# Angle of Contact

The surface of liquid near the plane of contact, with another medium is in general curved. The angle between tangent to the liquid surface at the point of contact and solid surface inside the liquid is termed as angle of contact. It is denoted by θ. It is different at interfaces of different pairs of liquids and solids. The value of θ determines whether a liquid will spread on the surface of a solid or it will form droplets on it. For example, water forms droplets on lotus leaf as shown in Fig. 1 while spreads over a clean plastic plate as shown in Fig. 2.

Fig. 1: Different shapes of water drops with interfacial tensions on a lotus leaf.

Fig. 2: Different shapes of water drops with interfacial tensions on a clean plastic plate.

We consider the three interfacial tensions at all the three interfaces, liquid-air, solid-air and solid-liquid denoted by Sla, Ssa and Ssl , respectively as given in Fig. 1 and 2. At the line of contact, the surface forces between the three media must be in equilibrium. From the Fig. 2 the following relation is easily derived.

$S_{la}$ cos θ + $S_{sl}$ = $S_{sa}$            (1)

The angle of contact is an obtuse angle if $S_{sl}$ > $S_{la}$ as in the case of water-leaf interface while it is an acute angle if $S_{sl}$ < $S_{la}$ as in the case of water-plastic interface. When θ is an obtuse angle then molecules of liquids are attracted strongly to themselves and weakly to those of solid, it costs a lot of energy to create a liquid-solid surface, and liquid then does not wet the solid. This is what happens with water on a waxy or oily surface, and with mercury on any surface. On the other hand, if the molecules of the liquid are strongly attracted to those of the solid, this will reduce Ssl and therefore, cos θ may increase or θ may decrease. In this case θ is an acute angle. This is what happens for water on glass or on plastic and for kerosene oil on virtually anything (it just spreads). Soaps, detergents and dying substances are wetting agents. When they are added the angle of contact becomes small so that these may penetrate well and become effective. Water proofing agents on the other hand are added to create a large angle of contact between the water and fibres.