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Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow

Published online by Cambridge University Press:  18 June 2020

Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window] ,
Jinggang Zhang ,
Yan Ba ,
Ningning Wang  and
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window]
Haihu Liu*
Affiliation:
School of Energy and Power Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, China
Jinggang Zhang
Affiliation:
School of Energy and Power Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, China
Yan Ba
Affiliation:
School of Astronautics, Northwestern Polytechnical University, 127 West Youyi Road,Xi’an710072, China
Ningning Wang
Affiliation:
School of Energy and Power Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, China
Lei Wu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, China
*
† Email address for correspondence: [email protected]
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Abstract

A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number ($Ca_{e}$) and study the effect of $Ca_{e}$, viscosity ratio ($\unicode[STIX]{x1D706}$) and surfactant coverage on the droplet behaviour. Results show that at low $Ca_{e}$ the droplet eventually reaches steady deformation and a constant moving velocity $u_{d}$. The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each $\unicode[STIX]{x1D706}$, a linear relationship is found between contact-line capillary number and $Ca_{e}$, but not between wall stress and $u_{d}$ due to Marangoni effects. As $\unicode[STIX]{x1D706}$ increases, $u_{d}$ decreases monotonically, but the deformation first increases and then decreases for each $Ca_{e}$. Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase $Ca_{e}$ and study droplet breakup for varying $\unicode[STIX]{x1D706}$, where the role of surfactants on the critical $Ca_{e}$ ($Ca_{e,c}$) of droplet breakup is identified by comparing with the clean case. As in the clean case, $Ca_{e,c}$ first decreases and then increases with increasing $\unicode[STIX]{x1D706}$, but its minima occurs at $\unicode[STIX]{x1D706}=0.5$ instead of $\unicode[STIX]{x1D706}=1$ in the clean case. The presence of surfactants always decreases $Ca_{e,c}$, and its effect is more pronounced at low $\unicode[STIX]{x1D706}$. Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest $\unicode[STIX]{x1D706}$ in the surfactant-covered case.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Breakup/coalescence Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A33
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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