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Controlling droplet bouncing and coalescence with surfactant

  • K.-L. Pan (a1), Y.-H. Tseng (a2), J.-C. Chen (a1), K.-L. Huang (a1), C.-H. Wang (a1) and M.-C. Lai (a3)...


The collision between aqueous drops in air typically leads to coalescence after impact. Rebounding of the droplets with similar sizes at atmospheric conditions is not generated, unless with significantly large pressure or high impact parameters exhibiting near-grazing collision. Here we demonstrate experimentally the creation of a non-coalescent regime through addition of a small amount of water-soluble surfactant. We perform a direct simulation to account for the continuum and short-range flow dynamics of the approaching interfaces, as affected by the soluble surfactant. Based on the immersed-boundary formulation, a conservative scheme is developed for solving the coupled surface-bulk convection–diffusion concentration equations, which presents excellent mass preservation in the solvent as well as conservation of total surfactant mass. We show that the Marangoni effect, caused by non-uniform distributions of surfactant on the droplet surface and surface tension, induces stresses that oppose the draining of gas in the interstitial gap, and hence prohibits merging of the interfaces. In such gas–liquid systems, the repulsion caused by the addition of surfactant, as frequently observed in liquid–liquid systems such as emulsions in the form of an electric double-layer force, was found to be too weak to dominate in the attainable range of interfacial separation distances. These results thus identify the key mechanisms governing the impact dynamics of surfactant-coated droplets in air and imply the potential of using a small amount of surfactant to manipulate impact outcomes, for example, to prevent coalescence between droplets or interfaces in gases.


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Adalsteinsson, D. & Sethian, J 2003 Transport and diffusion of material quantities on propagating interfaces via level set methods. J. Comput. Phys. 185, 271288.
Adam, J. R., Lindblad, N. R. & Hendricks, C. D. 1968 The collision, coalescence, and disruption of water droplets. J. Appl. Phys. 39, 51735180.
Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183204.
Bauer, W., Bertsch, G. F. & Schulz, H. 1992 Bubble and ring formation in nuclear fragmentation. Phys. Rev. Lett. 69, 18881891.
Berger, M. J. & Colella, P. 1989 Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 6484.
Berger, M. J. & Oliger, J. 1984 Adaptive mesh refinement for hyperbolic partial differential equaitons. J. Comput. Phys. 53, 484512.
Bergeron, V., Bonn, D., Martin, J. Y. & Vovelle, L. 2000 Controlling droplet deposition with polymer additives. Nature 405, 772775.
Bertalmio, M., Cheng, L. T., Osher, S. J. & Sapiro, G. 2001 Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys. 174, 759780.
Brazier-Smith, P. R., Jennings, S. G. & Latham, J. 1972 The interaction of falling water drops: coalescence. Proc. R. Soc. Lond. A 326, 393408.
Burger, M. 2005 Numerical simulation of anisotropic surface diffusion with curvature-dependent energy. J. Comput. Phys. 203, 602625.
Ceniceros, H. D. 2003 The effects of surfactants on the formation and evolution of capillary waves. Phys. Fluids 15 (1), 245256.
Chen, J. C.2010 Surfactant effect on binary droplet collision. Taipei. Master thesis, National Taiwan University.
Chen, K. Y., Feng, K. A., Kim, Y. & Lai, M. C. 2011 A note on pressure accuracy in immersed boundary method for Stokes flow. J. Comput. Phys. 230, 43774383.
Chen, K. Y. & Lai, M. C. 2014 A conservative scheme for solving coupled surface-bulk convection–diffusion equations with an application to interfacial flows with soluble surfactant. J. Comput. Phys. 257, 118.
Chiu, H. H. 2000 Advances and challenges in droplet and spray combustion. I: toward a unified theory of droplet aerothermochemistry. Prog. Energy Combust. Sci. 26, 381416.
Chou, P. C.2008 High-speed binary water droplet collision with different surface tension. Taipei: Master thesis, National Taiwan University.
Conlisk, A. T., Zambrano, H., Li, H., Kazoe, Y. & Yoda, M.2012 Particle-wall interactions in micro/nanochannels. In 50th AIAA Aerospace Sciences Meeting. AIAA, 2012–0089.
Dai, B. & Leal, L. G. 2008 The mechanism of surfactant effects on drop coalescence. Phys. Fluids 20, 040802.
De Ruiter, J., Oh, J. M., Ende, D. & Mugele, F. 2012 Dynamics of collapse of air films in drop impact. Phys. Rev. Lett. 108, 074505.
Driscoll, M. M. & Nageland, S. R. 2011 Ultrafast interference imaging of air in splashing dynamics. Phys. Rev. Lett. 107, 154502.
Dziuk, G. & Elliott, C. M. 2007 Finite element on evolving surfaces. IMA J. Numer. Anal. 27, 262292.
Eastoe, J. & Dalton, J. S. 2000 Dynamic surface tension and adsorption mechanisms of surfactants at the air–water interface. Adv. Colloid Interface Sci. 85, 103144.
Eggleton, C. D. & Stebe, K. J. 1998 An adsorption-desorption-controlled surfactant on a deforming droplet. J. Colloid Interface Sci. 208, 6880.
Elliott, C. M., Stinner, B., Styles, V. & Welford, R. 2011 Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA J. Numer. Anal. 31, 786812.
Grant, G., Brenton, J. & Drysdale, D. 2000 Fire suppression by water sprays. Prog. Energy Combust. Sci. 26, 79130.
Gunn, R. 1965 Collision characteristics of freely falling water drops. Science 150, 695701.
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135163.
Illingworth, J. & Kittler, J. 1988 A survey of the Hough transform. Comput. Vis. Graph. Image Process. 44, 87116.
Israelachvili, J. N. 2011 Intermolecular and Surface Forces, 3rd edn. Academic.
Jiang, X. & James, A. J. 2007 Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces. J. Engng Maths 59, 99121.
Jiang, Y. J., Umemura, A. & Law, C. K. 1992 An experimental investigation on the collision behaviour of hydrocarbon droplets. J. Fluid Mech. 234, 171190.
Kolinski, J. M., Rubinstein, S. M., Mandre, M., Brenner, M. P., Weitz, D. A. & Mahadevan, L. 2012 Skating on a film of air: drops impacting on a surface. Phys. Rev. Lett. 108, 074503.
Kuan, C. K., Pan, K. L. & Shyy, W. 2014 Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method. J. Fluid Mech. 759, 104133.
Lai, M. C., Huang, C. Y. & Huang, Y. M. 2011 Simulating the axisymmetric interfacial flows with insoluble surfactant by immered boundary method. Intl J. Numer. Anal. Model. 8, 105117.
Lai, M. C., Tseng, Y. H. & Huang, H. 2008 An immersed boundary method for interfacial flow with insoluble surfactant. J. Comput. Phys. 227, 72797293.
Lai, M. C., Tseng, Y. H. & Huang, H. 2010 Numerical simulation of moving contact lines with insoluble surfactant by immersed boundary method. Commun. Comput. Phys. 8, 735757.
Lamb, H. 1932 Hydrodynamics. Dover.
Leung, S., Lowengrub, J. S. & Zhao, H. K. 2011 A grid based particle method for high order geometrical motions and local inextensible flows. J. Comput. Phys. 230, 25402561.
Lin, S. Y., Lee, Y. C., Yang, M. W & Liu, H. S. 2003 Surface equation of state of nonionic CE surfactants. Langmuir 19, 31643171.
Lipp, M. M., Lee, K. Y. C., Zasadzinski, J. A. & Waring, A. J. 1996 Phase and morphology changes in lipid monolayers induced by SP-B protein and its amino-terminal peptide. Science 273, 11961198.
Moretto, L. G., Tso, K., Colonna, N. & Wozniak, G. J. 1992 New Rayleigh–Taylor-like surface instability and nuclear multifragmentation. Phys. Rev. Lett. 69, 18841887.
Nobari, M. R., Jan, Y.-J. & Tryggvason, G. 1996 Head on collision of drops – a numerical investigation. Phys. Fluid 8, 2942.
Pan, K.-L. & Chen, J.-C.2012 Manipulation of droplet rebounding and separation using surfactant. In 50th AIAA Aerospace Sciences Meeting. AIAA Paper, 2012–0093.
Pan, K. L., Chou, P. C. & Tseng, Y. J. 2009 Binary droplet collision at high Weber number. Phys. Rev. E 80, 036301.
Pan, K. L. & Hung, C. Y. 2010 Droplet impact upon a wet surface with varied fluid and surface properties. J. Colloid Interface Sci. 352, 186193.
Pan, K. L. & Law, C. K. 2007 Dynamics of droplet-film collision. J. Fluid Mech. 587, 122.
Pan, K. L., Law, C. K. & Zhou, B. 2008 Experimental and mechanistic description of merging and bouncing in head-on binary droplet collision. J. Appl. Phys. 103, 064901.
Perkins, W. R., Dause, R. B., Parente, R. A., Minchey, S. R., Neuman, K. C., Gruner, S. M., Taraschi, T. F. & Janofft, A. S. 1996 Role of lipid polymorphism in pulmonary surfactant. Science 273, 330332.
Peskin, C. S. 1972 Flow patterns around heart valves: a nermical method. J. Comput. Phys. 10, 252271.
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220252.
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.
Petsev, D. N. 2000 Theoretical analysis of film thickness transition dynamics and coalescence of charged miniemulsion droplets. Langmuir 16, 20932100.
Purvis, R. & Smith, F. T. 2004 Air-water interactions near droplet impact. Eur. J. Appl. Maths 15, 853871.
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 5980.
Rätz, A. & Voigt, A. 2006 PDEs on surfaces – a diffuse interface approach. Commun. Math. Sci. 4, 575590.
Stebe, K. J., Lin, S. Y. & Maldarelli, C. 1991 Remobilizing surfactant retarded fluid particle interfaces. I: stress-free conditions at the interfaces of micellar solutions of surfactants with fast sorption kinetics. Phys. Fluids A 3, 320.
Tabor, R. F., Eastoe, J. & Dowding, P. 2009 Adsorption and desorption of nonionic surfactants on silica from toluene studied by ATR-FTIR. Langmuir 25, 97859791.
Teigen, K. E., Li, X., Lowengrub, J. S., Wang, F. & Voigt, A. 2009 A diffuse interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformation interface. Commun. Math. Sci. 7, 10091037.
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 2537.
Valkovska, D. S. & Danov, K. D. 2000 Determination of bulk and surface diffusion coefficients from experiemntal data for thin liquid film drainage. J. Colloid Interface sci. 223, 314316.
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50, 215234.
Wadhwa, N., Vlachos, P. & Jung, S. 2013 Noncoalescence in the oblique collision of fluid jets. Phys. Rev. Lett. 110, 124502.
Yang, X., Zhang, X., Li, Z. & He, G. 2009 A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 228, 78217836.
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.
Yeo, L. Y., Matar, O. K., Susana Perez de Ortiz, E. & Hewitt, G. F. 2003 Film drainage between two surfactant-coated drops colliding at constant approach velocity. J. Colloid Interface Sci. 257, 93107.
Zhang, J., Eckmann, D. M. & Ayyaswamy, P. S. 2006 A front tracking method for a defomable intravascular bubble in a tube with soluble surfactant transpout. J. Comput. Phys. 214, 366396.
Zhang, L., Xu, B., Jiang, B. & Liu, Y. 2010 Effect of electric double layer repulsion on oil droplet coalescence process. Chem. Engng Technol. 33, 878884.
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