Effect of gravity on contact angle: A theoretical investigation

Using the Gibbs description of an interphase, the necessary conditions for equilibrium of a closed, two-phase fluid system in the presence of gravity are the Laplace and Young equations and a condition on the chemical potentials. The last condition has been neglected in all previous examinations of contact angles in a gravitational field. After introducing explicit expressions for the chemical potentials, we find that the condition on the chemical potentials can be used to determine the pressure profile within the system. In a “two-interface” system in which a liquid phase is both above and below a vapor phase and the vapor phase forms a solid–vapor interphase in one region, the pressure profile in the liquid phases is the same as it would have been if the vapor phase were not there; thus in a gravitational field, the pressure is smaller in the liquid phase above the vapor phase than it is in the liquid phase below the vapor phase. This results in the contact angle at the upper three-phase line necessarily being smaller than that at the lower three-phase line. This difference in contact angles is conventionally referred to as contact angle hysteresis; however, we show that it is simply an equilibrium property of a capillary system in a gravitational field. The contact angle difference predicted to exist in the presence of gravity does not violate the Young equation, but the Young equation does impose a restriction on the equilibrium adsorption isotherms at the solid–vapor and solid–liquid interfaces.