Capillary Rise

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Capillary Rise
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2D/Zero Contact Angle

• Y-L

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Quantitative Capillary Rise

• In our 2-D case, there is only one radius of
  curvature

122 lu
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Gravity and Bond Number
No Gravity
Gravity
2x Gravity

• Gravitational/capillary forces
• g gravitational acceleration
• r characteristic pore radius
• Dr difference in fluid densities
• g interfacial tension between fluids

Surface tension
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Exercise

• The water-water vapor interfacial tension is
  72.13 x 10-3 N m-1 at 25C. Compute the capillary
  rise in a clean glass slit of radius 0.001 m in
  the Earths gravitational field. We choose a slit
  to reduce the problem to a 2 dimensional one, in
  which there is only one possible radius of
  curvature. Assume the contact angle is zero. Show
  all units.
• Compute the Bond number for the capillary rise
  problem above.

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Exercise continued

• Propose and run a lattice Boltzmann model
  illustrating capillary rise at the same Bond
  number. Remember that r should be at least 5 or
  so lattice units and that the pool of liquid
  that the capillary will be immersed into should
  be wide enough that a pool height unaffected by
  capillary rise can serve as a reference level for
  measuring the liquid rise in your capillary. What
  is the expected capillary rise in your model?
  Show all calculations and units.
• Remember to use a surface adhesion parameter that
  corresponds closely to a zero contact angle too
  big or too small may cause problems. You may be
  able to estimate an appropriate value from the
  previous exercise where you simulated different
  contact angles (some refinement of this may also
  be needed).
• Provided you use the standard parameters Y0
  4, r0 200, and G -5, the lattice Boltzmann
  liquid-vapor interfacial tension is 13.85 lu mu
  ts-2.
• Plot the steady-state result of your model. What
  is the observed capillary rise? Compare the ratio
  h/r for the case on Earth, the predicted LB case,
  and the simulated case.