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Controlling droplet bouncing and coalescence with surfactant. (English) Zbl 1460.76797

Summary: 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.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
Full Text: DOI

References:

[1] Adalsteinsson, D.; Sethian, J., Transport and diffusion of material quantities on propagating interfaces via level set methods, J. Comput. Phys., 185, 271-288, (2003) · Zbl 1047.76093 · doi:10.1016/S0021-9991(02)00057-8
[2] Adam, J. R.; Lindblad, N. R.; Hendricks, C. D., The collision, coalescence, and disruption of water droplets, J. Appl. Phys., 39, 5173-5180, (1968) · doi:10.1063/1.1655940
[3] Ashgriz, N.; Poo, J. Y., Coalescence and separation in binary collisions of liquid drops, J. Fluid Mech., 221, 183-204, (1990) · doi:10.1017/S0022112090003536
[4] Bauer, W.; Bertsch, G. F.; Schulz, H., Bubble and ring formation in nuclear fragmentation, Phys. Rev. Lett., 69, 1888-1891, (1992) · doi:10.1103/PhysRevLett.69.1888
[5] Berger, M. J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82, 64-84, (1989) · Zbl 0665.76070 · doi:10.1016/0021-9991(89)90035-1
[6] Berger, M. J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equaitons, J. Comput. Phys., 53, 484-512, (1984) · Zbl 0536.65071 · doi:10.1016/0021-9991(84)90073-1
[7] Bergeron, V.; Bonn, D.; Martin, J. Y.; Vovelle, L., Controlling droplet deposition with polymer additives, Nature, 405, 772-775, (2000) · doi:10.1038/35015525
[8] Bertalmio, M.; Cheng, L. T.; Osher, S. J.; Sapiro, G., Variational problems and partial differential equations on implicit surfaces, J. Comput. Phys., 174, 759-780, (2001) · Zbl 0991.65055 · doi:10.1006/jcph.2001.6937
[9] Brazier-Smith, P. R.; Jennings, S. G.; Latham, J., The interaction of falling water drops: coalescence, Proc. R. Soc. Lond. A, 326, 393-408, (1972) · doi:10.1098/rspa.1972.0016
[10] Burger, M., Numerical simulation of anisotropic surface diffusion with curvature-dependent energy, J. Comput. Phys., 203, 602-625, (2005) · Zbl 1143.80343 · doi:10.1016/j.jcp.2004.08.024
[11] Ceniceros, H. D., The effects of surfactants on the formation and evolution of capillary waves, Phys. Fluids, 15, 1, 245-256, (2003) · Zbl 1185.76078 · doi:10.1063/1.1528940
[12] Chen, J. C.2010 Surfactant effect on binary droplet collision. Taipei. Master thesis, National Taiwan University.
[13] Chen, K. Y.; Feng, K. A.; Kim, Y.; Lai, M. C., A note on pressure accuracy in immersed boundary method for Stokes flow, J. Comput. Phys., 230, 4377-4383, (2011) · Zbl 1416.76098 · doi:10.1016/j.jcp.2011.03.019
[14] Chen, K. Y.; Lai, M. C., A conservative scheme for solving coupled surface-bulk convection – diffusion equations with an application to interfacial flows with soluble surfactant, J. Comput. Phys., 257, 1-18, (2014) · Zbl 1349.35180 · doi:10.1016/j.jcp.2013.10.003
[15] Chiu, H. H., Advances and challenges in droplet and spray combustion. I: toward a unified theory of droplet aerothermochemistry, Prog. Energy Combust. Sci., 26, 381-416, (2000) · doi:10.1016/S0360-1285(00)00016-2
[16] Chou, P. C.2008 High-speed binary water droplet collision with different surface tension. Taipei: Master thesis, National Taiwan University.
[17] 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.
[18] Dai, B.; Leal, L. G., The mechanism of surfactant effects on drop coalescence, Phys. Fluids, 20, (2008) · Zbl 1182.76174
[19] De Ruiter, J.; Oh, J. M.; Ende, D.; Mugele, F., Dynamics of collapse of air films in drop impact, Phys. Rev. Lett., 108, (2012) · doi:10.1103/PhysRevLett.108.074505
[20] Driscoll, M. M.; Nageland, S. R., Ultrafast interference imaging of air in splashing dynamics, Phys. Rev. Lett., 107, (2011) · doi:10.1103/PhysRevLett.107.154502
[21] Dziuk, G.; Elliott, C. M., Finite element on evolving surfaces, IMA J. Numer. Anal., 27, 262-292, (2007) · Zbl 1120.65102 · doi:10.1093/imanum/drl023
[22] Eastoe, J.; Dalton, J. S., Dynamic surface tension and adsorption mechanisms of surfactants at the air – water interface, Adv. Colloid Interface Sci., 85, 103-144, (2000) · doi:10.1016/S0001-8686(99)00017-2
[23] Eggleton, C. D.; Stebe, K. J., An adsorption-desorption-controlled surfactant on a deforming droplet, J. Colloid Interface Sci., 208, 68-80, (1998) · doi:10.1006/jcis.1998.5816
[24] Elliott, C. M.; Stinner, B.; Styles, V.; Welford, R., Numerical computation of advection and diffusion on evolving diffuse interfaces, IMA J. Numer. Anal., 31, 786-812, (2011) · Zbl 1241.65081 · doi:10.1093/imanum/drq005
[25] Grant, G.; Brenton, J.; Drysdale, D., Fire suppression by water sprays, Prog. Energy Combust. Sci., 26, 79-130, (2000) · doi:10.1016/S0360-1285(99)00012-X
[26] Gunn, R., Collision characteristics of freely falling water drops, Science, 150, 695-701, (1965) · doi:10.1126/science.150.3697.695
[27] Hicks, P. D.; Purvis, R., Air cushioning and bubble entrapment in three-dimensional droplet impacts, J. Fluid Mech., 649, 135-163, (2010) · Zbl 1189.76630 · doi:10.1017/S0022112009994009
[28] Illingworth, J.; Kittler, J., A survey of the Hough transform, Comput. Vis. Graph. Image Process., 44, 87-116, (1988) · doi:10.1016/S0734-189X(88)80033-1
[29] Israelachvili, J. N., Intermolecular and Surface Forces, (2011), Academic
[30] Jiang, X.; James, A. J., Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces, J. Engng Maths, 59, 99-121, (2007) · Zbl 1178.76277 · doi:10.1007/s10665-006-9091-9
[31] Jiang, Y. J.; Umemura, A.; Law, C. K., An experimental investigation on the collision behaviour of hydrocarbon droplets, J. Fluid Mech., 234, 171-190, (1992) · doi:10.1017/S0022112092000740
[32] Kolinski, J. M.; Rubinstein, S. M.; Mandre, M.; Brenner, M. P.; Weitz, D. A.; Mahadevan, L., Skating on a film of air: drops impacting on a surface, Phys. Rev. Lett., 108, (2012) · doi:10.1103/PhysRevLett.108.074503
[33] Kuan, C. K.; Pan, K. L.; Shyy, W., Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method, J. Fluid Mech., 759, 104-133, (2014) · doi:10.1017/jfm.2014.558
[34] Lai, M. C.; Huang, C. Y.; Huang, Y. M., Simulating the axisymmetric interfacial flows with insoluble surfactant by immered boundary method, Intl J. Numer. Anal. Model., 8, 105-117, (2011) · Zbl 1208.76099
[35] Lai, M. C.; Tseng, Y. H.; Huang, H., An immersed boundary method for interfacial flow with insoluble surfactant, J. Comput. Phys., 227, 7279-7293, (2008) · Zbl 1201.76182 · doi:10.1016/j.jcp.2008.04.014
[36] Lai, M. C.; Tseng, Y. H.; Huang, H., Numerical simulation of moving contact lines with insoluble surfactant by immersed boundary method, Commun. Comput. Phys., 8, 735-757, (2010) · Zbl 1364.76125
[37] Lamb, H., Hydrodynamics, (1932), Dover · JFM 26.0868.02
[38] Leung, S.; Lowengrub, J. S.; Zhao, H. K., A grid based particle method for high order geometrical motions and local inextensible flows, J. Comput. Phys., 230, 2540-2561, (2011) · Zbl 1316.65089 · doi:10.1016/j.jcp.2010.12.029
[39] Lin, S. Y.; Lee, Y. C.; Yang, M. W.; Liu, H. S., Surface equation of state of nonionic CE surfactants, Langmuir, 19, 3164-3171, (2003) · doi:10.1021/la026574u
[40] Lipp, M. M.; Lee, K. Y. C.; Zasadzinski, J. A.; Waring, A. J., Phase and morphology changes in lipid monolayers induced by SP-B protein and its amino-terminal peptide, Science, 273, 1196-1198, (1996) · doi:10.1126/science.273.5279.1196
[41] Moretto, L. G.; Tso, K.; Colonna, N.; Wozniak, G. J., New Rayleigh-Taylor-like surface instability and nuclear multifragmentation, Phys. Rev. Lett., 69, 1884-1887, (1992) · doi:10.1103/PhysRevLett.69.1884
[42] Nobari, M. R.; Jan, Y.-J.; Tryggvason, G., Head on collision of drops – a numerical investigation, Phys. Fluid, 8, 29-42, (1996) · Zbl 1023.76588 · doi:10.1063/1.868812
[43] 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.
[44] Pan, K. L.; Chou, P. C.; Tseng, Y. J., Binary droplet collision at high Weber number, Phys. Rev. E, 80, (2009)
[45] Pan, K. L.; Hung, C. Y., Droplet impact upon a wet surface with varied fluid and surface properties, J. Colloid Interface Sci., 352, 186-193, (2010) · doi:10.1016/j.jcis.2010.08.033
[46] Pan, K. L.; Law, C. K., Dynamics of droplet-film collision, J. Fluid Mech., 587, 1-22, (2007) · Zbl 1141.76317 · doi:10.1017/S002211200700657X
[47] Pan, K. L.; Law, C. K.; Zhou, B., Experimental and mechanistic description of merging and bouncing in head-on binary droplet collision, J. Appl. Phys., 103, (2008)
[48] Perkins, W. R.; Dause, R. B.; Parente, R. A.; Minchey, S. R.; Neuman, K. C.; Gruner, S. M.; Taraschi, T. F.; Janofft, A. S., Role of lipid polymorphism in pulmonary surfactant, Science, 273, 330-332, (1996) · doi:10.1126/science.273.5273.330
[49] Peskin, C. S., Flow patterns around heart valves: a nermical method, J. Comput. Phys., 10, 252-271, (1972) · Zbl 0244.92002 · doi:10.1016/0021-9991(72)90065-4
[50] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220-252, (1977) · Zbl 0403.76100 · doi:10.1016/0021-9991(77)90100-0
[51] Peskin, C. S., The immersed boundary method, Acta Numerica, 11, 479-517, (2002) · Zbl 1123.74309 · doi:10.1017/S0962492902000077
[52] Petsev, D. N., Theoretical analysis of film thickness transition dynamics and coalescence of charged miniemulsion droplets, Langmuir, 16, 2093-2100, (2000) · doi:10.1021/la991162f
[53] Purvis, R.; Smith, F. T., Air-water interactions near droplet impact, Eur. J. Appl. Maths, 15, 853-871, (2004) · Zbl 1109.76020 · doi:10.1017/S0956792504005674
[54] Qian, J.; Law, C. K., Regimes of coalescence and separation in droplet collision, J. Fluid Mech., 331, 59-80, (1997) · doi:10.1017/S0022112096003722
[55] Rätz, A.; Voigt, A., PDEs on surfaces – a diffuse interface approach, Commun. Math. Sci., 4, 575-590, (2006) · Zbl 1113.35092 · doi:10.4310/CMS.2006.v4.n3.a5
[56] Stebe, K. J.; Lin, S. Y.; Maldarelli, C., 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, 3-20, (1991) · doi:10.1063/1.857862
[57] Tabor, R. F.; Eastoe, J.; Dowding, P., Adsorption and desorption of nonionic surfactants on silica from toluene studied by ATR-FTIR, Langmuir, 25, 9785-9791, (2009) · doi:10.1021/la901138h
[58] Teigen, K. E.; Li, X.; Lowengrub, J. S.; Wang, F.; Voigt, A., A diffuse interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformation interface, Commun. Math. Sci., 7, 1009-1037, (2009) · Zbl 1186.35168 · doi:10.4310/CMS.2009.v7.n4.a10
[59] Unverdi, S. O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100, 25-37, (1992) · Zbl 0758.76047 · doi:10.1016/0021-9991(92)90307-K
[60] Valkovska, D. S.; Danov, K. D., Determination of bulk and surface diffusion coefficients from experiemntal data for thin liquid film drainage, J. Colloid Interface sci., 223, 314-316, (2000) · doi:10.1006/jcis.1999.6657
[61] Vinokur, M., On one-dimensional stretching functions for finite-difference calculations, J. Comput. Phys., 50, 215-234, (1983) · Zbl 0505.76006 · doi:10.1016/0021-9991(83)90065-7
[62] Wadhwa, N.; Vlachos, P.; Jung, S., Noncoalescence in the oblique collision of fluid jets, Phys. Rev. Lett., 110, (2013) · doi:10.1103/PhysRevLett.110.124502
[63] Yang, X.; Zhang, X.; Li, Z.; He, G., A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, J. Comput. Phys., 228, 7821-7836, (2009) · Zbl 1391.76590 · doi:10.1016/j.jcp.2009.07.023
[64] Yarin, A. L., Drop impact dynamics: splashing, spreading, receding, bouncing, Annu. Rev. Fluid Mech., 38, 159-192, (2006) · Zbl 1097.76012 · doi:10.1146/annurev.fluid.38.050304.092144
[65] Yeo, L. Y.; Matar, O. K.; Susana Perez De Ortiz, E.; Hewitt, G. F., Film drainage between two surfactant-coated drops colliding at constant approach velocity, J. Colloid Interface Sci., 257, 93-107, (2003) · doi:10.1016/S0021-9797(02)00033-4
[66] Zhang, J.; Eckmann, D. M.; Ayyaswamy, P. S., A front tracking method for a defomable intravascular bubble in a tube with soluble surfactant transpout, J. Comput. Phys., 214, 366-396, (2006) · Zbl 1137.76819 · doi:10.1016/j.jcp.2005.09.016
[67] Zhang, L.; Xu, B.; Jiang, B.; Liu, Y., Effect of electric double layer repulsion on oil droplet coalescence process, Chem. Engng Technol., 33, 878-884, (2010) · doi:10.1002/ceat.201000001
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