The shapes of liquid menisci near heterogeneous walls and the effect of line tension on contact angle hysteresis

Abstract

According to the classical theory of capillarity, which does not consider the influence of line tension, the wetting behaviour of solids is governed by the Young equation of capillarity and a unique contact angle. This approach assumes that the surface of the solid is ideal. Real solids, however, are both rough and chemically heterogeneous and these surface characteristics lead to non-uniform wetting. Non-uniform wetting of solids may be characterized in part by contact angle hysteresis or the difference in equilibrium contact angles which exists between adjacent heterogeneous patches on a solid. The presence of these patches, which vary in size, inhibits uniform spreading. In addition, the line of contact between the liquid and the solid may experience large contortions in the vicinity of the patch-patch boundary. Using these basic physical ideas, a strategy is proposed for using a stripwise, heterogeneous wall to evaluate numerically the effect of line tension upon the magnitude of the contact line contortions and the degree of contact angle hysteresis. The strategy uses a combination of incremental loading coupled with the Newton-Raphson method to generate a series of non-zero line tension solutions. One solution sequence begins from an initial analytical solution that corresponds to the zero line tension case while another solution sequence begins from the case of infinite line tension. These two sequences, which correspond to the outer and inner solutions of the modified Young equation of capillarity, i.e. modified to include a line tension term, are matched numerically to generate a complete contact line profile for different line tension values. The primary conclusion which results is that the critical patch size for the generation of contact angle hysteresis can be significantly larger than the dimension connected with the thickness of the liquid-vapour interface, of the order of one micron.