The effect of surface heterogeneity on the drop size dependence of contact angles

Abstract

Different patterns of drop size dependence of contact angles have been observed experimentally. Some investigators reported a decrease of contact angle with an increase in drop size, while others reported an increase. Still others reported that there is no drop size dependence of contact angles. These phenomena can be explained by positive line tension effect, “negative line tension” effect, and negligible line tension effect, respectively. In addition, some researchers observed significant fluctuations of their contact angle data. The existence of the “negative line tension” and negligible line tension effects and the fluctuation of contact angles may be caused by surface heterogeneity. Two heterogeneous solid models, models 1 and 2, are developed in this paper. Model 1 demonstrates, by using a concentric ring model, that the fluctuations of the contact angle data are due to surface heterogeneity. Model 2 illustrates, by using a patchwise heterogeneous model, that all three patterns of contact angle-drop size relation can be produced with different degrees of surface heterogeneity. The different patterns of drop size dependence of contact angles, therefore, may be caused at least by surface heterogeneity.