Effect of corrugations of the three-phase line on the drop size dependence of contact angles

Abstract

Conflicting observations of the drop size dependence of contact angles have been reported in literature: while some investigators reported an increase of contact angle with an increase in drop size, others reported a decrease. The former was discussed in terms of negative line tension, and the latter was considered as an effect of positive line tension. While some investigators accept the possibility of positive as well as negative line tension, the present authors suspect that line tension, at least for solid—liquid—fluid systems, is positive. In the present paper, by developing a model to calculate the mean contact angle of a sessile drop with a corrugated three-phase line, we show that the observed increase of contact angles with the increase in drop size does not necessarily imply a negative line tension; it may well be a consequence of the corrugations of the three-phase line caused by heterogeneity of the solid surface.