Abstract
A three-dimensional unsteady theoretical model of droplet spreading process on an inclined surface is developed and numerically analyzed to investigate the droplet spreading dynamics via the lattice Boltzmann simulation. The contact line motion and morphology evolution for the droplet spreading on an inclined surface, which are, respectively, represented by the advancing/receding spreading factor and droplet wetted length, are evaluated and analyzed. The effects of surface wettability and inclination on the droplet spreading behaviors are examined. The results indicate that, dominated by gravity and capillarity, the droplet experiences a complex asymmetric deformation and sliding motion after the droplet comes into contact with the inclined surfaces. The droplet firstly deforms near the solid surface and mainly exhibits a radial expansion flow in the start-up stage. An evident sliding-down motion along the inclination is observed in the middle stage. And the surface-tension-driven retraction occurs during the retract stage. Increases in inclination angle and equilibrium contact angle lead to a faster droplet motion and a smaller wetted area. In addition, increases in equilibrium contact angle lead to a shorter duration time of the middle stage and an earlier entry into the retract stage.
Similar content being viewed by others
References
Wijshoff H.: The dynamics of the piezo inkjet printhead operation. Phys. Rep. 491(4), 77–177 (2010)
Zhao Y.J., Zhao X.W., Sun C., Li J., Zhu R., Gu Z.Z.: Encoded silica colloidal crystal beads as supports for potential multiplex immunoassay. Anal. Chem. 80(5), 1598–1605 (2008)
Zhao, Y.J., Zhao, X.W., Hu, J., Xu, M., Zhao, W.J., Sun, L.G., Zhu, C., Xu, H., Gu, Z.Z.: Encoded porous beads for label-free multiplex detection of tumor markers. Adv. Mater 21, 569–572 (2009)
De Gennes P.G.: Wetting: statics and dynamics. Rev. Mod. Phys. 57(3), 827 (1985)
Bonn D., Eggers J., Indekeu J., Meunier J., Rolley E.: Wetting and spreading. Rev. Mod. Phys. 81(2), 739 (2009)
Bergeron V., Bonn D., Martin J.Y., Vovelle L.: Controlling droplet deposition with polymer additives. Nature 405(6788), 772–775 (2000)
Xie J., Xu J.L., Xing F., Wang Z.X., Liu H.: The phase separation concept condensation heat transfer in horizontal tubes for low-grade energy utilization. Energy 69, 787–800 (2014)
Biance A.L., Clanet C., Quéré D.: First steps in the spreading of a liquid droplet. Phys. Rev. E 69(1), 016301 (2004)
Bird J.C., Mandre S., Stone H.A.: Short-time dynamics of partial wetting. Phys. Rev. Lett. 100(23), 234501 (2008)
Huh C., Scriven L.: Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35(1), 85–101 (1971)
Tanner L.: The spreading of silicone oil drops on horizontal surfaces. J. Phys. D Appl. Phys. 12(9), 1473 (1979)
Winkels K.G., Weijs J.H., Eddi A., Snoeijer J.H.: Initial spreading of low-viscosity drops on partially wetting surfaces. Phys. Rev. E 85(5), 055301 (2012)
Bussmann M., Mostaghimi J., Chandra S.: On a three-dimensional volume tracking model of droplet impact. Phys. Fluids 11(6), 1406–1417 (1999)
Šikalo Š., Tropea C., Ganić E.N.: Impact of droplets onto inclined surfaces. J. Colloid Interface Sci. 286(2), 661–669 (2005)
Reznik S., Yarin A.: Spreading of a viscous drop due to gravity and capillarity on a horizontal or an inclined dry wall. Phys. Fluids 14, 118–132 (2002)
Fukai J., Shiiba Y., Yamamoto T., Miyatake O., Poulikakos D., Megaridis C., Zhao Z.: Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling. Phys. Fluids 7, 236 (1995)
Gunjal P.R., Ranade V.V., Chaudhari R.V.: Dynamics of drop impact on solid surface: experiments and VOF simulations. AlChE J. 51(1), 59–78 (2005)
Šikalo Š., Wilhelm H.-D., Roisman I., Jakirlić S., Tropea C.: Dynamic contact angle of spreading droplets: experiments and simulations. Phys. Fluids 17, 062103 (2005)
Sussman M., Smereka P., Osher S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146–159 (1994)
Pasandideh-Fard M., Chandra S., Mostaghimi J.: A three-dimensional model of droplet impact and solidification. Int. J. Heat Mass Transf. 45(11), 2229–2242 (2002)
Lunkad S.F., Buwa V.V., Nigam K.: Numerical simulations of drop impact and spreading on horizontal and inclined surfaces. Chem. Eng. Sci. 62(24), 7214–7224 (2007)
Unverdi S.O., Tryggvason G.: A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100(1), 25–37 (1992)
Sun D.K., Bo Z.: Numerical simulation of hydrodynamic focusing of particles in straight channel flows with the immersed boundary-lattice Boltzmann method. Int. J. Heat Mass Transf. 80, 139–149 (2015)
Tian F.B., Luo H.X., Zhu L.D., Liao J.C., Lu X.Y.: An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 230(19), 7266–7283 (2011)
Liao Q., Yang Y.X., Zhu X., Chen R.: Lattice Boltzmann simulation of substrate solution through a porous granule immobilized PSB-cell for biohydrogen production. Int. J. Hydrog. Energy 38(35), 15700–15709 (2013)
Shan X.W., Chen H.D.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47(3), 1815 (1993)
Attar E., Körner C.: Lattice Boltzmann method for dynamic wetting problems. J. Colloid Interface Sci. 335(1), 84–93 (2009)
Kamali M., Gillissen J., Sundaresan S., Vanden Akker H.: Contact line motion without slip in lattice Boltzmann simulations. Chem. Eng. Sci. 66(14), 3452–3458 (2011)
Xing X.Q., Butler D.L., Ng S.H., Wang Z.F., Danyluk S., Yang C.: Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model. J. Colloid Interface Sci. 311(2), 609–618 (2007)
Gunstensen A.K., Rothman D.H., Zaleski S., Zanetti G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320 (1991)
Swift M.R., Osborn W.R., Yeomans J.M.: Lattice Boltzmann Simulation of Nonideal Fluids. Phys. Rev. Lett. 75(5), 830–833 (1995)
Körner C., Thies M., Hofmann T., Thürey N., Rüde U.: Lattice Boltzmann model for free surface flow for modeling foaming. J. Stat. Phys. 121(1–2), 179–196 (2005)
Castrejon-Pita J.R., Betton E.S., Kubiak K.J., Wilson M.C.T., Hutchings I.M.: The dynamics of the impact and coalescence of droplets on a solid surface. Biomicrofluidics 5(1), 014112 (2011)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S. Balachandar.
Rights and permissions
About this article
Cite this article
Shen, C., Yu, C. & Chen, Y. Spreading dynamics of droplet on an inclined surface. Theor. Comput. Fluid Dyn. 30, 237–252 (2016). https://doi.org/10.1007/s00162-015-0377-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-015-0377-2