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Role of surfactant-induced Marangoni stresses in drop-interface coalescence

Published online by Cambridge University Press:  23 August 2021

C.R. Constante-Amores
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
A. Batchvarov
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
L. Kahouadji
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
S. Shin
Affiliation:
Department of Mechanical and System Design Engineering, Hongik University, Seoul 04066, Republic of Korea
J. Chergui
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Université Paris Saclay, 91400 Orsay, France
D. Juric
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Université Paris Saclay, 91400 Orsay, France
O.K. Matar*
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
Email address for correspondence: [email protected]

Abstract

We study the effect of surfactants on the dynamics of a drop-interface coalescence using full three-dimensional direct numerical simulations. We employ a hybrid interface-tracking/level-set method, which takes into account Marangoni stresses that arise from surface-tension gradients, interfacial and bulk diffusion and sorption kinetic effects. We validate our predictions against the experimental data of Blanchette and Bigioni (Nat. Phys., vol. 2, issue 4, 2006, pp. 254–257) and perform a parametric study that demonstrates the delicate interplay between the flow fields and those associated with the surfactant bulk and interfacial concentrations. The results of this work unravel the crucial role of the Marangoni stresses in the flow physics of coalescence, with particular attention paid to their influence on the neck reopening dynamics in terms of stagnation-point inhibition, and near-neck vorticity generation. We demonstrate that surfactant-laden cases feature a rigidifying effect on the interface compared with the surfactant-free case, a mechanism that underpins the observed surfactant-induced phenomena.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Aarts, D.G.A.L., Lekkerkerker, H.N.W., Guo, H., Wegdam, G.H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.CrossRefGoogle ScholarPubMed
Agrawal, M.L. & Neuman, R.D. 1988 Surface diffusion in monomolecular films: II. Experiment and theory. J. Colloid Interface Sci. 121 (2), 366380.CrossRefGoogle Scholar
Alhareth, A.A. & Thoroddsen, S.T. 2020 Partial coalescence of a drop on a larger-viscosity pool. Phys. Fluids 32 (12), 122115.CrossRefGoogle Scholar
Ambravaneswaran, B., Phillips, S.D. & Basaran, O.A. 2000 Theoretical analysis of a dripping faucet. Phys. Rev. Lett. 85, 53325335.CrossRefGoogle ScholarPubMed
Ananthakrishnan, P. & Yeung, R.W. 1994 Nonlinear interaction of a vortex pair with clean and surfactant-covered free surfaces. Wave Motion 19 (4), 343365.CrossRefGoogle Scholar
Anthony, C.R., Harris, M.T. & Basaran, O.A. 2020 Initial regime of drop coalescence. Phys. Rev. Fluids 5, 033608.CrossRefGoogle Scholar
Anthony, C.R., Kamat, P.M., Thete, S.S., Munro, J.P., Lister, J.R., Harris, M.T. & Basaran, O.A. 2017 Scaling laws and dynamics of bubble coalescence. Phys. Rev. Fluids 2, 083601.CrossRefGoogle Scholar
Aryafar, H. & Kavehpour, H.P. 2006 Drop coalescence through planar surfaces. Phys. Fluids 18 (7), 072105.CrossRefGoogle Scholar
Asaki, T.J., Thiessen, D.B. & Marston, P.L. 1995 Effect of an insoluble surfactant on capillary oscillations of bubbles in water: observation of a maximum in the damping. Phys. Rev. Lett. 75, 43364336.CrossRefGoogle ScholarPubMed
Batchelor, G.K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchvarov, A., Kahouadji, L., Constante-Amores, C.R., Norões Gonçalves, G.F., Shin, S., Chergui, J., Juric, D., Craster, R.V. & Matar, O.K. 2021 Three-dimensional dynamics of falling films in the presence of insoluble surfactants. J. Fluid Mech. 906, A16.CrossRefGoogle Scholar
Batchvarov, A., Kahouadji, L., Magnini, M., Constante-Amores, C.R., Craster, R.V., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2020 Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number. Phys. Rev. Fluids 5, 093605.CrossRefGoogle Scholar
Blanchette, F. & Bigioni, T.P. 2006 Partial coalescence of drops at liquid interfaces. Nat. Phys. 2 (4), 254257.CrossRefGoogle Scholar
Blanchette, F. & Bigioni, T.P. 2009 Dynamics of drop coalescence at fluid interfaces. J. Fluid Mech. 620, 333352.CrossRefGoogle Scholar
Blanchette, F., Messio, L. & Bush, J.W.M. 2009 The influence of surface tension gradients on drop coalescence. Phys. Fluids 21 (7), 072107.CrossRefGoogle Scholar
Brenner, M.P., Lister, J.R. & Stone, H.A. 1996 Pinching threads, singularities and the number 0.0304$\ldots$. Phys. Fluids 8 (11), 28272836.CrossRefGoogle Scholar
Brøns, M., Thompson, M.C., Leweke, T. & Hourigan, K. 2014 Vorticity generation and conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 6393.CrossRefGoogle Scholar
Castrejón-Pita, J.R., Castrejón-Pita, A.A., Thete, S.S., Sambath, K., Hutchings, I.M., Hinch, J.L., John, R. & Basaran, O.A. 2015 Plethora of transitions during breakup of liquid filaments. Proc. Natl Acad. Sci. USA 112 (15), 45824587.CrossRefGoogle ScholarPubMed
Charles, G.E. & Mason, S.G. 1960 The coalescence of liquid drops with flat liquid/liquid interfaces. J. Colloid Sci. 15 (3), 236267.CrossRefGoogle Scholar
Constante-Amores, C.R., Kahouadji, L., Batchvarov, A., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2020 Dynamics of retracting surfactant-laden ligaments at intermediate Ohnesorge number. Phys. Rev. Fluids 5, 084007.CrossRefGoogle Scholar
Constante-Amores, C.R., Kahouadji, L., Batchvarov, A., Shin, S., Chergui, J., Juric, D. & Matar, O.K. 2021 Dynamics of a surfactant-laden bubble bursting through an interface. J. Fluid Mech. 911, A57.CrossRefGoogle Scholar
Craster, R.V., Matar, O.K. & Papageorgiou, D.T. 2002 Pinchoff and satellite formation in surfactant covered viscous threads. Phys. Fluids 14 (4), 13641376.CrossRefGoogle Scholar
Cresswell, R.W. & Morton, B.R. 1995 Drop-formed vortex rings-the generation of vorticity. Phys. Fluids 7 (6), 13631370.CrossRefGoogle Scholar
Day, R.F., Hinch, E.J. & Lister, J.R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704707.CrossRefGoogle Scholar
Deka, H., Biswas, G., Sahu, K.C., Kulkarni, Y. & Dalal, A. 2019 Coalescence dynamics of a compound drop on a deep liquid pool. J. Fluid Mech. 866, R2.CrossRefGoogle Scholar
Dong, T., Weheliye, W.H. & Angeli, P. 2019 Laser induced fluorescence studies on the distribution of surfactants during drop/interface coalescence. Phys. Fluids 31 (1), 012106.CrossRefGoogle Scholar
Dooley, B.S., Warncke, A.E., Gharib, M. & Tryggvason, G. 1997 Vortex ring generation due to the coalescence of a water drop at a free surface. Exp. Fluids 22 (5), 369374.CrossRefGoogle Scholar
Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface. Phys. Rev. Lett. 71, 3458.CrossRefGoogle ScholarPubMed
Eggers, J., Lister, J.R. & Stone, H.A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293310.CrossRefGoogle Scholar
Fallest, D.W., Lichtenberger, A.M., Fox, C.J. & Daniels, K.E. 2010 Fluorescent visualization of a spreading surfactant. New J. Phys. 12 (7), 073029.CrossRefGoogle Scholar
Hoepffner, J. & Paré, G. 2013 Recoil of a liquid filament: escape from pinch-off through creation of a vortex ring. J. Fluid Mech. 734, 183197.CrossRefGoogle Scholar
Houssainy, S., Kabachek, S. & Kavehpour, H.P. 2020 Closed-form theoretical model of the secondary drop size in partial coalescence-capturing pertinent timescales and viscous forces. Phys. Fluids 32 (5), 052101.CrossRefGoogle Scholar
Joos, P., Bleys, G. & Petre, G. 1982 Adsorption kinetics of nonanediol and nonane dicarbonic acid at the air/water interface. J. Chim. Phys. 79, 387393.CrossRefGoogle Scholar
Kamat, P.M., Wagoner, B.W., Castrejón-Pita, A.A., Castrejón-Pita, J.R., Anthony, C.R. & Basaran, O.A. 2020 Surfactant-driven escape from endpinching during contraction of nearly inviscid filaments. J. Fluid Mech. 899, A28.CrossRefGoogle Scholar
Kamat, P.M., Wagoner, B.W., Thete, S.S. & Basaran, O.A. 2018 Role of Marangoni stress during breakup of surfactant-covered liquid threads: reduced rates of thinning and microthread cascades. Phys. Rev. Fluids 3, 043602.CrossRefGoogle Scholar
Kavehpour, H.P. 2015 Coalescence of drops. Annu. Rev. Fluid Mech. 47 (1), 245268.CrossRefGoogle Scholar
Liao, Y.C., Franses, E.I. & Basaran, O.A. 2006 Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer. Phys. Fluids 18 (2), 022101.CrossRefGoogle Scholar
Longuet-Higgins, M.S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659679.CrossRefGoogle Scholar
Lundgren, T. & Koumoutsakos, P. 1999 On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351366.CrossRefGoogle Scholar
Manikantan, H. & Squires, T.M. 2020 Surfactant dynamics: hidden variables controlling fluid flows. J. Fluid Mech. 892, P1.CrossRefGoogle ScholarPubMed
Martin, D.W. & Blanchette, F. 2015 Simulations of surfactant effects on the dynamics of coalescing drops and bubbles. Phys. Fluids 27 (1), 012103.CrossRefGoogle Scholar
Martínez-Calvo, A. & Sevilla, A. 2021 Universal thinning of liquid filaments under dominant surface forces. Phys. Rev. Lett. 125, 114502.CrossRefGoogle Scholar
McGough, P.T. & Basaran, O.A. 2006 Repeated formation of fluid threads in breakup of a surfactant-covered jet. Phys. Rev. Lett. 96, 054502.CrossRefGoogle ScholarPubMed
Muradoglu, M. & Tryggvason, G. 2014 Simulations of soluble surfactants in 3D multiphase flow. J. Comput. Phys. 274, 737757.CrossRefGoogle Scholar
Notz, P.K., Chen, A.U. & Basaran, O.A. 2001 Satellite drops: unexpected dynamics and change of scaling during pinch-off. Phys. Fluids 13 (3), 549552.CrossRefGoogle Scholar
Paulsen, J. 2013 Approach and coalescence of liquid drops in air. Phys. Rev. E 88, 063010.CrossRefGoogle ScholarPubMed
Paulsen, J.D., Burton, J.C. & Nagel, S.R. 2011 Viscous to inertial crossover in liquid drop coalescence. Phys. Rev. Lett. 106, 114501.CrossRefGoogle ScholarPubMed
Paulsen, J.D., Burton, J.C., Nagel, S.R., Appathurai, S., Harris, M.T. & Basaran, O.A. 2012 The inexorable resistance of inertia determines the initial regime of drop coalescence. Proc. Natl Acad. Sci. USA 109 (18), 68576861.CrossRefGoogle ScholarPubMed
Paulsen, J.D., Carmigniani, R., Kannan, A., Burton, J.C. & Nagel, S.R. 2014 Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5, 3182.CrossRefGoogle Scholar
Peck, B. & Sigurdson, L. 1998 On the kinetics at a free surface. IMA J. Appl. Maths 61 (1), 113.CrossRefGoogle Scholar
Raes, F., Van Dingenen, R., Vignati, E., Wilson, J., Putaud, J.-P., Seinfeld, J.H. & Adams, P. 2000 Formation and cycling of aerosols in the global troposphere. Atmos. Environ. 34 (25), 42154240.CrossRefGoogle Scholar
Shim, S. & Stone, H.A. 2017 Damped coalescence cascade of liquid drops. Phys. Rev. Fluids 2, 044001.CrossRefGoogle Scholar
Shin, S., Chergui, J. & Juric, D. 2017 A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. J. Mech. Sci. Technol. 31, 17391751.CrossRefGoogle Scholar
Shin, S., Chergui, J., Juric, D., Kahouadji, L., Matar, O.K. & Craster, R.V. 2018 A hybrid interface tracking–level set technique for multiphase flow with soluble surfactant. J. Comput. Phys. 359, 409435.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2009 A hybrid interface method for three-dimensional multiphase flows based on front-tracking and level set techniques. Intl J. Numer. Meth. Fluids 60, 753778.CrossRefGoogle Scholar
Siderius, A., Kehl, S.K. & Leaist, D.G. 2002 Surfactant diffusion near critical micelle concentrations. J. Solution Chem. 31 (8), 607625.CrossRefGoogle Scholar
Strickland, S.L., Shearer, M. & Daniels, K.E. 2015 Spatiotemporal measurement of surfactant distribution on gravity–capillary waves. J. Fluid Mech. 777, 523543.CrossRefGoogle Scholar
Sun, K., Zhang, P., Che, Z. & Wang, T. 2018 Marangoni-flow-induced partial coalescence of a droplet on a liquid/air interface. Phys. Rev. Fluids 3, 023602.CrossRefGoogle Scholar
Thoraval, M.J., Li, Y. & Thoroddsen, S.T. 2016 Vortex-ring-induced large bubble entrainment during drop impact. Phys. Rev. E 93, 033128.CrossRefGoogle ScholarPubMed
Thoroddsen, S.T., Qian, B., Etoh, T.G. & Takehara, K. 2007 The initial coalescence of miscible drops. Phys. Fluids 19 (7), 072110.CrossRefGoogle Scholar
Thoroddsen, S.T. & Takehara, K. 2000 The coalescence cascade of a drop. Phys. Fluids 12 (6), 12651267.CrossRefGoogle Scholar
Timmermans, M.-L.E. & Lister, J.R. 2002 The effect of surfactant on the stability of a liquid thread. J. Fluid Mech. 459, 289306.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.CrossRefGoogle Scholar
Wee, H., Wagoner, B.W., Kamat, P.M. & Basaran, O.A. 2020 Effects of surface viscosity on breakup of viscous threads. Phys. Rev. Lett. 124, 204501.CrossRefGoogle ScholarPubMed
Xia, X., He, C., Yu, D., Zhao, J. & Zhang, P. 2017 Vortex-ring-induced internal mixing upon the coalescence of initially stationary droplets. Phys. Rev. Fluids 2, 113607.CrossRefGoogle Scholar
Xu, Q. 2007 Computational and theoretical analysis of ink-jets drop formation and breakup. PhD thesis, Purdue University.Google Scholar
Ziegler, V.E. & Wolf, B.A. 2005 Bimodal drop size distributions during the early stages of shear induced coalescence. Polymer 46 (22), 92659273.CrossRefGoogle Scholar