A variational approach to moving contact line hydrodynamics

By Tiezheng Qian, Xiaoping Wang, P. Sheng. Journal of Fluid Mechanics, 2006

404 citations recorded by the source corpus.

In immiscible two-phase flows, the contact line denotes the intersection of the fluid–fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial-slip regime, extending to mesoscopic length scales. The sharp (fluid–fluid) interface limit of the hydrodynamic model, together with some general implications of slip versus no slip, are discussed.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/55afdf4ef8fc31307e994fe8676b04ae2979c8c3

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Citations in the corpus

Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants (2019, methodology): “Thus the NBC interpolates between the no-slip limit and the limit of zero tangential viscous stress (Qian et al. 2006).”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, methodology): “We also refer the reader to [16] and [92] for other physical derivations of the dynamic boundary conditions, obtained by taking the continuum limit of lattice models within a direct mean-field approximation and by applying a density functional theory, respectively, to [189] for the derivation of dyn”
Sharp-interface limit of the Cahn–Hilliard model for moving contact lines (2010, background): “It is possible to introduce a slip velocity here (Qian et al. 2006b), which would allow more freedom in fitting the data and perhaps also a better representation of the true physics.”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “…fields and turned out to be e ffi cient tools for the study of a wide variety of segregation-like phenomena [8], for instance, diblock copolymer [9], image inpainting [10, 11], tumor growth [12, 13], biology [14], two-phase flows [7, 15–18], moving contact line dynamics [19, 20], and so on.”