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Controlling droplet bouncing and coalescence with surfactant

Published online by Cambridge University Press:  28 June 2016

K.-L. Pan*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
Y.-H. Tseng
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 81148, Taiwan, ROC
J.-C. Chen
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
K.-L. Huang
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
C.-H. Wang
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
M.-C. Lai
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan, ROC
*
Email address for correspondence: [email protected]

Abstract

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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Papers
Copyright
© 2016 Cambridge University Press 

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References

Adalsteinsson, D. & Sethian, J 2003 Transport and diffusion of material quantities on propagating interfaces via level set methods. J. Comput. Phys. 185, 271288.Google Scholar
Adam, J. R., Lindblad, N. R. & Hendricks, C. D. 1968 The collision, coalescence, and disruption of water droplets. J. Appl. Phys. 39, 51735180.Google Scholar
Ashgriz, N. & Poo, J. Y. 1990 Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech. 221, 183204.Google Scholar
Bauer, W., Bertsch, G. F. & Schulz, H. 1992 Bubble and ring formation in nuclear fragmentation. Phys. Rev. Lett. 69, 18881891.Google Scholar
Berger, M. J. & Colella, P. 1989 Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 6484.Google Scholar
Berger, M. J. & Oliger, J. 1984 Adaptive mesh refinement for hyperbolic partial differential equaitons. J. Comput. Phys. 53, 484512.CrossRefGoogle Scholar
Bergeron, V., Bonn, D., Martin, J. Y. & Vovelle, L. 2000 Controlling droplet deposition with polymer additives. Nature 405, 772775.Google Scholar
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.Google Scholar
Brazier-Smith, P. R., Jennings, S. G. & Latham, J. 1972 The interaction of falling water drops: coalescence. Proc. R. Soc. Lond. A 326, 393408.Google Scholar
Burger, M. 2005 Numerical simulation of anisotropic surface diffusion with curvature-dependent energy. J. Comput. Phys. 203, 602625.Google Scholar
Ceniceros, H. D. 2003 The effects of surfactants on the formation and evolution of capillary waves. Phys. Fluids 15 (1), 245256.Google Scholar
Chen, J. C.2010 Surfactant effect on binary droplet collision. Taipei. Master thesis, National Taiwan University.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Chou, P. C.2008 High-speed binary water droplet collision with different surface tension. Taipei: Master thesis, National Taiwan University.Google Scholar
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.Google Scholar
Dai, B. & Leal, L. G. 2008 The mechanism of surfactant effects on drop coalescence. Phys. Fluids 20, 040802.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Driscoll, M. M. & Nageland, S. R. 2011 Ultrafast interference imaging of air in splashing dynamics. Phys. Rev. Lett. 107, 154502.CrossRefGoogle ScholarPubMed
Dziuk, G. & Elliott, C. M. 2007 Finite element on evolving surfaces. IMA J. Numer. Anal. 27, 262292.Google Scholar
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.Google Scholar
Eggleton, C. D. & Stebe, K. J. 1998 An adsorption-desorption-controlled surfactant on a deforming droplet. J. Colloid Interface Sci. 208, 6880.Google Scholar
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.Google Scholar
Grant, G., Brenton, J. & Drysdale, D. 2000 Fire suppression by water sprays. Prog. Energy Combust. Sci. 26, 79130.CrossRefGoogle Scholar
Gunn, R. 1965 Collision characteristics of freely falling water drops. Science 150, 695701.CrossRefGoogle ScholarPubMed
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135163.Google Scholar
Illingworth, J. & Kittler, J. 1988 A survey of the Hough transform. Comput. Vis. Graph. Image Process. 44, 87116.CrossRefGoogle Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces, 3rd edn. Academic.Google Scholar
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.CrossRefGoogle Scholar
Jiang, Y. J., Umemura, A. & Law, C. K. 1992 An experimental investigation on the collision behaviour of hydrocarbon droplets. J. Fluid Mech. 234, 171190.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Lai, M. C., Tseng, Y. H. & Huang, H. 2008 An immersed boundary method for interfacial flow with insoluble surfactant. J. Comput. Phys. 227, 72797293.Google Scholar
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.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics. Dover.Google Scholar
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.Google Scholar
Lin, S. Y., Lee, Y. C., Yang, M. W & Liu, H. S. 2003 Surface equation of state of nonionic CE surfactants. Langmuir 19, 31643171.Google Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
Nobari, M. R., Jan, Y.-J. & Tryggvason, G. 1996 Head on collision of drops – a numerical investigation. Phys. Fluid 8, 2942.Google Scholar
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.Google Scholar
Pan, K. L., Chou, P. C. & Tseng, Y. J. 2009 Binary droplet collision at high Weber number. Phys. Rev. E 80, 036301.Google Scholar
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.Google Scholar
Pan, K. L. & Law, C. K. 2007 Dynamics of droplet-film collision. J. Fluid Mech. 587, 122.Google Scholar
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.Google Scholar
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.Google Scholar
Peskin, C. S. 1972 Flow patterns around heart valves: a nermical method. J. Comput. Phys. 10, 252271.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220252.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.CrossRefGoogle Scholar
Petsev, D. N. 2000 Theoretical analysis of film thickness transition dynamics and coalescence of charged miniemulsion droplets. Langmuir 16, 20932100.Google Scholar
Purvis, R. & Smith, F. T. 2004 Air-water interactions near droplet impact. Eur. J. Appl. Maths 15, 853871.Google Scholar
Qian, J. & Law, C. K. 1997 Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 5980.Google Scholar
Rätz, A. & Voigt, A. 2006 PDEs on surfaces – a diffuse interface approach. Commun. Math. Sci. 4, 575590.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 2537.CrossRefGoogle Scholar
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.Google Scholar
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50, 215234.Google Scholar
Wadhwa, N., Vlachos, P. & Jung, S. 2013 Noncoalescence in the oblique collision of fluid jets. Phys. Rev. Lett. 110, 124502.Google Scholar
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.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159192.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar