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Modelling steady shear flows of Newtonian liquids with non-Newtonian interfaces

Published online by Cambridge University Press:  31 January 2017

Patrick T. Underhill ,
Amir H. Hirsa Open the ORCID record for Amir H. Hirsa [Opens in a new window]  and
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]
Patrick T. Underhill
Affiliation:
Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Amir H. Hirsa*
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Juan M. Lopez
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
*
†Email address for correspondence: hirsaa@rpi.edu
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Abstract

In countless biological and technological processes, the flow of Newtonian liquids with a non-Newtonian interface is a common occurrence, such as in monomolecular films in ‘solid’ phases atop of aqueous bulk fluid. There is a lack of models that can predict the flow under conditions different from those used to measure the rheological response of the interface. Here, we present a model which describes interfacial hydrodynamics, including two-way coupling to a bulk Newtonian fluid described by the Navier–Stokes equations, that allows for shear-thinning response of the interface. The model includes a constitutive equation for the interface under steady shear that takes the Newtonian functional form but where the surface shear viscosity is generalized to be a function of the local shear rate. In the limit of a highly viscous interface, the interfacial hydrodynamics is decoupled from the bulk flow and the model can be solved analytically. This provides not only insight into the flow but also a means to validate the numerical technique for solving the two-way coupled problem. The numerical results of the coupled problem shed new light on existing experimental results on steadily sheared monolayers of dipalmitoylphosphatidylcholine (DPPC), the primary constituent of lung surfactant and the bilayers of mammalian cell walls. For low packing density DPPC monolayers, a Newtonian shear-independent surface shear viscosity model can reproduce the interfacial flows, but at high packing density, the shear-thinning properties of the new model presented here are needed.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Non-Newtonian Flows: Non-Newtonian Flows Non-Newtonian Flows: Rheology
Type
Papers
Information
Journal of Fluid Mechanics , Volume 814 , 10 March 2017 , pp. 5 - 23
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Copyright
© 2017 Cambridge University Press 

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References

Adamson, A. W. & Gast, A. P. 1997 Physical Chemistry of Surfaces, 6th edn. Wiley-Interscience.Google Scholar
Bird, B. R., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics. Wiley.Google Scholar
Choi, S. Q., Steltenkamp, S., Zasadzinski, J. A. & Squires, T. M. 2011 Active microrheology and simultaneous visualization of sheared phospholipid monolayers. Nat. Commun. 2, 312.Google Scholar
Dhar, P., Cao, Y., Fischer, T. M. & Zasadzinski, J. A. 2010 Active interfacial shear microrheology of aging protein films. Phys. Rev. Lett. 104, 016001.Google Scholar
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.Google Scholar
Elfring, G., Leal, L. G. & Squires, T. M. 2016 Surface viscosity and Marangoni stresses at surfactant laden interfaces. J. Fluid Mech. 792, 712–739.Google Scholar
Erni, P. 2011 Deformation modes of complex fluid interfaces. Soft Matt. 7, 7586–7600.Google Scholar
Espinosa, G., López-Montero, I., Monroy, F. & Langevin, D. 2011 Shear rheology of lipid monolayers and insights on membrane fluidity. Proc. Natl Acad. Sci. USA 108, 6008–6013.Google Scholar
Fuller, G. G. & Vermant, J. 2011 Editorial: dynamics and rheology of complex fluid–fluid interfaces. Soft Matt. 7, 7583–7585.CrossRefGoogle Scholar
Fuller, G. G. & Vermant, J. 2012 Complex fluid–fluid interfaces: rheology and structure. Annu. Rev. Chem. Biomol. Engng 3, 519–543.CrossRefGoogle ScholarPubMed
Gauchet, S., Durand, M. & Langevin, D. 2015 Foam drainage. Possible influence of a non-Newtonian surface shear viscosity. J. Colloid Interface Sci. 449, 373–376.CrossRefGoogle ScholarPubMed
Hirsa, A. H., Lopez, J. M. & Miraghaie, R. 2002 Determination of surface shear viscosity via deep-channel flow with inertia. J. Fluid Mech. 470, 135–149.Google Scholar
Ivanova, A. N., Ignes-Mullol, J. & Schwartz, D. K. 2001 Microrheology of a sheared Langmuir monolayer: elastic recovery and interdomain slippage. Langmuir 17, 3406–3411.Google Scholar
Jiang, T.-S., Chen, J.-D. & Slattery, J. C. 1983 Nonlinear interfacial stress-deformation behavior measured with several interfacial viscometers. J. Colloid Interface Sci. 96, 7–19.Google Scholar
Kim, K. H., Choi, S. Q., Zasadzinski, A. & Squires, T. M. 2011 Interfacial microrheology of DPPC monolayers at the air–water interface. Soft Matt. 7, 7782–7789.CrossRefGoogle Scholar
Kurnaz, M. L. & Schwartz, D. K. 1997 Channel flow in a Langmuir monolayer: unusual velocity profiles in a liquid-crystalline mesophase. Phys. Rev. E 56, 3378–3384.Google Scholar
Langevin, D. 2014a Rheology of adsorbed surfactant monolayers at fluid surfaces. Annu. Rev. Fluid Mech. 46, 47–65.CrossRefGoogle Scholar
Langevin, D. 2014b Surface shear rheology of monolayers at the surface of water. Adv. Colloid Interface Sci. 207, 121–130.CrossRefGoogle ScholarPubMed
Lopez, J. M. & Hirsa, A. H. 2015 Coupling of the interfacial and bulk flow in knife-edge viscometers. Phys. Fluids 27, 042102.Google Scholar
Maestro, A., Bonales, L. J., Ritacco, H., Fischer, T. M., Rubio, R. G. & Ortega, F. 2011 Surface rheology: macro- and microrheology of poly(tert-butyl acrylate) monolayers. Soft Matt. 7, 7761–7771.CrossRefGoogle Scholar
Mannheimer, R. J. & Schechter, R. S. 1970 An improved apparatus and analysis for surface rheological measurements. J. Colloid Interface Sci. 32, 195–211.Google Scholar
McConnell, H. M. 1991 Structures and transitions in lipid monolayers at the air–water interface. Annu. Rev. Phys. Chem. 42, 171–195.Google Scholar
Ortega, F., Ritacco, H. & Rubio, R. G. 2010 Interfacial microrheology: particle tracking and related techniques. Curr. Opin. Colloid Interface Sci. 15, 237–245.Google Scholar
Raghunandan, A., Lopez, J. M. & Hirsa, A. H. 2015 Bulk flow driven by a viscous monolayer. J. Fluid Mech. 785, 283–300.Google Scholar
Reynaert, S., Brooks, C. F., Moldenaers, P., Vermant, J. & Fuller, G. G. 2008 Analysis of the magnetic rod interfacial stress rheometer. J. Rheol. 52, 261–285.CrossRefGoogle Scholar
Sadoughi, A. H., Lopez, J. M. & Hirsa, A. H. 2013 Transition from Newtonian to non-Newtonian surface shear viscosity of phospholipid monolayers. Phys. Fluids 25, 032107.Google Scholar
Sagis, L. M. C. 2010 Modelling surface rheology of complex interfaces with extended irreversible thermodynamics. Physica A 389, 673–684.CrossRefGoogle Scholar
Sagis, L. M. C. 2011 Dynamic properties of interfaces in soft matter: experiments and theory. Rev. Mod. Phys. 83, 1367–1403.Google 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
Slattery, J. C., Sagis, L. & Oh, E.-S. 2007 Interfacial Transport Phenomena, 2nd edn. Springer.Google Scholar
Vandebril, S., Franck, A., Fuller, G. G., Moldnaers, P. & Vermant, J. 2010 A double wall-ring geometry for interfacial shear rheology. Rheol. Acta 49, 131–144.CrossRefGoogle Scholar