Thermal fluctuations of a three phase contact line. II. Three fluid phases

Abstract

We describe a phenomenological model for the thermal fluctuations of a three-phase contact line in the case of three fluid phases. The model is an extension of an earlier model for the case of two fluids and one solid. In the previous model only one interface was allowed to fluctuate, and the contact line was constrained to move along the solid surface. In the present case all three two-phase interfaces can fluctuate, and the contact line can move in any direction. Our model includes the effects of line tension, the three surface tensions, and gravity. We investigate the behavior of the fluctuations in the limit of a wetting transition. Since the line tension appears to diverge in the limit of a first order transition, and vanishes in the limit of a second order transition, we consider each of these cases separately. We obtain the mean square fluctuation magnitude analytically if the line tension is identically zero. If the line tension is positive we obtain an integral expression for the mean square fluctuation magnitude, and derive modified exponents for the fluctuation magnitude as a function of contact angle near both a first and second order wetting transition. Our model breaks down if the line tension is negative, just as in the earlier model.