Hydrodynamic Slip Boundary Condition for the Moving Contact Line

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Hydrodynamic Slip Boundary Condition for the
Moving Contact Line

• in collaboration with
• Xiao-Ping Wang (Mathematics Dept, HKUST)
• Ping Sheng (Physics Dept, HKUST)

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?
No-Slip Boundary Condition
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from Navier Boundary Conditionto No-Slip
Boundary Condition
shear rate at solid surface

• slip length, from nano- to micrometer
• Practically, no slip in macroscopic flows

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No-Slip Boundary Condition ?

• Apparent Violation seen from
• the moving/slipping contact line
• Infinite Energy Dissipation
• (unphysical singularity)

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Previous Ad-hoc models No-slip B.C. breaks down

• Nature of the true B.C. ?
  (microscopic slipping mechanism)
• If slip occurs within a length scale S in the
  vicinity of the contact line, then what is the
  magnitude of S ?

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Molecular dynamics simulationsfor two-phase
Couette flow

• Fluid-fluid molecular interactions
• Wall-fluid molecular interactions
• Densities (liquid)
• Solid wall structure (fcc)
• Temperature
• System size
• Speed of the moving walls

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Modified Lennard-Jones Potentials
for like molecules
for molecules of different species
for wetting property of the fluid
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boundary layer
tangential momentum transport
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The Generalized Navier B. C.
when the BL thickness shrinks down to 0
viscous part
non-viscous part Origin?
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uncompensated Young stress
nonviscous part
viscous part
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Uncompensated Young Stressmissed in Navier B. C.

• Net force due to hydrodynamic deviation from
  static force balance (Youngs equation)
• NBC NOT capable of describing the motion of
  contact line
• Away from the CL, the GNBC implies NBC for single
  phase flows.

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Continuum Hydrodynamic ModelingComponents

• Cahn-Hilliard free energy functional retains the
  integrity of the interface (Ginzburg-Landau type)
• Convection-diffusion equation (conserved
  order parameter)
• Navier - Stokes equation (momentum
  transport)
• Generalized Navier Boudary Condition

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molecular positions projected onto the xz plane
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near-total slip at moving CL
Symmetric Coutte V0.25 H13.6
no slip
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profiles at different z levels

symmetric Coutte V0.25 H13.6
asymmetricCoutte V0.20 H13.6
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asymmetric Poiseuille gext0.05 H13.6
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The boundary conditions and the parameter values
are bothlocal properties, applicable to flows
with different macroscopic/external conditions
(wall speed, system size, flow type).
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Summary

• A need of the correct B.C. for moving CL.
• MD simulations for the deduction of BC.
• Local, continuum hydrodynamics formulated from
  Cahn-Hilliard free energy, GNBC, plus general
  considerations.
• Material constants determined (measured) from
  MD.
• Comparisons between MD and continuum results show
  the validity of GNBC.