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Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface

  • Quanzi Yuan (a1) and Ya-Pu Zhao (a1)

Dynamic wetting of a droplet on lyophilic pillars was explored using a multiscale combination method of experiments and molecular dynamics simulations. The excess lyophilic area not only provided excess driving force, but also pinned the liquid around the pillars, which kept the moving contact line in a dynamic balance state every period of the pillars. The flow pattern and the flow field of the droplet on the pillar-arrayed surface, influenced by the concerted effect of the liquid–solid interactions and the surface roughness, were revealed from the continuum to the atomic level. Then, the scaling analysis was carried out employing molecular kinetic theory. Controlled by the droplet size, the density of roughness and the pillar height, two extreme regimes were distinguished, i.e. $R\sim {t}^{1/ 3} $ for the rough surface and $R\sim {t}^{1/ 7} $ for the smooth surface. The scaling laws were validated by both the experiments and the simulations. Our results may help in understanding the dynamic wetting of a droplet on a pillar-arrayed lyophilic substrate and assisting the future design of pillar-arrayed lyophilic surfaces in practical applications.

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Berendsen, H. J. C., Grigera, J. R. & Straatsma, T. P. 1987 The missing term in effective pair potentials. J. Phys. Chem. 91, 62696271.
Blake, T. D. 1993 Wettability. Dekker.
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299, 113.
Blake, T. D. & De Coninck, J. 2002 The influence of solid–liquid interactions on dynamic wetting. Adv. Colloid Interface Sci. 96, 2136.
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739805.
Concus, P. & Finn, R. 1969 On the behaviour of a capillary surface in a wedge. Proc. Natl Acad. Sci. USA 63, 292299.
Courbin, L., Denieul, E., Dressaire, E., Roper, M., Ajdari, A. & Stone, H. A. 2007 Imbibition by polygonal spreading on microdecorated surfaces. Nat. Mater. 6, 661664.
Cox, R. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.
De Coninck, J. & Blake, T. D. 2008 Wetting and molecular dynamics simulations of simple liquids. Annu. Rev. Mater. Res. 38, 122.
Derjaguin, B. V., Churaev, N. V. & Muller, V. M. 1987 Surface Forces. Consultants Bureau.
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665684.
Dussan, V. E. B. 1979 On the spreading of liquids on solid-surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371400.
Fetzer, R., Ramiasa, M. & Ralston, J. 2009 Dynamics of liquid–liquid displacement. Langmuir 25, 80698074.
Fu, J., Mao, P. & Han, J. 2009 Continuous-flow bioseparation using microfabricated anisotropic nanofluidic sieving structures. Nat. Protoc. 4, 16811698.
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.
Glasstone, S., Laidler, K. & Eyring, H. 1941 The Theory of Rate Processes. McGraw-Hill.
González, M. A. & Abascal, J. L. F. 2010 The shear viscosity of rigid water models. J. Chem. Phys. 132, 096101.
Greenspan, H. 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125143.
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317328.
Hocking, L. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76, 801817.
Huh, C. & Scriven, L. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85101.
Ishino, C., Reyssat, M., Reyssat, E., Okumura, K. & Quéré, D. 2007 Wicking within forests of micropillars. Europhys. Lett. 79, 56005.
Karniadakis, G., Beşkök, A. & Aluru, N. R. 2005 Microflows and Nanoflows: Fundamentals and Simulation. Springer.
Kim, S. J., Moon, M. W., Lee, K. R., Lee, D. Y., Chang, Y. S. & Kim, H. Y. 2011 Liquid spreading on superhydrophilic micropillar arrays. J. Fluid Mech. 680, 477487.
McHale, G., Shirtcliffe, N., Aqil, S., Perry, C. & Newton, M. 2004 Topography driven spreading. Phys. Rev. Lett. 93, 36102.
Nagrath, S., Sequist, L. V., Maheswaran, S., Bell, D. W., Irimia, D., Ulkus, L., Smith, M. R., Kwak, E. L., Digumarthy, S. & Muzikansky, A. 2007 Isolation of rare circulating tumour cells in cancer patients by microchip technology. Nature 450, 12351239.
Parker, A. R. & Lawrence, C. R. 2001 Water capture by a desert beetle. Nature 414, 3334.
Plimpton, S. 1995 Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 119.
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Mater. Res. 38, 7199.
Ren, W. Q. & E, W. N. 2007 Boundary conditions for the moving contact line problem. Phys. Fluids 19, 022101.
Ren, W. Q., Hu, D. & E, W. N. 2010 Continuum models for the contact line problem. Phys. Fluids 22, 102103.
Seemann, R., Brinkmann, M., Kramer, E., Lange, F. & Lipowsky, R. 2005 Wetting morphologies at microstructured surfaces. Proc. Natl Acad. Sci. USA 102, 18481852.
Skelley, A. M., Kirak, O., Suh, H., Jaenisch, R. & Voldman, J. 2009 Microfluidic control of cell pairing and fusion. Nat. Meth. 6, 147152.
Srivastava, N., Din, C., Judson, A., MacDonald, N. C. & Meinhart, C. D. 2010 A unified scaling model for flow through a lattice of microfabricated posts. Lab on a Chip 10, 11481152.
Tanner, L. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 14731484.
Teletzke, G. F., Davis, H. T. E. D. & Scriven, L. 1987 How liquids spread on solids. Chem. Engng Commun. 55, 4182.
Vega, C. & De Miguel, E. 2007 Surface tension of the most popular models of water by using the test-area simulation method. J. Chem. Phys. 126, 154707.
Wang, C. L., Lu, H. J., Wang, Z. G., Xiu, P., Zhou, B., Zuo, G. H., Wan, R. Z., Hu, J. & Fang, H. P. 2009 Stable liquid water droplet on a water monolayer formed at room temperature on ionic model substrates. Phys. Rev. Lett. 103, 137801.
Weislogel, M. M. & Lichter, S. 1998 Capillary flow in an interior corner. J. Fluid Mech. 373, 349378.
Wenzel, R. N. 1936 Resistance of solid surfaces to wetting by water. Ind. Engng Chem. 28, 988994.
Xiao, R., Enright, R. & Wang, E. N. 2010 Prediction and optimization of liquid propagation in micropillar arrays. Langmuir 26, 1507015075.
Young, T. 1805 An essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. 95, 6587.
Yuan, Q. Z. & Zhao, Y. P. 2010 Precursor film in dynamic wetting, electrowetting, and electro-elasto-capillarity. Phys. Rev. Lett. 104, 246101.
Yuan, Q. Z. & Zhao, Y. P. 2012 Topology-dominated dynamic wetting of the precursor chain in a hydrophilic interior corner. Proc. R. Soc. A 468, 310322.
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