Adsorption at the solid-liquid interface as the source of contact angle dependence on the curvature of the three-phase line.

We review the thermodynamic approach to determining the surface tension of solid-fluid interfaces. If the pressure is in the narrow range where the contact angle, θ, can exist, then for isothermal systems, adsorption at the solid-liquid interface affects γ(SL) or θ, but γ(SV) is very nearly equal γ(LV), the surface tension of the adsorbing fluid. For a liquid partially filling a cylinder, the pressure in the liquid phase at the three-phase line, x(3)(L), depends on the curvature of the three-phase line, C(cl), but the line tension can play no role, since it acts perpendicular to the cylinder wall. C(cl) is decreased as the cylinder diameter is increased; x(3)(L) is increased; and θ increases. For a given value of C(cl), x(3)(L) can be changed by rotating the cylinder or by changing the height of the three-phase line in a gravitational field. In all cases, for water in borosilicate glass cylinders, the value of θ is shown to increase as x(3)(L) is increased. This behaviour requires the Gibbsian adsorption at the solid-liquid interface to be negative, indicating the liquid concentration in the interphase is less than that in the bulk liquid. For sessile droplets, the value of θ depends on both x(3)(L) and C(cl). If the value of θ for spherical sessile droplets is measured as a function of C(cl), the adsorption at the solid-liquid interface that would give that dependence can be determined. It is unnecessary to introduce the line tension hypothesis to explain the dependence of θ on C(cl). Adsorption at the solid-liquid interface gives a full explanation.