MCL - Molecular hydrodynamics of the moving contact line...

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Molecular hydrodynamics of the moving contact line in collaboration with Ping Sheng ( Physics Dept, HKUST ) Xiao-Ping Wang ( Mathematics Dept, HKUST ) Tiezheng Qian Mathematics Department Hong Kong University of Science and Technology Physics Department, Zhejiang University, Dec 18, 2007
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The borders between great empires are often populated by the most interesting ethnic groups. Similarly, the interfaces between two forms of bulk matter are responsible for some of the most unexpected actions. ----- P.G. de Gennes, Nobel Laureate in Physics , in his 1994 Dirac Memorial Lecture: Soft Interfaces
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The no-slip boundary condition and the moving contact line problem The generalized Navier boundary condition (GNBC) from molecular dynamics (MD) simulations Implementation of the new slip boundary condition in a continuum hydrodynamic model (phase-field formulation) Comparison of continuum and MD results A variational derivation of the continuum model, for both the bulk equations and the boundary conditions, from Onsager’s principle of least energy dissipation
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No-Slip Boundary Condition , A Paradigm 0 = slip v τ 0 = slip v ? n
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James Clerk Maxwell Many of the great names in mathematics and physics have expressed an opinion on the subject, including Bernoulli, Euler, Coulomb, Navier, Helmholtz, Poisson, Poiseuille, Stokes, Couette, Maxwell, Prandtl, and Taylor. Claude-Louis Navier
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from Navier Boundary Condition to No-Slip Boundary Condition : slip length , from nano- to micrometer Practically, no slip in macroscopic flows γ τ = s slip l v 0 / / R l U v s slip : shear rate at solid surface s l R U / (1823)
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Partial wetting Complete wetting Static wetting phenomena Plant leaves after the rain
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What happens near the moving contact line had been an unsolved problems for decades. Moving Contact Line Dynamics of wetting
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1 2 cos γ θ = + s Young’s equation:
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Thomas Young (1773-1829) was an English polymath , contributing to the scientific understanding of vision, light, solid mechanics, physiology, and Egyptology . Manifestation of the contact angle: From partial wetting (droplet) to complete wetting (film)
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s d θ θ≠ velocity discontinuity and diverging stress at the MCL  → 0 a R a dx x U η
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No-Slip Boundary Condition ? 1.
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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MCL - Molecular hydrodynamics of the moving contact line...

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