Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow. (25th August 2020)

• Record Type: Journal Article
• Authors: Liu, Haihu; Zhang, Jinggang; Ba, Yan; Wang, Ningning; Wu, Lei
• Is Part Of: Journal of fluid mechanics. Volume 897(2020)
• Publication Date: 2020-08-25
• Subjects: contact lines, -- breakup/coalescence, -- Marangoni convection; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.416
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : 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.