ABSTRACT
For the measurement of advancing contact angle θA, the test plate is immersed inversely into a liquid bath, as shown in Fig. 24b. The critical depth of the test plate can be obtained in the same manner as for the receding contact angle, so we do not discuss the details here. The relationship between the critical depth at which instability occurs and θA can be calculated if we use (π−θA) instead of θR in Eq. (59) as
(61)
According to the same reason as for Eq. (60), the measurement of the advancing contact angle is limited to the following region:
(62)
Fig. 29 shows the relationship between θR or θA and calculated by Eqs. (50), (51), (53), and (54) for cylinder and by Eqs. (54) and (61) for plate. The calculated results are presented in the figures for several values of cylinder radius and inclinations and
As seen in the figures, each critical height or depth corresponds to one contact angle, which indicates the validity of the method. In Fig. 29a for a circular cylinder, each curve for various converges to one curve in the region of θR>90° or θA<90°. This is because the meniscus falls off the solid surface exactly at the bottom of the cylinder, as described by Fig. 26, and the critical height is not dependent on the cylinder radius. In Fig. 29a, we can see that the gradient of the theoretical curves becomes steep close to θR=0° and θA=180° for all cylinder radii. This is due to the fact that the gradient of the meniscus curve becomes nearly horizontal
at the attachment point for those contact angles. Hence the critical height varies only slightly with the change of contact angle, i.e., dH/dθR≈0. This might be evident if we calculate (dH/dθ) at θ=0° from Eq. (22), which determines the height of the meniscus attached to a horizontal plate. The above fact indicates an inaccuracy in the measurement around such contact angles. A similar tendency is observed in Fig. 29b for the plate used as the test solid. However, the accuracy can be improved if we use the test plate and support with large inclination in order to make the gradient of the meniscus curve steep at the attachment point. In fact, the theoretical curves of and have a gentle gradient near θR=0° and θA=180° compared with other curves, as shown in Fig. 29b. However, the region in which measure-ment is possible becomes more limited as
or increases, as described by Eq. (60) or Eq. (62). The vertical bar | in Fig. 29b shows the limit of measurement. It would be desirable to prepare some supports with different inclinations to measure various contact angles with sufficient accuracy.
