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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: [email protected]
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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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