Influence of inhomogeneous substrate curvature on line tension

Abstract

Line tension accompanying equilibrium liquidlike films adsorbed at cylinder-shaped substrates equipped with chemical heterogeneities is studied within an effective interfacial Hamiltonian approach. The heterogeneity has the form of a stripe of width 2L. The leading corrections to the line tension coefficient due to nonzero substrate curvature R(-1) are derived. Their character is shown to be sensitively dependent on the system's temperature regime. For temperatures low enough that both the homogeneous components of the heterogeneous substrate remain nonwetted, the leading curvature correction is found to be proportional to R(-1). For temperatures such that one of the solid surface components is wetted by the fluid, one obtains corrections to the line tension of the order of either (L/R) ln R or R(-1/2) depending on the relative values of R and the heterogeneity width 2L . For temperatures exceeding wetting temperatures of both the substrate components, the line tension is shown to decay to 0 in the limit R --> infinity according to the power law eta approximately R(-1/2).