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Surface viscosity and Marangoni stresses at surfactant laden interfaces

Published online by Cambridge University Press:  04 March 2016

Gwynn J. Elfring ,
L. Gary Leal  and
Todd M. Squires
Gwynn J. Elfring
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
L. Gary Leal
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
Todd M. Squires*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
*
†Email address for correspondence: squires@engineering.ucsb.edu
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Abstract

We calculate here the force on a probe at a viscous, compressible interface, laden with soluble surfactant that equilibrates on a finite time scale. The motion of the probe through the interface drives variations in the surfactant concentration at the interface that in turn leads to a Marangoni flow that contributes to the force on the probe. We demonstrate that the Marangoni force on the probe depends non-trivially on the surface shear and dilatational viscosities of the interface indicating the difficulty in extracting these material properties from force measurements at compressible interfaces.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 712 - 739
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Copyright
© 2016 Cambridge University Press 

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References

Barentin, C., Muller, P., Ybert, C., Joanny, J.-F. & di Meglio, J.-M. 2000 Shear viscosity of polymer and surfactant monolayers. Eur. Phys. J. 2, 153–159.Google Scholar
Barentin, C., Ybert, C., Di Meglio, J.-M. & Joanny, J.-F. 1999 Surface shear viscosity of Gibbs and Langmuir monolayers. J. Fluid Mech. 397, 331–349.Google Scholar
Camley, B. A., Esposito, C., Baumgart, T. & Brown, F. L. H. 2010 Lipid bilayer domain fluctuations as a probe of membrane viscosity. Biophys. J. 99, L44–L46.CrossRefGoogle ScholarPubMed
Cicuta, P. & Terentjev, E. M. 2005 Viscoelasticity of a protein monolayer from anisotropic surface pressure measurements. Eur. Phys. J. E 16 (2), 147–158.CrossRefGoogle ScholarPubMed
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 25–53.Google Scholar
Danov, K., Aust, R., Durst, F. & Lange, U. 1995 Influence of the surface viscosity on the hydrodynamic resistance and surface diffusivity of a large Brownian particle. J. Colloid Interface Sci. 175, 36–45.CrossRefGoogle Scholar
Dimova, R., Danov, K., Pouligny, B. & Ivanov, I. B. 2000 Drag of a solid particle trapped in a thin film or at an interface: influence of surface viscosity and elasticity. J. Colloid Interface Sci. 226, 35–43.Google Scholar
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.Google Scholar
Evans, E. & Sackmann, E. 1988 Translational and rotational drag coefficients for a disk moving in a liquid membrane associated with a rigid substrate. J. Fluid Mech. 194, 553–561.CrossRefGoogle Scholar
Fischer, T. M. 2004a Comment on ‘Shear viscosity of Langmuir monolayers in the low-density limit’. Phys. Rev. Lett. 92, 139603.Google Scholar
Fischer, T. M. 2004b The drag on needles moving in a Langmuir monolayer. J. Fluid Mech. 498, 123–137.Google Scholar
Fuller, G. G. & Vermant, J. 2012 Complex fluid–fluid interfaces: rheology and structure. Annu. Rev. Chem. Biomol. Engng 3, 519–543.Google Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.Google Scholar
Hughes, B. D., Pailthorpe, B. A. & White, L. R. 1981 The translational and rotational drag on a cylinder moving in a membrane. J. Fluid Mech. 110, 349–372.Google Scholar
Kotula, A. P. & Anna, S. L. 2015 Regular perturbation analysis of small amplitude oscillatory dilatation of an interface in a capillary pressure tensiometer. J. Rheol. 59, 85–117.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Levine, A. J. & MacKintosh, F. C. 2002 Dynamics of viscoelastic membranes. Phys. Rev. E 66, 061606.Google Scholar
Lubensky, D. K. & Goldstein, R. E. 1996 Hydrodynamics of monolayer domains at the air–water interface. Phys. Fluids 8, 843–854.CrossRefGoogle Scholar
Masoud, H. & Stone, H. A. 2014 A reciprocal theorem for Marangoni propulsion. J. Fluid Mech. 741, R4.Google Scholar
Probstein, R. F. 1994 Physicochemical Hydrodynamics: An Introduction. John Wiley & Sons.CrossRefGoogle Scholar
Prosser, A. J. & Franses, E. I. 2001 Adsorption and surface tension of ionic surfactants at the air–water interface: review and evaluation of equilibrium models. Colloids Surf. A 178, 1–40.Google Scholar
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593–602.CrossRefGoogle Scholar
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72, 3111–3113.Google Scholar
Samaniuk, J. R. & Vermant, J. 2014 Micro and macrorheology at fluid–fluid interfaces. Soft Matt. 10, 7023–7033.Google Scholar
Scriven, L. E. 1960 Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12, 98–108.CrossRefGoogle Scholar
Shlomovitz, R., Evans, A. A., Boatwright, T., Dennin, M. & Levine, A. J. 2013 Measurement of monolayer viscosity using noncontact microrheology. Phys. Rev. Lett. 110, 137802.Google Scholar
Sickert, M., Rondelez, F. & Stone, H. A. 2007 Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers. Europhys. Lett. 79, 66005.Google Scholar
Slattery, J. C., Sagis, L. & Oh, E.-S. 2006 Interfacial Transport Phenomena. Springer.Google Scholar
Stevenson, P. 2005 Remarks on the shear viscosity of surfaces stabilised with soluble surfactants. J. Colloid Interface Sci. 290, 603–606.Google Scholar
Stone, H. A. 1990 A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys. Fluids A 2, 111–112.CrossRefGoogle Scholar
Stone, H. A. & Ajdari, A. 1998 Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth. J. Fluid Mech. 369, 151–173.Google Scholar
Stone, H. A. & Masoud, H. 2015 Mobility of membrane-trapped particles. J. Fluid Mech. 781, 494–505.Google Scholar
Verwijlen, T., Leiske, D. L., Moldenaers, P., Vermant, J. & Fuller, G. G. 2012 Extensional rheometry at interfaces: analysis of the Cambridge interfacial tensiometer. J. Rheol. 56, 1225.Google Scholar
Verwijlen, T., Moldenaers, P. & Vermant, J. 2013 A fixture for interfacial dilatational rheometry using a rotational rheometer. Eur. Phys. J. 222, 83–97.Google Scholar
Zell, Z. A., Nowbahar, A., Mansard, V., Leal, L. G., Deshmukh, S. S., Mecca, J. M., Tucker, C. J. & Squires, T. M. 2014 Surface shear inviscidity of soluble surfactants. Proc. Natl Acad. Sci. USA 111, 3677–3682.Google Scholar