Contact angle hysteresis and the energy principle
DeFazio, Joseph Anthony
Dyson, D. C.
Doctor of Philosophy
Experimental evidence suggests that contact angle hysteresis is related, in some cases, to surface roughness or heterogeneity on a microscopic scale. This work investigates the effect of periodic roughness or heterogeneity on quasi-static motion of a liquid/vapor/solid contact line. We determine the static stable equilibrium configuration(s) of the liquid/vapor interface in a system by minimizing the sum of the Helmholtz free energy and gravitational potential energy (or the total energy) of the system. This is the energy principle. Our model presumes that both the surface of the solid and the liquid/vapor interface can be generated by drawing normals through a curve in a vertical plane. The solid is dipped into a liquid reservoir. A uniform gravitational field is present. The Young's Law contact angle varies along the curve in the vertical generating plane corresponding to the surface of the solid. Only a single contact line is allowed. This model is a much more general treatment of these problems than found in the literature. Application of the energy principle results in a family of possible liquid/vapor interfacial configurations. The capillary length of the liquid/vapor pair is the determining length scale of the model. If the wavelength of surface roughness or heterogeneity is much smaller than the capillary length, then hysteresis of the apparent contact angle occurs. (The apparent contact angle is measured as though the surface of the solid is a vertical plane.) The effect of relaxing the single contact line assumption is studied when the solid boundary surface is a sawtooth. Here, the general framework of the model breaks down. However, this case is treatable using a more specific theory. In certain cases, trapped droplets or bubbles are formed which are stable in a limited technical sense, and which suppress apparent contact angle hysteresis. Then the apparent contact angle may approach either 180$\sp\circ$ or 0$\sp\circ$ as the wavelength of the boundary surface approaches zero.