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Roughness Effects on Continuous and Discrete Flows in Superhydrophobic Microchannels

Published online by Cambridge University Press:  20 August 2015

Junfeng Zhang  and
Daniel Y. Kwok
Junfeng Zhang*
Affiliation:
School of Engineering, Laurentian University, Sudbury, Ontario, P3E 2C6, Canada
Daniel Y. Kwok*
Affiliation:
School of Engineering, Laurentian University, Sudbury, Ontario, P3E 2C6, Canada
*
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

The dynamic behaviors of continuous and discrete flows in superhydrophobic microchannels are investigated with a lattice Boltzmann model. Typical characters of the superhydrophobic phenomenon are well observed from our simulations, including air trapped in the surface microstructures, high contact angles, low contact angle hysteresis, and reduced friction to fluid motions. Increasing the roughness of a hydrophobic surface can produce a large flow rate through the channel due to the trapped air, implying less friction or large apparent slip. The apparent slip length appears to be independent to the channel width and could be considered as a surface property. For a moving droplet, its behavior is affected by the surface roughness from two aspects: the contact angle difference between its two ends and the surface-liquid interfacial friction. As a consequence, the resulting droplet velocity changes with the surface roughness as firstly decreasing and then increasing. Simulation results are also compared with experimental observations and better agreement has been obtained than that from other numerical method. The information from this study could be valuable for microfluidic systems.

Keywords

68.08.Bc05.70.Np83.50.RpLattice Boltzmann methodinterfacial slipsuperhydrophobicitysolid-fluid interactionroughness effectmicrochannels
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1094 - 1105
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Buick, J. M., Ph.D. Thesis: Lattice Boltzmann Methods in Interfacial Wave Modelling, The University of Edinburgh, U.K., 1997.Google Scholar
[2]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid. Mech., 30 (1998), 329–364.Google Scholar
[3]Cho, S. K., Moon, H., and Kim, C. J., Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits, J. MEMS., 12(1) (2002), 70–80.Google Scholar
[4]Choi, C., Westin, A., and Breuer, K., Apparent slip flows in hydrophilic and hydrophobic microchannels, Phys. Fluids, 5 (2003), 2897–2902.Google Scholar
[5]Choi, C.-H. and Kim, C.-J., Large slip of aqueous liquid flow over a nanoengineered super-hydrophobic surface, Phys. Rev. Lett., 96 (2006), 066001.CrossRefGoogle Scholar
[6]Choi, C.-H., Ulmanella, U., Kim, J., Ho, C.-M., and Kim, C.-J., Effective slip and friction reduction in nanograted superhydrophobic microchannels, Phys. Fluids, 18 (2006), 087105.Google Scholar
[7]Cieplak, M., Koplik, J., and Banavar, J. R., Boundary conditions at a fluid-solid interface, Phys. Rev. Lett., 86 (2001), 803–806.Google Scholar
[8]Darhuber, A. and Troian, S., Principles of microfluidic actuation by modulation of surface stresses, Ann. Rev. Fluid. Mech., 37 (2005), 425–455.Google Scholar
[9]Davies, J., Maynes, D., Webb, B. W., and Woolford, B., Laminar flow in a microchannel with superhydrophobic walls exhibiting transverse ribs, Phys. Fluids, 18 (2006), 087110.CrossRefGoogle Scholar
[10]Erbil, H., Demirel, A., Avci, Y., and Mert, Q., Transformation of a simple plastic into a super-hydrophobic surface, Science, 299(5611) (2003), 1377–1380.CrossRefGoogle Scholar
[11]Gleiche, M., Chi, L., Gedig, E., and Fuchs, H., Anisotropic contact-angle hysteresis of chemically nanostructured surfaces, Chemphyschem., 2(3) (2001), 187.Google Scholar
[12]Haeberle, S. and Zengerle, R., Microfluidic platforms for lab-on-a-chip applications, Lab. Chip, 7 (2007), 1094–1110.Google Scholar
[13]Johnson, R. E. Jr. and Dettre, R. H., Contact angle hysteresis: contact angle measurements on rough surfaces, Adv. Chem. Ser., 43 (1963), 112–144.Google Scholar
[14]Joseph, P., Cottin-Bizonne, C., Benoit, J.-M., Ybert, C., Journet, C., Tabeling, P., and Bocquet, L., Slippage of water past superhydrophobic carbon nanotube forests in microchannels, Phys. Rev. Lett., 97 (2006), 156104.Google Scholar
[15]Kim, J. and Kim, C. J., Nanostructured surfaces for dramatic reduction of flow resistance in droplet-based microfluidics, Proc. IEEE Int. Conf. MEMS., (2002), 479–482.Google Scholar
[16]Lauga, E. and Stone, H., Effective slip in pressure-driven Stokes flow, J. Fluid. Mech., 489 (2003), 55.Google Scholar
[17]Lee, S.-W., Kwok, D. Y., and Laibinis, P. E., Chemical influences on adsorption-mediated self-propelled drop movement, Phys. Rev. E, 65 (2002), 051602.Google Scholar
[18]Maynes, D., Jeffs, K., Woolford, B., and Webb, B. W., Laminar flow in a microchannel with hy-drophobic surface patterned microribs oriented parallel to the flow direction, Phys. Fluids, 19 (2007), 093603.CrossRefGoogle Scholar
[19]Miwa, M., Nakajima, A., Fujishima, A., Hashimoto, K., and Watanabe, T., Effects of the surface roughness on sliding angles of water droplets on superhydrophobic surfaces, Langmuir, 16 (2000), 5754–5760.CrossRefGoogle Scholar
[20]Nakajima, A., Hashimoto, K., and Watanabe, T., Recent studies on super-hydrophobic films, Monatshefte fur Chemie, 132 (2001), 31–41.Google Scholar
[21]Narhe, R. and Beysens, D., Nucleation and growth on a superhydrophobic grooved surface, Phys. Rev. Lett., 93(7) (2004), 076103.Google Scholar
[22]Ou, J. and Rothstein, J. P., Direct velocity measurements of the flow past drag-reducing ultra-hydrophobic surfaces, Phys. Fluids, 17 (2005), 103606.Google Scholar
[23]Qian, Y. H., D. d’Humieres, and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.Google Scholar
[24]Fabrettoand, M.Ralston, J. and Sedev, R., Contact angle measurements using the Wilhelmy balance for asymmetrically treated samples, J. Adhesion. Sci. Tech., 18(1) (2004), 29–37.Google Scholar
[25]Richard, D. and Quere, D., Viscous drops rolling on a tilted non-wettable solid, Europhys. Lett., 48 (3) (1999), 286–291.Google Scholar
[26]Rowlinson, J. and Widom, B., Molecular Theory of Capilary, Claredon, Oxford, 1982.Google Scholar
[27]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., and Toschi, F., Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows, Phys. Rev. Lett., 97 (2006), 204503.Google Scholar
[28]Shan, X. and Chen, H., Simulation of nonideal gases and liquid-gas phase-transitions by the lattice Boltzmann equation, Phys. Rev. E, 49 (1994), 2941–2948.Google Scholar
[29]Succi, S., Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis, Phys. Rev. Lett., 89 (2002), 064502.Google Scholar
[30]Sullivan, D. E., Surface tension and contact angle of a liquid–solid interface, J. Chem. Phys., 74(4) (1981), 2604–2615.CrossRefGoogle Scholar
[31]Swift, M. R., Osborn, W. R., and Yeomans, J. M., Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75 (1995), 830–833.Google Scholar
[32]Takeda, K., Nakajima, A., Hashimoto, K., and Watanabe, T., Jump of water droplet from a super-hydrophobic film by vertical electric field, Surface. Sci., 519 (2002), L589–L592.CrossRefGoogle Scholar
[33]Tretheway, D. and Meinhart, C., Apparent fluid slip at hydrophobic microchannel walls, Phys. Fluids, 14 (2002), L9–L12.Google Scholar
[34]Widom, B., Structure of interfaces from uniformity of the chemical potential, J. Stat. Phys., 19 (1978), 563.Google Scholar
[35]Yang, A. J. M., Fleming, P. D., and Gibbs, J. H., Molecular theory of surface tension, J. Chem. Phys., 64(9) (1976), 3732.Google Scholar
[36]Yang, Z. L., Dinh, T. N., Nourgaliev, R. R., and Sehgal, B. R., Numerical investigation of bubble coalescence characteristics under nucleate boiling condition by a lattice Boltzmann model, Int. J. Therm. Sci., 39 (2000), 1–17.Google Scholar
[37]Zhai, L., Cebeci, F., Cohen, R., and Rubner, M., Stable superhydrophobic coatings from poly-electrolyte multilayers, Nano. Lett., 4(7) (2004), 1349–1353.Google Scholar
[38]Zhang, J., Lattice Boltzmann method for microfluidics: models and applications, Microfluid. Nanofluid., DOI:10.1007/s10404-010-0624-1 (in press), 2010.Google Scholar
[39]Zhang, J., Grandke, K., and Kwok, D. Y., Comment on “surface characterization of hydrosily-lated polypropylene: contact angle measurement and atomic force microscopy”, Langmuir, 19(24) (2003), 10457–10458.Google Scholar
[40]Zhang, J. and Kwok, D. Y., Calculation of solid-liquid work of adhesion patterns from combining rules for intermolecular potentials, J. Phys. Chem. B, 106 (2002), 12594.Google Scholar
[41]Zhang, J. and Kwok, D. Y., Apparent slip over a solid-liquid interface with a no-slip boundary condition, Phys. Rev. E, 70 (2004), 056701.CrossRefGoogle Scholar
[42]Zhang, J. and Kwok, D. Y., Lattice Boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces, Langmuir, 20 (2004), 8137–8141.Google Scholar
[43]Zhang, J. and Kwok, D. Y., Contact line and contact angle dynamics in superhydrophobic channels, Langmuir, 22(11) (2006), 4998–5004.Google Scholar
[44]Zhang, J., Li, B., and Kwok, D. Y., Mean-field free-energy approach to the lattice Boltzmann method for liquid-vapor and solid-fluid interfaces, Phys. Rev. E, 69 (2004), 032602.Google Scholar
[45]Zhu, Y. and Granick, S., Limits of the hydrodynamic no-slip boundary condition, Phys. Rev. Lett., 88 (2002), 106102.Google Scholar