Shape of a drop on a vertical fiber

Abstract

The differential equations governing the shape of a drop on a vertical fiber in the presence of gravity have been numerically integrated to yield the dimensionless drop length L = lc 1 2 [where c = ( π h - π l) g/ σ], equatorial radius, R e = r e c 1 2 , interfacial area, A = ac, and volume, V = vc 3 2 , in terms of the upper and lower contact angles, θ r or θ b, for a given dimensionless fiber radius, R f = r f c 1 2 . The results enable θ f and θ b to be obtained from known values of N = R e R f and L = L R f . The ratios R e R f = r e r f and L/ R f = l/ r f may be readily obtained from measured values. The contact angles obtained for given values of N and L are significantly different from the values determined by B. J. Carroll [ J. Colloid Interface Sci. 57, 488 (1986)] and J. I. Yamaki and Y. Katayama [ J. Appl. Polym. Sci. 19, 2897 (1975)] and the absence of gravity, particularly when N is large, the discrepancy increasing with R f.