradient on the solid-liquid interface, with the consideration of interaction between solid and liquid molecules. The computation results are well compared with the theoretical prediction available for smaller surface tension gradient, whereas the translation velocity of droplet is smaller than the theoretical value for larger gradient, because some assumptions, such as the quasi-equilibrium and non-deformable droplet, are not satisfied in the theoretical analysis anymore. Vortical structure with a solid-like core is found in the droplet when it moves to the hydrophilic end. The variations of velocity and contact angle of droplet are found to be oscillating with time for larger gradient of wettability.
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Keywords:
- wettability /
- lattice Boltzmann method /
- Marangoni effect /
- droplet
[1] ［1］Bain C D, Burnett-Hall G D, Montgonerie R R 1994 Nature 372 414
[2] ［2］Mugele F, Baret J C 2005 J. Phys.: Condens. Matter 17 R705
[3] ［3］Squires T M, Quake S R 2005 Rev. Mod. Phys. 77 977
[4] ［4］Wang F, He F 2006 Acta Phys. Sin. 55 1005 ［王飞、何枫 2006 55 1005］
[5] ［5］Zhang X H, Zhang X J, Liu Y H, Schaefer J A, Wen S Z 2007 Acta Phys. Sin. 56 4722 ［张晓昊、张向军、刘永和、 Schaefer J A、温诗铸 2007 56 4722］
[6] ［6］Cassie A B D 1948 Discuss. Faraday Soc. 3 11
[7] ［7］Brochard F 1989 Langmuir 5 432
[8] ［8］Fabrice D D S, Thierry O 1995 Phys. Rev. Lett. 75 2972
[9] ［9］Yeo L Y, Craster R V, Matar O K 2007 J. Colloid Interface Sci. 306 368
[10] ］Martys N S, Chen H 1996 Phys. Rev. E 53 743
[11] ］Raiskinmki P 2000 Comput. Mat. Sci. 18 7
[12] ］Fang H, Wan R, Fan L 2000 Chin. Phys. 9 515
[13] ］Fan L, Fang H, Lin Z 2001 Phys. Rev. E 63 051603
[14] ］Kang Q, Zhang D, Chen S 2002 Phys. Fluids 14 3203
[15] ］Huang J J, Shu C, Chew Y T 2009 Phys. Fluids 21 022103
[16] ］Xing X Q, Butler D L, Yang C 2006 Comp. Math. Sci. 7 1
[17] ］Swift M R, Orlandini E, Osborn W R, Yeomans J M 1996 Phys. Rev. E 54 5041
[18] ］Dupuis A, Yeomans J M 2005 Langmuir 21 2624
[19] ］Zhang J, Li B, Kwok D Y 2004 Phys. Rev. E 69 032602
[20] ］Kawasaki A, Onishi J, Chen Y, Ohashi H 2007 Comp. Math. Appl. 55 1492
[21] ］Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing: Scientific Press) (in Chinese) ［郭照立、郑楚光 2009 格子Boltzmann方法的原理和应用（北京：科学出版社）］
[22] ］Raphal E 1988 C. R. Acad. Sci. Paris 306 751
[23] ］Hu G H, Xu A J, Xu Z, Zhou Z W 2008 Phys. Fluid. 20 102101
[24] ］Koplik J, Banavar J R 2000 Phys. Rev. Lett. 84 4401
-
[1] ［1］Bain C D, Burnett-Hall G D, Montgonerie R R 1994 Nature 372 414
[2] ［2］Mugele F, Baret J C 2005 J. Phys.: Condens. Matter 17 R705
[3] ［3］Squires T M, Quake S R 2005 Rev. Mod. Phys. 77 977
[4] ［4］Wang F, He F 2006 Acta Phys. Sin. 55 1005 ［王飞、何枫 2006 55 1005］
[5] ［5］Zhang X H, Zhang X J, Liu Y H, Schaefer J A, Wen S Z 2007 Acta Phys. Sin. 56 4722 ［张晓昊、张向军、刘永和、 Schaefer J A、温诗铸 2007 56 4722］
[6] ［6］Cassie A B D 1948 Discuss. Faraday Soc. 3 11
[7] ［7］Brochard F 1989 Langmuir 5 432
[8] ［8］Fabrice D D S, Thierry O 1995 Phys. Rev. Lett. 75 2972
[9] ［9］Yeo L Y, Craster R V, Matar O K 2007 J. Colloid Interface Sci. 306 368
[10] ］Martys N S, Chen H 1996 Phys. Rev. E 53 743
[11] ］Raiskinmki P 2000 Comput. Mat. Sci. 18 7
[12] ］Fang H, Wan R, Fan L 2000 Chin. Phys. 9 515
[13] ］Fan L, Fang H, Lin Z 2001 Phys. Rev. E 63 051603
[14] ］Kang Q, Zhang D, Chen S 2002 Phys. Fluids 14 3203
[15] ］Huang J J, Shu C, Chew Y T 2009 Phys. Fluids 21 022103
[16] ］Xing X Q, Butler D L, Yang C 2006 Comp. Math. Sci. 7 1
[17] ］Swift M R, Orlandini E, Osborn W R, Yeomans J M 1996 Phys. Rev. E 54 5041
[18] ］Dupuis A, Yeomans J M 2005 Langmuir 21 2624
[19] ］Zhang J, Li B, Kwok D Y 2004 Phys. Rev. E 69 032602
[20] ］Kawasaki A, Onishi J, Chen Y, Ohashi H 2007 Comp. Math. Appl. 55 1492
[21] ］Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing: Scientific Press) (in Chinese) ［郭照立、郑楚光 2009 格子Boltzmann方法的原理和应用（北京：科学出版社）］
[22] ］Raphal E 1988 C. R. Acad. Sci. Paris 306 751
[23] ］Hu G H, Xu A J, Xu Z, Zhou Z W 2008 Phys. Fluid. 20 102101
[24] ］Koplik J, Banavar J R 2000 Phys. Rev. Lett. 84 4401
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