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Simulating surfactant spreading: Influence of a physically motivated equation of state

  • DINA SINCLAIR (a1), RACHEL LEVY (a1) and KAREN E. DANIELS (a2)
Abstract

In this paper, we present numerical simulations that demonstrate the effect of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension in surfactant-driven thin liquid films. Previous choices of the model EoS have been an ad-hoc decreasing function. Here, we instead propose an empirically motivated EoS; this provides a route to resolve some discrepancies and raises new issues to be pursued in future experiments. In addition, we test the influence of the choice of initial conditions and values for the non-dimensional groups. We demonstrate that the choice of EoS improves the agreement in surfactant distribution morphology between simulations and experiments, and influences the dynamics of the simulations. Because an empirically motivated EoS has regions with distinct gradients, future mathematical models may be improved by considering more than one timescale. We observe that the non-dimensional number controlling the relative importance of gravitational versus capillary forces has a larger influence on the dynamics than the other non-dimensional groups, but is nonetheless not a likely cause of discrepancy between simulations and experiments. Finally, we observe that the experimental approach using a ring to contain the surfactant could affect the surfactant and fluid dynamics if it disrupts the intended initial surfactant distribution. However, the fluid meniscus itself does not significantly affect the dynamics.

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This work was funded by NSF grant DMS-FRG #096815 (RL and KED), Howard Hughes Medical Institute Undergraduate Science Education Program Award #52006301 (RL), and Research Corporation Cottrell Scholar Award #19788 (RL).

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2] T. E. Angelini , M. Roper , R. Kolter , D. A. Weitz & M. P. Brenner (2009) Bacillus subtilis spreads by surfing on waves of surfactant. Proc. Natl. Acad. Sci. 106 (43), 1810918113.

[3] J. W. Barrett , H. Garcke & R. Nürnberg (2003) Finite element approximation of surfactant spreading on a thin film. SIAM J. Numer. Anal. 41 (4), 14271464.

[5] R. J. Braun (2012) Dynamics of the tear film. Annu. Rev. Fluid Mech. 44, 267297.

[6] J. Bull & J. Grotberg (2003) Surfactant spreading on thin viscous films: Film thickness evolution and periodic wall stretch. Exp. Fluids 34 (1), 115.

[8] R. Craster & O. Matar (2000) Surfactant transport on mucus films. J. Fluid Mech. 425, 235258.

[9] R. Craster & O. Matar (2009) Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131.

[10] A. De Wit , D. Gallez & C. Christov (1994) Nonlinear evolution equations for thin liquid films with insoluble surfactants. Phys. Fluids (1994-present) 6 (10), 32563266.

[12] D. W. Fallest , A. M. Lichtenberger , C. J. Fox & K. E. Daniels (July 2010) Fluorescent visualization of a spreading surfactant. New J. Physics 12 (7), 73029.

[14] D. P. Gaver & J. B. Grotberg (1990) The dynamics of a localized surfactant on a thin film. J. Fluid Mech. 213, 127148.

[15] D. P. Gaver & J. B. Grotberg (1992) Droplet spreading on a thin viscous film. J. Fluid Mech. 235, 399414.

[16] D. Halpern & J. Grotberg (1993) Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: A model of airway closure. J. Biomech. Eng. 115 (3), 271277.

[17] A. H. Heidari , R. J. Braun , A. H. Hirsa , S. A. Snow & S. Naire (2002) Hydrodynamics of a bounded vertical film with nonlinear surface properties. J. Colloid Interface Sci. 253 (2), 295307.

[20] O. Jensen (1994) Self-similar, surfactant-driven flows. Phys. Fluids (1994-present) 6 (3), 10841094.

[22] O. Jensen & J. Grotberg (1993) The spreading of heat or soluble surfactant along a thin liquid film. Phys. Fluids A: Fluid Dyn. (1989–1993) 5 (1), 5868.

[23] V. Kaganer , H. Möhwald & P. Dutta (April 1999) Structure and phase transitions in Langmuir monolayers. Rev. Mod. Phys. 71 (3), 779819.

[26] R. Levy , D. B. Hill , M. G. Forest & J. B. Grotberg (2014) Pulmonary fluid flow challenges for experimental and mathematical modeling. Integrative Comparative Biol. 54 (6), 9851000.

[27] R. Levy & M. Shearer (2006) The motion of a thin liquid film driven by surfactant and gravity. SIAM J. Appl. Math. 66 (5), 15881609.

[28] R. Levy , M. Shearer & T. P. Witelski (2007) Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves. Eur. J. Appl. Math. 18 (06), 679708.

[30] A. Oron , S. H. Davis & S. G. Bankoff (1997) Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931.

[36] M. Renardy (1996) A singularly perturbed problem related to surfactant spreading on thin films. Nonlinear Anal.: Theory, Methods Appl. 27 (3) (1996), 287296.

[37] J. D. A. Shrive , J. D. Brennan , R. S. Brown & U. J. Krull (1995) Optimization of self-quenching response of nitrobenzoxadiazole dipalmitoylphosphatidylethanolaminein phospholipid membranes for biosensor development. Appl. Spectrosc. 49, 304313.

[39] S. L. Strickland , M. Hin , M. R. Sayanagi , C. Gaebler , K. E. Daniels , R. Levy & C. Conti (April 2014) Self-healing dynamics of surfactant coatings on thin viscous films. Phys. Fluids 26 (4), 042109.

[40] E. R. Swanson , S. L. Strickland , M. Shearer & K. E. Daniels (2015) Surfactant spreading on a thin liquid film: Reconciling models and experiments. J. Eng. Math. 94, 6379.

[41] F. Tiberg & A.-M. Cazabat (1994) Spreading of thin films of ordered nonionic surfactants – Origin of the stepped shape of the spreading precursor. Langmuir 10 (7), 23012306.

[42] S. M. Troian , E. Herbolzheimer , S. A. Safran , J. F. Joanny , X. L. Wu & S. A. Safran (1989) Fingering instability in thin wetting films. Phys. Rev. Lett. 62, 14961499.

[43] S. M. Troian , E. Herbolzheimer & S. A. Safran (1990) Model for the fingering instability of spreading surfactant drops. Phys. Rev. Lett. 65, 333336.

[44] M. Warner , R. Craster & O. Matar (2004) Fingering phenomena associated with insoluble surfactant spreading on thin liquid films. J. Fluid Mech. 510, 169200.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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