Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants
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2014-06-05
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Abstract
A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as well as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically. © 2014 AIP Publishing LLC.
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Zhang, Z, S Xu and W Ren (2014). Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants. Physics of Fluids, 26(6). pp. 062103–062103. 10.1063/1.4881195 Retrieved from https://hdl.handle.net/10161/27458.
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Scholars@Duke
Shixin Xu
Shixin Xu is an Assistant Professor of Mathematics whose research spans several dynamic and interconnected fields. His primary interests include machine learning and data-driven models for disease prediction, multiscale modeling of complex fluids, neurovascular coupling, homogenization theory, and numerical analysis. His current projects reflect a diverse and impactful portfolio:
- Developing predictive models based on image data to identify hemorrhagic transformation in acute ischemic stroke.
- Conducting electrodynamics modeling of saltatory conduction along myelinated axons to understand nerve impulse transmission.
- Engaging in electrochemical modeling to explore the interactions between electric fields and chemical processes.
- Investigating fluid-structure interactions with mass transport and reactions, crucial for understanding physiological and engineering systems.
These projects demonstrate his commitment to addressing complex problems through interdisciplinary approaches that bridge mathematics with biological and physical sciences.
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