Interfacial tension of liquids from the height and contact angle of a single sessile drop

The height of a sessile drop of liquid when placed on a smooth solid surface increases as the drop volume increases, until it reaches a limiting value for a very large drop. The magnitude of the height and the contact angle depends on the different physical properties of the system. A large value for the contact angle is often associated with a large value for height and vice versa. From the data of measured limiting height, Z _Θ ^∞ and contact angle,Θ, the surface or interfacial tension,γ, can be estimated using the following equation: $$\gamma = \Delta \rho \cdot g \cdot (Z_\Theta ^\infty )^2 /2(1 - \cos (\Theta ))$$ whereΔ? is the density difference between the sessile drop and that of its surrounding medium,g is the gravitational force of acceleration. In this study, the magnitude ofγ of water for various systems is estimated. These values agree with the literature values. Furthermore, the values ofγ for various liquid₁/ solid/liquid₂ systems agree with data from other methods. Thus, the above equation is valid for different liquid-solid systems. It is further shown that very accurate measurements of contact angle,Θ, can be carried out for systems in which Z _Θ Δ _? andγ are known. The variation ofΘ with the height and volume of the sessile drop is analyzed for different systems.