THERMAL FLUCTUATIONS OF A 3 PHASE CONTACT LINE .1. 2 FLUID PHASES AND ONE SOLID-PHASE

We describe a phenomenological model for the thermal fluctuations of the line of contact between two fluid phases and one solid phase. The line of contact between the three phases is constrained to lie along the solid surface, which is assumed to be smooth, flat, and horizontal with respect to gravity. In order to model the fluctuations of the contact line we must account not only for the fluctuations of the contact line itself, but also the corresponding fluctuations of the fluid-fluid interface. We develop a model for the energy of a superposition of sinusoidal fluctuations of all possible wavelengths. Our model for the fluctuation energy includes the effects of line tension, surface tension, and gravity. This fluctuation energy is then used in a modified capillary wave model based on the usual capillary wave model for a two-phase fluid interface to calculate the mean square magnitude of thermal fluctuations. We find that if the line tension is zero the rms fluctuation amplitude of the contact line is roughly proportional to the corresponding amplitude for a two-phase fluid interface, where the factor of proportionality is the reciprocal of the contact angle. Positive line tension significantly reduces the rms fluctuation amplitude near a second order wetting transition. If the line tension is negative, the fluctuation energy becomes negative for short wavelength fluctuations and small-theta, and our model breaks down. We discuss the implications of our results.