2 results
Modelling the passive breakup of a surfactant-contaminated droplet in a T-junction microchannel
- Jinggang Zhang, Yongguang Wang, Li Chen, Linjun Shen, Haihang Cui
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- Journal:
- Journal of Fluid Mechanics / Volume 986 / 10 May 2024
- Published online by Cambridge University Press:
- 06 May 2024, A23
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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 ${\psi _b}$.
Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow
- Haihu Liu, Jinggang Zhang, Yan Ba, Ningning Wang, Lei Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 897 / 25 August 2020
- Published online by Cambridge University Press:
- 18 June 2020, A33
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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.