Influence of surface viscosity on droplets in shear flow
Abstract
© 2016 Cambridge University Press.The behaviour of a single droplet in an immiscible
external fluid, submitted to shear flow is investigated using numerical simulations.
The surface of the droplet is modelled by a Boussinesq-Scriven constitutive law involving
the interfacial viscosities and a constant surface tension. A numerical method using
Loop subdivision surfaces to represent droplet interface is introduced. This method
couples boundary element method for fluid flows and finite element method to take
into account the stresses due to the surface dilational and shear viscosities and
surface tension. Validation of the numerical scheme with respect to previous analytic
and computational work is provided, with particular attention to the viscosity contrast
and the shear and dilational viscosities characterized both by a Boussinesq number
Bq. Then, influence of equal surface viscosities on steady-state characteristics of
a droplet in shear flow are studied, considering both small and large deformations
and for a large range of bulk viscosity contrast. We find that small deformation analysis
is surprisingly predictive at moderate and high surface viscosities. Equal surface
viscosities decrease the Taylor deformation parameter and tank-treading angle and
also strongly modify the dynamics of the droplet: when the Boussinesq number (surface
viscosity) is large relative to the capillary number (surface tension), the droplet
displays damped oscillations prior to steady-state tank-treading, reminiscent from
the behaviour at large viscosity contrast. In the limit of infinite capillary number
Ca, such oscillations are permanent. The influence of surface viscosities on breakup
is also investigated, and results show that the critical capillary number is increased.
A diagram (Bq; Ca) of breakup is established with the same inner and outer bulk viscosities.
Additionally, the separate roles of shear and dilational surface viscosity are also
elucidated, extending results from small deformation analysis. Indeed, shear (dilational)
surface viscosity increases (decreases) the stability of drops to breakup under shear
flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each
Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the
study shows that for certain combinations of shear and dilational viscosities, drop
deformation for a given capillary number is the same as in the case of a clean surface
while the inclination angle varies.
Type
Journal articlePermalink
https://hdl.handle.net/10161/11715Published Version (Please cite this version)
10.1017/jfm.2016.39Publication Info
Gounley, J; Boedec, G; Jaeger, M; & Leonetti, M (2016). Influence of surface viscosity on droplets in shear flow. Journal of Fluid Mechanics, 791. pp. 464-494. 10.1017/jfm.2016.39. Retrieved from https://hdl.handle.net/10161/11715.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
John Gounley
Affiliate
My research focuses on algorithms for fluid-structure interactions in blood flow,
such as deformable blood cells, circulating tumor cells, and vessel walls.

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