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Simulation of a falling droplet in a vertical channel with rectangular obstacles. (English) Zbl 1408.76524

Summary: Droplet microfluidic systems have attracted a large amount of research due to their numerous applications in biomedical micro-devices and drug discovery/delivery platforms. One of the most important problems in such systems is to investigate deformation, coalescence, and breakup of droplets within the channel. The present study demonstrates numerical simulation of a falling droplet subject to gravitational force in a channel with embedded rectangular obstacles. The lattice Boltzmann method incorporated using the He-Chen-Zhang method for two phase flow is employed. Two rectangular obstacles with inverse aspect ratios are introduced to investigate the mechanism of breakup and deformation of the droplet. The influence of gravity magnitude, viscosity and surface tension on the deformation rate of droplet for two different aspect ratios of the obstacle is studied. It is observed that increasing the gravity force, decreasing the viscosity or surface tension increase droplet deformation rate resulting in more stretched filaments, and so breakup occurs in a shorter time.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
76M28 Particle methods and lattice-gas methods
Full Text: DOI

References:

[1] Rahman, M. A.; Balzan, M.; Heidrick, T.; Fleck, B. A., Effects of the gas phase molecular weight and bubble size on effervescent atomization, Int. J. Multiph. Flow., 38, 1, 35-52, (2012)
[2] Chang, Hung-Ju; Tsai, Ming Hsiu; Hwang, Weng-Sing, The simulation of micro droplet behavior of molten lead-free solder in inkjet printing process and its experimental validation, Appl. Math. Model., 36, 7, 3067-3079, (2012)
[3] Eow, J. S.; Ghadiri, M., Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology, Chem. Eng. J., 85, 357-368, (2002)
[4] Tan, Y.-C.; Cristini, V.; Lee, A. P., Monodi spersed microfluidic droplet generation by shear focusing microfluidic device, Sens. Actuators B: Chem., 114, 350-356, (2006)
[5] Su, G.; Longest, P. W.; Pidaparti, R. M., A novel micro pump droplet generator for aerosol drug delivery: design simulations, Biomicrofluidics, 4, 044108, (2010)
[6] Clift, R.; Grace, J. R.; Weber, M. R., Bubbles, Drops, and Particles, (1978), Academic Press New York
[7] Zhao, Z.; Poulikakos, D.; Fukai, J., Heat transfer and fluid dynamics during the collision of a liquiddroplet on a substrate-II. experiments, Int. J. Heat Mass Transfer, 39, 13, 2791-2802, (1996) · Zbl 0964.76558
[8] Sikalo, S.; Marengo, M.; Tropea, C.; Ganic, E. N., Analysis of impact of droplets on horizontal surfaces, Exp. Therm Fluid Sci., 25, 7, 503-510, (2002)
[9] Sikalo, S.; Tropea, C.; Ganic, E. N., Impact of droplets onto inclined surfaces, J. Colloid Interface Sci., 286, 2, 661-669, (2005)
[10] Gerlach, D.; Tomar, G.; Biswas, G.; Durst, F., Comparison of volume-of-fluid methods for surface tension dominant two-phase flows, Int. J. Heat Mass Transfer, 49, 740-754, (2006) · Zbl 1189.76363
[11] Moshiri, M.; Manzari, M. T.; Hannani, S. K.; Rasouli, A., Simulation of multiphase flows in porous media with gravitational effects using dominant wave method, Internat. J. Numer. Methods Heat Fluid Flow, 23, 7, 1204-1221, (2013) · Zbl 1356.76244
[12] Ray, B.; Biswas, G.; Sharma, A., Oblique drop impact on deep and shallow liquid, Commun. Comput. Phys., 11, 1386-1396, (2012) · Zbl 1373.76187
[13] Mashayek, F.; Ashgriz, N.; Minkowycz, W. J.; Shotorban, B., Coalescence collision of liquid drops, Int. J. Heat Mass Transfer, 46, 1, 77-89, (2003) · Zbl 1023.76051
[14] Kadivar, E.; Alizadeh, A., Numerical simulation and scaling of droplet deformation in a hyperbolic flow, Eur. Phys. J. E, 40, 31, (2017)
[15] Liu, H., Science and Engineering of Droplets: Fundamentals and Applications, (2000), Noyes Publications New York
[16] Sukop, M. C.; Thorne, D. T., Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, (2005), Springer Berlin
[17] Mohamad, A. A., Lattice Boltzmann Method, Fundamentals and Engineering Applications with Computer Codes, (2011), Springer-Verlag London · Zbl 1247.80003
[18] Shan, X.; Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47, 3, 1815, (1993)
[19] Swift, M. R.; Osborn, W. R.; Yeomans, J. M., Lattice Boltzmann simulation of non ideal fluids, Phys. Rev. Lett., 75, 5, 830, (1995)
[20] Gunstensen, A. K.; Rothman, D. H.; Zaleski, S.; Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A, 43, 4320-4327, (1991)
[21] He, X.; Shan, X.; Doolen, G. D., A discrete Boltzmann equation model for non-ideal gases, Phys. Rev. E, 57, R13, (1998)
[22] He, X.; Doolen, G. D., Thermodynamic foundations of kinetic theory and lattice Boltzmann models formultiphase flows, J. Stat. Phys., 107-112, (2002)
[23] He, X.; Chen, S.; Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and itsapplication in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152, 642-663, (1999) · Zbl 0954.76076
[24] Zhang, R.; He, X.; Chen, S., Interface and surface tension in incompressible lattice Boltzmann multiphase model, Comput. Phys. Comm., 129, 121-130, (2000) · Zbl 0990.76073
[25] Premnath, K. N.; Abraham, J., Lattice Boltzmann simulations of drop-drop interactions in two-phase flows, Internat. J. Modern Phys. C, 16, 1, 25-44, (2005) · Zbl 1105.76047
[26] Zhang, R.; He, X.; Doolen, G.; Chen, S., Surface tension effects on two-dimensional two-phase Kelvin-Helmholtz instabilities, Adv. Water Resour., 24, 461-478, (2001)
[27] Bosse, T.; Kleiser, L.; Hrtela, C.; Meiburg, E., Numerical simulation of finite Reynolds numbersuspension drops settling under gravity, Phys. Fluids, 17, 037101, (2005) · Zbl 1187.76064
[28] Ni, M.-J.; Komori, S.; Morley, N. B., Direct simulation of falling droplet in a closed channel, Int. J. Heat Mass Transfer, 49, 366-376, (2006) · Zbl 1189.76129
[29] Fakhari, A.; Rahimian, M. H., Simulation of falling droplet by the lattice Boltzmann method, Commun. Nonlinear Sci. Numer. Simul., 14, 3046-3055, (2009) · Zbl 1221.76163
[30] Fakhari, A.; Rahimian, M. H., Investigation of deformation and breakup of a falling droplet using amultiple-relaxation-time lattice Boltzmann method, Comput. & Fluids, 40, 156-171, (2011) · Zbl 1245.76117
[31] Bararnia, H.; Ganji, D. D., Breakup and deformation of a falling droplet under high voltage electricfield, Adv. Powder Technol., 24, 6, 992-998, (2013)
[32] Shen, S.; Bi, F.; Guo, Y., Simulation of droplets impact on curved surfaces with lattice Boltzmann method, Int. J. Heat Mass Transfer, 55, 6938-6943, (2012)
[33] Pasandideh-Fard, M.; Bussmann, M.; Chandra, S.; Mostaghimi, J., Simulating droplet impact on a substrate of arbitrary shape, Atomization Sprays, 11, 397-414, (2001)
[34] Ellits, A. S.; Smith, F. T.; White, A. H., Droplet impact on to a rough surface, J. Mech. Appl. Math., 64, 2, 107-139, (2010) · Zbl 1248.76013
[35] Khalili, M.; Yahyazadeh, H.; Gorji-Bandpy, M.; Ganji, D. D., Application of volume of fluid method for simulation of a droplet impacting a fiber, Propul. Power Res., 5, 2, 123-133, (2016)
[36] Fakhari, A.; Bolster, D., Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios, J. Comput. Phys., 334, 620-638, (2017) · Zbl 1375.76145
[37] Carnahan, N. F.; Starling, K. E., Equation of state for non-attracting rigid spheres, J. Chem. Phys., 51, 2, 635-636, (1959)
[38] Zhang, R., Lattice Boltzmann Approach for Immiscible Multiphase Flow, (2000), University of Delaware, (Ph.D. thesis)
[39] Merdasi, A.; Ebrahimi, S.; Moosavi, A.; Shafii, M. B.; Kowsary, F., Numerical simulation of collision between two droplets in the T-shaped microchannel with lattice Boltzmann method, AIP Adv., 6, 11, 115307-115319, (2016)
[40] Qian, Y. H.; d’Humieres, D.; Lallemand, P., Lattice BGK models for Navier -Stokes equation, Europhys. Lett., 17, 479-484, (1992) · Zbl 1116.76419
[41] Yan, Y.; Zu, Y., A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio, J. Comput. Phys., 227, 763-775, (2007) · Zbl 1388.76318
[42] Lee, T.; Liu, L., Wall boundary conditions in the lattice Boltzmann equation method for non-ideal gases, Phys. Rev. E, 78, 017702, (2008)
[43] Huang, J.; Huang, H.; Wang, X., Wetting boundary conditions in phase-field-based simulation of binary fluids: some comparative studies and new development, Internat. J. Numer. Methods Fluids, 77, 123-158, (2015)
[44] Li, Q.; Luo, K. H.; Kang, Q. J.; He, Y. L.; Chen, Q.; Liu, Q., Lattice Boltzmann methods for multiphase flow and phase-change heat transfer, Prog. Energy Combust. Sci., 52, 62-105, (2016)
[45] Raman, K. A.; Jaiman, R. K.; Lee, T. S.; Low, H. T., Lattice Boltzmann simulations of droplet impact onto surfaces with varying wettabilities, Int. J. Heat Mass Transfer, 95, 336-354, (2016)
[46] Wang, L.; Sun, J., The application of axisymmetric lattice Boltzmann two-phase model on simulations of liquid film dewetting, J. Appl. Phys., 122, 085305, (2017)
[47] Ding, H.; Spelt, P. D.M., The wetting condition in diffuse interface simulations of contact line motion, Phys. Rev. E, 75, 046708, (2007)
[48] Wang, L.; Huang, H.; Lu, X. Y., Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method, Phys. Rev. E, 87, 013301, (2013)
[49] Zhou, W.; Loney, D.; Fedorov, A. G.; Degertekin, F. L.; Rosen, D. W., Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E, 89, 033311, (2014)
[50] Han, J.; Triggvason, G., Secondary breakup of axisymmetric liquid drops I. acceleration by a constant body force, Phys. Fluids, 11, 12, 3650-3667, (1999) · Zbl 1149.76400
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