Sweeping of the entrapped fluid out of the groove in a three-dimensional channel using lattice Boltzmann method. (English) Zbl 1408.76411
Summary: The entrapment of fluid inside a groove is an important topic of research from the past few decades. In many engineering applications, it is seen that the droplet is displaced under the action of gravitational force on one of the wetted grooved wall of a rectangular three-dimensional channel. It is reported in literature that the entrapment of a fluid droplet inside a groove is undesirable in various applications. Thus, the present study deals with the method of sweeping out the entrapped fluid inside the groove by the displacement of a large size three-dimensional immiscible droplet under gravity. To analyze this problem, a three-dimensional lattice Boltzmann method (LBM) is used and Shan-Chen (S-C) model is implemented to incorporate multiphase-multicomponent flow. The present problem deals with the single grooved wetted wall of a rectangular three-dimensional channel. The wettability of the groove surface is considered as uniform hydrophobic in two different cases, whereas the wettability of the three-dimensional channel wall outside of the groove is considered as uniform hydrophilic. The analysis shows that the sweeping of the entrapped fluid out of the groove largely depends on the capillary number and groove dimensions. It is also observed that sweeping of the entrapped fluid takes place only for a uniform hydrophobic surface of the groove with a contact angle equal to \(118^\circ\). In case of a hydrophobic surface with a contact angle equal to \(90^\circ\), the large size droplet is completely trapped inside the groove and not able to sweep out the previously entrapped fluid.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
References:
| [1] | Schleizer, A. D.; Bonnecaze, R. T., Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows, J. Fluid Mech., 383, 29-54, (1999) · Zbl 0939.76022 |
| [2] | Dimitrakopoulos, P.; Higdon, J. J.L., On the displacement of three-dimensional fluid droplets adhering to a plane wall in viscous pressure-driven flows, J. Fluid Mech., 435, 327-350, (2001) · Zbl 1156.76383 |
| [3] | Dupuis, A.; Yeomans, J. M., Modeling droplets on superhydrophobic surfaces: equilibrium states and transitions, Langmuir, 21, 2624-2629, (2005) |
| [4] | Zu, Y. Q.; Yan, Y. Y., Wetting behaviours of a single droplet on biomimetic micro structured surfaces, J. Bionic Eng., 7, 191-198, (2010) |
| [5] | Zu, Y. Q.; Yan, Y. Y., Lattice Boltzmann method for modelling droplets on chemically heterogeneous and microstructured surfaces with large liquid-gas density ratio, J. Appl. Math., 76, 5, 743-760, (2011) |
| [6] | Kumar, A.; Williams, S. J.; Chuang, H.; Greend, N. G.; Wereleye, S. T., Hybrid opto-electric manipulation in microfluidics—opportunities and challenges, Lab Chip, 11, 2135-2148, (2011) |
| [7] | Vananroye, A.; Cardinael, R.; Puyvelde, P. V.; Moldenaers, P., Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow, J. Rheol., 52, 1459-1475, (2008) |
| [8] | Chang, Q.; Alexander, J. I.D., Analysis of single droplet dynamics on striped surface domains using a lattice Boltzmann method, Microfluid Nanofluid, 2, 4, 309-326, (2006) |
| [9] | Ahmed, G.; Sellier, M.; Jermy, M.; Taylor, M., Modeling the effects of contact angle hysteresis on the sliding of droplets down inclined surfaces, Eur. J. Mech. B Fluids, 48, 218-230, (2014) |
| [10] | Huang, J. J.; Shu, C.; Chew, Y. T.; Zheng, H. W., Numerical study of 2D multiphase flows over grooved surface by lattice Boltzmann method, Internat. J. Modern Phys. C, 18, 492-500, (2007) · Zbl 1167.76034 |
| [11] | Huang, J. J.; Shu, C.; Chew, Y. T., Lattice Boltzmann study of droplet motion inside a grooved channel, Phys. Fluids, 21, (2009) · Zbl 1183.76254 |
| [12] | Hu, H.; Huang, S.; Chen, L., Displacement of liquid droplets on micro-grooved surfaces with air flow, Exp. Therm Fluid Sci., 49, 86-93, (2013) |
| [13] | Son, S.; Chen, L.; Derome, D.; Carmeliet, J., Numerical study of gravity-driven droplet displacement on a surface using the pseudopotential multiphase lattice Boltzmann model with high density ratio, Comput. Fluids, 117, 42-53, (2015) · Zbl 1390.76766 |
| [14] | Q. Wang, Y. Li, Z. Yu, B. Guo, Numerical simulation of gravity-driven droplet displacement on an inclined micro-grooved surface, in: ASME 2016 5th International Conference on Micro/Nanoscale Heat and Mass Transfer, 2016, p. V001T01A006.; Q. Wang, Y. Li, Z. Yu, B. Guo, Numerical simulation of gravity-driven droplet displacement on an inclined micro-grooved surface, in: ASME 2016 5th International Conference on Micro/Nanoscale Heat and Mass Transfer, 2016, p. V001T01A006. |
| [15] | Bhardwaj, S.; Dalal, A., Mesoscopic analysis of three-dimensional droplet displacement on wetted grooved wall of a rectangular channel, Eur. J. Mech. B Fluids, 67, 35-53, (2018) · Zbl 1408.76410 |
| [16] | He, X. Y.; Chen, S. Y.; Zhang, R. Y., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152, 642-663, (1999) · Zbl 0954.76076 |
| [17] | Shan, X.; Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47, 1815-1819, (1993) |
| [18] | Succi, S., The lattice Boltzmann equation: for fluid dynamics and beyond, (2001), Oxford University Press · Zbl 0990.76001 |
| [19] | Kang, Q.; Zhang, D.; Chen, S., Displacement of a two dimensional immiscible droplet in a channel, Phys. Fluids, 40, 3203-3214, (2002) · Zbl 1185.76192 |
| [20] | Kang, Q.; Zhang, D.; Chen, S., Displacement of a three dimensional immiscible droplet in a channel, J. Fluid Mech., 545, 41-66, (2005) · Zbl 1085.76557 |
| [21] | 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 |
| [22] | Li, Q.; He, Y. L.; Tang, G. H.; Tao, W. Q., Lattice Boltzmann modeling of microchannel flows in the transition flow regime, Microfluid Nanofluid, 10, 607-618, (2011) |
| [23] | Fei, K.; Chen, W. H.; Hong, C. W., Microfluidic analysis of CO_{2} bubble dynamics using thermal lattice-Boltzmann method, Microfluid Nanofluid, 5, 119-129, (2008) |
| [24] | Hao, L.; Cheng, P., Lattice Boltzmann simulations of water transport in gas diffusion layer of a polymer electrolyte membrane fuel cell, J. Power Sources, 195, 3870-3881, (2010) |
| [25] | Zhang, J., Lattice Boltzmann method for microfluidics: models and applications, Microfluid Nanofluid, 10, 1-28, (2011) |
| [26] | Cho, S. C.; Wang, Y.; Chen, K. S., Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, deformation, and detachment. i: theoretical and numerical analyses, J. Power Sources, 206, 119-128, (2012) |
| [27] | Cho, S. C.; Wang, Y.; Chen, K. S., Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, deformation and detachment. ii: comparisons of analytical solution with numerical and experimental results, J. Power Sources, 210, 191-197, (2012) |
| [28] | Randive, P.; Dalal, A.; Mukherjee, P., Probing the influence of superhydrophobicity and mixed wettability on droplet displacement behavior, Microfluid Nanofluid, 17, 657-674, (2014) |
| [29] | Randive, P.; Dalal, A., Influence of viscosity ratio and wettability on droplet displacement behavior: A mesoscale analysis, Comput. & Fluids, 102, 15-31, (2014) |
| [30] | Randive, P.; Dalal, A., Influence of geometry on mobilization of trapped blob, Eur. J. Mech. B Fluids, 53, 1-10, (2015) · Zbl 1408.76421 |
| [31] | Mukherjee, P. P.; Wang, C. Y.; Kang, Q., Mesoscopic modeling of two-phase behavior and flooding phenomena in polymer electrolyte fuel cells, Electrochim. Acta, 54, 6861-6875, (2009) |
| [32] | Martys, N. S.; Chen, H., Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann methods, Phys. Rev. E, 53, 743-750, (1996) |
| [33] | Shan, X.; Doolen, G., Diffusion in a multicomponent lattice Boltzmann equation model, Phys. Rev. E, 54, 3614-3620, (1996) |
| [34] | Marmur, A.; Volpe, C. D.; Siboni, S.; Amirfazli, A.; Drelich, J. W., Contact angles and wettability: towards common and accurate terminology, Surf. Innov., 5, 3-8, (2017) |
| [35] | Bhardwaj, S.; Dalal, A., Mesoscopic analysis of dynamic droplet behaviour on wetted flat and grooved surface for low viscosity ratio, J. Heat Transfer, 139, (2017) |
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