FIG. 17 Energy curve for various cone heights shown in Fig. 12. The system does not have energy minimum and becomes unstable in the direction of retreat of meniscus when is larger than 0.492.

A similar result can be obtained for the axisymmetric meniscus attached to an upward cone, as shown in Fig. 18. The coordinate z is taken to be the downward direction, while the other variables are the same as in Fig. 12. indicates the depth of the cone vertex. The system energy, instead of ĒW, can be calculated in the same manner as for the

downward cone. Here we consider the advance of the three-phase contact line. If we take the dry surface as a

reference state, the nondimensional energy ĒW required for the the three-phase contact line to wet the surface to radius in the inward direction can be calculated as

As stated previously in the derivation of Eq. (42b), the constant term is omitted from the above equation for the purpose of simplicity:

(45)

The total energy of the system shown in Fig. 18 is obtained from the sum of Eqs. (40), (41), and (45). Fig. 19 shows the calculated results for the advancing contact angle θA=90° as an example. The system exhibits both maximum and minimum energies at θ=90° for smaller than a critical depth, similarly as shown in Fig. 17. When is larger than 0.590, the energy has no extreme value and increases monotonically with as shown by Fig. 19b. Hence the liquid spreads and wets the entire surface of the upward cone. We can obtain the critical depth for each advancing contact angle. It is possible to measure θA by the same method as for the receding contact angle if we reverse the cone surface.