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Modelling the passive breakup of a surfactant-contaminated droplet in a T-junction microchannel

Published online by Cambridge University Press:  06 May 2024

Jinggang Zhang Open the ORCID record for Jinggang Zhang [Opens in a new window] ,
Yongguang Wang ,
Li Chen ,
Linjun Shen  and
Haihang Cui Open the ORCID record for Haihang Cui [Opens in a new window]
Jinggang Zhang*
Affiliation:
School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
Yongguang Wang
Affiliation:
School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
Li Chen
Affiliation:
School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
Linjun Shen
Affiliation:
School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
Haihang Cui*
Affiliation:
School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

A lattice Boltzmann method is used to explore the effect of surfactants on the unequal volume breakup of a droplet in a T-junction microchannel, and the asymmetry due to fabrication defects in real-life microchannels is modelled as the pressure difference between the two branch outlets ($\Delta {P^\ast }$). We first study the effect of the surfactants on the droplet dynamics at different dimensionless initial droplet lengths ($l_0^\ast $) and capillary numbers (Ca) under symmetric boundary conditions ($\Delta {P^\ast } = 0$). The results indicate that the presence of surfactants promotes droplet deformation and breakup at small and moderate $l_0^\ast $ values, while the surfactant effect is weakened at large $l_0^\ast $ values. When the branch channels are completely blocked by the droplet, a linear relationship is observed between the dimensionless droplet length ($l_d^\ast $) and dimensionless time (${t^\ast }$), and two formulas are proposed for predicting the evolution of $l_d^\ast $ with ${t^\ast }$ for the two systems. We then investigate the effect of the surfactants on the droplet breakup at different values of $\Delta {P^\ast }$ and bulk surfactant concentrations (${\psi _b}$) under asymmetric boundary conditions ($\Delta {P^\ast } \ne 0$). It is observed that, as $\Delta {P^\ast }$ increases, the volume ratio of the generated droplets (${V_1}/{V_2}$) decreases to 0 in both systems, while the rate of decrease is higher in the clean system, i.e. the presence of surfactants could cause a decreased pressure difference between the droplet tips. As ${\psi _b}$ increases, ${V_1}/{V_2}$ first increases rapidly, then remains almost constant and finally decreases slightly. We thus establish a phase diagram that describes the ${V_1}/{V_2}$ variation with $\Delta {P^\ast }$ and ${\psi _b}$.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Liquid bridges Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , A23
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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