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The immiscible displacement process in micro-channel, which widely existes in daily life and industrial production, is an important research subject. This subject is a typical contact line problem involving complicated fluid-fluid interactions and fluid-solid interactions which have attracted the interest of many scholars. Although the immiscible displacement in micro-channels has been studied by some researches, the problem is still not fully understood because the mechanism of the immiscible displacement is very complex. In order to further explain the physical mechanism of immiscible displacement process in micro-channels, detailed numerical simulations are carried out in a complex micro-channel containing a semicircular cavity and a semicircular by bulge using an improved pseudo-potential lattice Boltzmann method (LBM). This model overcomes the drawback of the dependence of the fluid properties on the grid size, which exists in the original pseudo-potential LBM. Initially, the cavity is filled with the liquid and the rest of the area is filled with its vapour. The semicircular bulge represents the roughness of the micro-channel. The approach is first validated by the Laplace law. The results show that the numerical results are in good agreement with the theoretical predictions. Then the model is employed to study the immiscible displacement process in the micro-channel. The effects of the surface wettability, the surface roughness, the viscosity ratio between the liquid phase and the gas phase, and the distance between the semicircular cavity and the semicircular bulge are studied. The simulation results show that the influence of the surface wettability on the displacement process is a decisive factor compared with other factors. With the increase of the contact angle, the displacement efficiency increases and the displacement time decreases. When the contact〉is larger than a certain value, all of the liquid can be displaced from the cavity. At that time, the displacement efficiency is equal to 1. The above results are consistent with the theoretical prediction that with the increase of the contact angle, the liquid is easily driven out of the cavity because the adhesion force of the liquid in the cavity decreases. On the other hand, the influence of the surface roughness on the displacement process is more complex. The displacement efficiency increases with the radius of the semicircle bulge increasing in a certain range. When the radius is larger than a certain value, the liquid cannot be ejected from the cavity due to the velocity around the cavity is too small. Furthermore, the liquid cannot be displaced from the cavity at a small viscosity ratio. As the viscosity ratio increases, the displacement efficiency increases and the displacement time decreases. As for the distance between the semicircular bulge and the semicircular cavity, it promotes the displacement process at an early stage. When the distance exceeds a certain value, it has little effect on the displacement process.
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Keywords:
- immiscible displacement /
- lattice Boltzmann method /
- displacement efficiency /
- displacement time
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[29] Guo Z, Zhao T S 2005 Phys. Rev. E 71 026701
[30] Yu Z, Fan L S 2009 J. Comput. Phys. 228 6456
[31] Guo Z, Zheng C, Shi B 2002 Phys. Rev. E 65 046308
[32] Martys N S, Chen H 1996 Phys. Rev. E 53 743
[33] Zhang R, He X, Chen S 2000 Comput. Phys. Commun. 129 121
[34] Fakhari A, Rahimian M H 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3046
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[37] Huang H, Lu X 2009 Phys. Fluids 21 092104
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[1] Tecklenburg J, Neuweiler I, Dentz M, Carrera J, Geiger S, Abramowski C, Silva O 2013 Adv. Water Res. 62 475
[2] Zhu X, Sui P C, Djilali N 2008 J. Power Sources 181 101
[3] Yang D, Krasowska M, Priest C, Ralston J 2014 Phys. Chem. Chem. Phys. 16 24473
[4] Islam S F, Sundara R V, Whitehouse S, Althaus T O, Palzer S, Hounslow M J, Salman A D 2016 Chem. Eng. Res. Des. 110 160
[5] Li W Z, Sun H M, Dong B 2013 Chin. J. Computat. Mech. 1 106 (in Chinese)[李维仲, 孙红梅, 董波 2013 计算力学学报 1 106]
[6] Primkulov B K, Lin F, Xu Z 2016 Colloids Surf. A:Physicochem. Eng. Aspects 497 336
[7] Koplik J, Banavar J R, Willemsen J F 1988 Phys. Rev. Lett. 60 1282
[8] Zhou G, Chen Z, Ge W, Li J 2010 Chem. Eng. Sci. 65 3363
[9] Jamaloei B Y, Kharrat R 2010 Transp. Porous Med. 81 1
[10] Pramanik S, Mishra M 2016 Phys. Rev. E 94 043106
[11] Yang K, Guo Z 2016 Comput. Fluids 124 157
[12] Kang Q, Zhang D, Chen S 2002 Phys. Fluids 14 3203
[13] Kang Q, Zhang D, Chen S 2005 J. Fluid Mech. 545 41
[14] Kang Q, Zhang D, Chen S 2004 Adv. Water Res. 27 13
[15] Huang H, Huang J J, Lu X Y 2014 Comput. Fluids 93 164
[16] Dong B, Yan Y Y, Li W, Song Y 2010 Comput. Fluids 39 768
[17] Dong B, Yan Y Y, Li W Z 2011 Transp. Porous. Med. 88 293
[18] Li W Z, Dong B, Song Y C 2012 J. Dalian Univ. Technol. 3 343 (in Chinese)[李维仲, 董波, 宋永臣 2012 大连理工大学学报 3 343]
[19] Li J, Song Y C, Li W Z 2009 J. Thermal Sci. Technol. 4 284 (in Chinese)[李娟, 宋永臣, 李维仲 2009 热科学与技术 4 284]
[20] Peng B L, Xu W, Wen R F, Lan Z, Bai T, Ma X H 2015 J. Eng. Thermophys. 4 820 (in Chinese)[彭本利, 徐威, 温荣福, 兰忠, 白涛, 马学虎 2015 工程热物理学报 4 820]
[21] Liang H, Chai Z, Shi B, Guo Z, Li Q 2015 Int. J. Mod. Phys. C 26 1550074
[22] Gunstensen A K, Rothman D H, Zaleski S, Zanetti G 1991 Phys. Rev. A 43 4320
[23] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[24] Shan X, Chen H 1994 Phys. Rev. E 49 2941
[25] Swift M R, Osborn W R, Yeomans J M 1995 Phys. Rev. Lett. 75 830
[26] Swift M R, Orlandini E, Osborn W R, Yeomans J M 1996 Phys. Rev. E 54 5041
[27] Luo L S 1998 Phys. Rev. Lett. 81 1618
[28] He X, Chen S, Zhang R 1999 J. Comput. Phys. 152 642
[29] Guo Z, Zhao T S 2005 Phys. Rev. E 71 026701
[30] Yu Z, Fan L S 2009 J. Comput. Phys. 228 6456
[31] Guo Z, Zheng C, Shi B 2002 Phys. Rev. E 65 046308
[32] Martys N S, Chen H 1996 Phys. Rev. E 53 743
[33] Zhang R, He X, Chen S 2000 Comput. Phys. Commun. 129 121
[34] Fakhari A, Rahimian M H 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3046
[35] Zheng H W, Shu C, Chew Y T 2006 J. Comput. Phys. 218 353
[36] Hao L, Cheng P 2000 J. Power Sources 190 435
[37] Huang H, Lu X 2009 Phys. Fluids 21 092104
[38] Li Q, Luo K H, Kang Q J, Chen Q 2014 Phys. Rev. E 90 053301
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