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, lithe pressure is in the narrow range where the contact angle, 0, can exist, then for isothermal systems, adsorption at the solid-liquid interface affects gamma(SL) or theta, but gamma(SV) is very nearly equal gamma(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. Cc, is decreased as the cylinder diameter is increased; x(3)(L) is increased; and theta 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 theta 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 theta depends on both x(3)(L) and C-cl. If the value of theta 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 theta on C-cl. Adsorption at the solid-liquid interface gives a full explanation. (C) 2009 Elsevier B.V. All rights reserved.