1. Capillary Rise

2. 2D/Zero Contact Angle
Y-L:

3. Quantitative Capillary Rise
In our 2-D case, there is only one radius of curvature
122 lu

4. 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

5. Exercise
The water-water vapor interfacial tension is x 10-3 N m-1 at 25C. Compute the capillary rise in a clean glass slit of radius m in the Earth’s 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.

6. 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 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.