Abstract
A two-dimensional immiscible droplet deformation phenomenon on a moving channel bottom wall is simulated using the lattice Boltzmann method. We considered the effect of the initial static contact angle, the capillary number, and the size of the droplet on the dynamic behavior of the moving droplet. When the initial static contact angle is less than 90°, the moving droplet is deformed and stretched, resulting in increasing width and decreasing height of the droplet. This is due to the hydrophilic (wetting) characteristic of the channel’s bottom wall. However, when the initial static contact angle is larger than 90°, the deformed and stretched droplet on the moving channel bottom wall is broken up, and is then pinched off or detached from the moving channel bottom wall, depending on the initial static contact angle and capillary number. This is due to the hydrophobic (non-wetting) characteristic of the wall.
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References
G. R. McNamara and G. Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata, Physical Review Letters, 61 (1988) 2332–2335.
F. J. Higuera and J. Jimenez, Boltzmann approach to lattice gas simulations, Europhysics Letters, 9 (1989) 663–668.
S. Chen, H. Chen, D. Martinez and W. Matthaeus, Lattice Boltzmann model for simulation of magnetohydrodymanics, Physical Review Letters, 67 (1991) 3776–3780.
Y. H. Qian, D. d’Humieres and P. Lallemand, Lattice BGK models for Navier-Stokes equation, Europhysics. Letters, 17 (1992) 479–484.
A. K. Gunstensen and D. H. Rothman, Lattice Boltzmann model of immiscible fluids, Physical Review A, 43 (1991) 4320–4327.
D. H. Rothman and J. M. Keller, Immiscible cellularautomation fluids, Journal of Statistical Physics, 52 (1988) 1119–1124.
D. Grunau, S. Chen and K. Eggert, A lattice Boltzmann model for multiphase fluids flows, Physics of Fluids, A5 (1993) 2557–2569.
X. Shan and H. Chen, Lattice Boltzmann model of simulating flows with multiple phases and components, Physical Review E, 47 (1993) 1815–1819.
X. Shan and G. Doolen, Multicomponent lattice-Boltzmann model with interparticle interaction, Journal of Statistical Physics, 81 (1995) 379–393.
X. He, S. Chen, R. Zhang, A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, Journal of Computational Physics, 152 (1999) 642–663.
X. He, X. Shan and G. D. Doolen, Discrete Boltzmann equation model for nonideal gases, Physical Review E, 57 (1998) R13–R16.
M. R. Swift, W. R. Osborn and J. M. Yeomans, Lattice Boltzmann simulation of nonideal fluids, Physical Review Letters, 75 (1995) 830–833.
T. Inamuro, T. Ogata, S. Tajima and N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, Journal of Computational Physics, 198 (2004) 628–644.
Y. Y. Yan and Y. Q. Zu, A lattice Boltzmann method for incompressible two-phase flow on partial wetting surface with large density ratio, Journal of Computational Physics, 227 (2007) 763–775.
M. Yoshino and Y. Mizutani, Lattice Boltzmann simulation of liquid-gas flows through solid bodies in a square duct, Mathematics and Computers in Simulation, 72 (2006) 264–269.
A. J. Briant, P. Papatzacos and J. M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid-gas system, Philosophical Transactions of the Royal Society A, 360 (2002) 485–495.
A. J. Briant, A. J. Wagner and J. M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid-gas system, Physical Review E, 69 (2004) 031602.
J. W. Cahn, Critical point wetting, The Journal of Chemical Physics, 66 (1977) 3667–3672.
Y. Kataoka and T. Inamuro, Numerical simulations of the behavior of a drop in a square pipe flow using the two-phase lattice Boltzmann method, Philosophical Transactions of The Royal Society A, 369 (2011) 2528–2536.
Y. Tanaka, Y. Washio, M. Yoshino and T. Hirata, Numerical simulation of dynamic behavior of droplet on solid surface by the two-phase lattice Boltzmann method, Computers & Fluids, 40 (2011) 68–78.
E. B. Dussan, The moving contact line: the slip boundary condition, Journal of Fluid Mechanics, 77 (1976) 665–684.
L. M. Hocking, A moving fluid interface on a rough surface, Journal of Fluid Mechanics, 76 (1976) 801–817.
K. M. Jansons, Moving contact lines on a two-dimensional rough surface, Journal of Fluid Mechanics, 154 (1985) 1–28.
M. Y. Zhou and P. Sheng, Dynamics of immiscible fluid displacement in a capillary tube, Physical Review Letters, 64 (1990) 882–885.
J. Koplik, J. R. Banavar and J. F. Willemsen, Molecular dynamics of a Poiseuille flow and moving contact lines, Physical Review Letters, 60 (1988) 1282–1286.
Y. D. Shikhmurzaev, Moving contact lines in liquid/liquid/solid systems, Journal of Fluid Mechanics, 334 (1997) 211–249.
A. D. Schleizer and R. T. Bonnecaze, Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows, Journal of Fluid Mechanics, 383 (1998) 29–54.
Q. Kang, D. Chen and S. Chen, Displacement of a twodimensional immiscible droplet in a channel, Physics of Fluid, 14 (2002) 3203–3214.
Q. Kang, D. Chen and S. Chen, Displacement of a threedimensional immiscible droplet in a duct, Journal of Fluid Mechanics, 545 (2005) 41–65.
H. Ding and P. D. M. Spelt, Onset of motion of a threedimensional droplet on a wall in shear flow at moderate Reynolds number, Journal of Fluid Mechanics, 599 (2008) 341–362.
H. Ding, M. N. H. Gilani and P. D. M. Spelt, Sliding, pinch-off and detachment of a droplet on a wall in shear flow, Journal of Fluid Mechanics, 53 (2008) 1–28.
L. Wu, M. Tsutahara, L. S. Kim and M. Y. Ha, Threedimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel, International Journal of Multiphase Flow, 34 (2008) 852–864.
D. H. Rothman and S. Zaleski, Lattice gas cellular automata, Cambridge University Press: Cambridge (1997).
J. U. Brackbill, D. B. Kothe and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, 100 (1992) 335–354.
Taylor, G. I. Proc and R. Soc. London, Ser. A 1932, 138, 41.
Taylor, G. I. Proc and R. Soc. London, Ser. A 1934, 146, 501.
S. Hou, X. Shan, Q. Zou, G. Doolen and W. Soll, Evaluation of two lattice Boltzmann models for multiphase flows, Journal of Computational Physics, 138 (1997) 695–713.
N. S. Martys and H. Chen, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method, Physical Review E, 53 (1996) 743–751.
B. R. Sehgal, R. R. Nourgaliev and T. N. Dinh, Numerical simulation of droplet deformation and break-up by lattice Boltzmann method, Progress in Nuclear Energy, 34 (1999) 471–488.
F. A. L. Dullien, Porous Media: Fluid Transport and Pore Structure, Academic, New York (1992).
S. Wolfram, Cellular automaton fluids. 1: Basic theory, Journal of Statistical Physics, 45 (1986) 471–526.
P. Lavallee, J. P. Boon and A. Noullez, Boundaries in lattice gas flows, Physic D: Nonlinear Phenomena, 47 (1991) 233–240.
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Recommended by Associate Editor Gihun Son
M. Y. Ha received his B.S. degree from Pusan National University, Korea in 1981, his M.S. degree, in 1983, from Korea Advanced Institute of Science and Technology, Korea, and his Ph.D. from Pennsylvania State University, USA in 1990. Dr. Ha is currently a Professor at the School of Mechanical Engineering at Pusan National University in Buasn, Korea. He serves as an Editor of the Journal of Mechanical Science and Technology. His research interests are focused on thermal management, computational fluid dynamics, and micro/nano fluids.
H. R. Kim received his M.S. degree in 2011 from Pusan National University, Korea. In his master course, he conducted a number of studies under the supervision of Prof. Man-Yeong Ha. His research interests are focused on thermofluid phenomena analysis for enhancing the efficiency of industrial devices.
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Kim, H.R., Ha, M., Yoon, H.S. et al. Dynamic behavior of a droplet on a moving wall. J Mech Sci Technol 28, 1709–1720 (2014). https://doi.org/10.1007/s12206-014-0316-y
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DOI: https://doi.org/10.1007/s12206-014-0316-y