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Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

Published online by Cambridge University Press:  02 November 2018

Zheng Yuan Luo Open the ORCID record for Zheng Yuan Luo [Opens in a new window] ,
Xing Long Shang  and
Bo Feng Bai
Zheng Yuan Luo
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Xing Long Shang
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Bo Feng Bai*
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
*
†Email address for correspondence: bfbai@mail.xjtu.edu.cn
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Abstract

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.

JFM classification

Complex Fluids: Complex Fluids Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 91 - 121
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Copyright
© 2018 Cambridge University Press 

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