Skip to main content Accessibility help
×
Home

Surface viscosity and Marangoni stresses at surfactant laden interfaces

  • Gwynn J. Elfring (a1), L. Gary Leal (a2) and Todd M. Squires (a2)

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.

Copyright

Corresponding author

Email address for correspondence: squires@engineering.ucsb.edu

References

Hide All
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, 153159.
Barentin, C., Ybert, C., Di Meglio, J.-M. & Joanny, J.-F. 1999 Surface shear viscosity of Gibbs and Langmuir monolayers. J. Fluid Mech. 397, 331349.
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, L44L46.
Cicuta, P. & Terentjev, E. M. 2005 Viscoelasticity of a protein monolayer from anisotropic surface pressure measurements. Eur. Phys. J. E 16 (2), 147158.
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 2553.
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, 3645.
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, 3543.
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.
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, 553561.
Fischer, T. M. 2004a Comment on ‘Shear viscosity of Langmuir monolayers in the low-density limit’. Phys. Rev. Lett. 92, 139603.
Fischer, T. M. 2004b The drag on needles moving in a Langmuir monolayer. J. Fluid Mech. 498, 123137.
Fuller, G. G. & Vermant, J. 2012 Complex fluid–fluid interfaces: rheology and structure. Annu. Rev. Chem. Biomol. Engng 3, 519543.
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.
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, 349372.
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, 85117.
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Levine, A. J. & MacKintosh, F. C. 2002 Dynamics of viscoelastic membranes. Phys. Rev. E 66, 061606.
Lubensky, D. K. & Goldstein, R. E. 1996 Hydrodynamics of monolayer domains at the air–water interface. Phys. Fluids 8, 843854.
Masoud, H. & Stone, H. A. 2014 A reciprocal theorem for Marangoni propulsion. J. Fluid Mech. 741, R4.
Probstein, R. F. 1994 Physicochemical Hydrodynamics: An Introduction. John Wiley & Sons.
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, 140.
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593602.
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72, 31113113.
Samaniuk, J. R. & Vermant, J. 2014 Micro and macrorheology at fluid–fluid interfaces. Soft Matt. 10, 70237033.
Scriven, L. E. 1960 Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12, 98108.
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.
Sickert, M., Rondelez, F. & Stone, H. A. 2007 Single-particle Brownian dynamics for characterizing the rheology of fluid Langmuir monolayers. Europhys. Lett. 79, 66005.
Slattery, J. C., Sagis, L. & Oh, E.-S. 2006 Interfacial Transport Phenomena. Springer.
Stevenson, P. 2005 Remarks on the shear viscosity of surfaces stabilised with soluble surfactants. J. Colloid Interface Sci. 290, 603606.
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, 111112.
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, 151173.
Stone, H. A. & Masoud, H. 2015 Mobility of membrane-trapped particles. J. Fluid Mech. 781, 494505.
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.
Verwijlen, T., Moldenaers, P. & Vermant, J. 2013 A fixture for interfacial dilatational rheometry using a rotational rheometer. Eur. Phys. J. 222, 8397.
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, 36773682.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Surface viscosity and Marangoni stresses at surfactant laden interfaces

  • Gwynn J. Elfring (a1), L. Gary Leal (a2) and Todd M. Squires (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.