Angle of contact

When the free surface of a liquid meets a solid surface, the liquid surface becomes CURVED right at the point of contact, and the angle at which it meets the solid becomes an important physical quantity. The ANGLE OF CONTACT $\theta$ between a given solid and liquid is defined as the angle, measured INSIDE the liquid, between the tangent to the liquid's surface at the point of contact and the solid surface. Its value differs for different solid-liquid pairs, and it is precisely this angle that decides whether a given liquid will spread out over a chosen solid surface or instead bead up into droplets on it. Consider three interfaces meeting at a single point of contact O: the solid-air interface, with surface tension $T_{sa}$; the solid-liquid interface, with surface tension $T_{sl}$; and the liquid-air interface, with surface tension $T_{la}$. Since the liquid is in stable equilibrium at O, these three surface-tension forces must themselves be in equilibrium, giving $T_{sa}=T_{sl}+T_{la}\cos\theta$, i.e. $\cos\theta=\dfrac{T_{sa}-T_{sl}}{T_{la}}$. Three cases follow directly. (i) If $T_{sa}>T_{sl}$ (so $T_{sa}-T_{sl}>0$), as at a water-plastic interface, $\cos\theta$ is positive and the contact angle $\theta$ is ACUTE (less than 90 degrees) -- the liquid tends to wet and spread over the solid. (ii) If $T_{sa}<T_{sl}$ (so $T_{sa}-T_{sl}<0$), as at a water-leaf interface, $\cos\theta$ is negative and the contact angle is OBTUSE (greater than 90 degrees) -- the liquid tends to bead up rather than spread. (iii) If $T_{sa}>T_{sl}+T_{la}$, no equilibrium value of theta exists at all, and the liquid spreads completely and indefinitely over the solid surface. This concept has direct practical applications: soaps and detergents are wetting agents that work by minimizing the ang …