several sweets. The contact angle will then vary with place. Even if
the solid is made up of one chemical substance, the surface may be
inhomogeneous: the various faces of a crystal generally differ in
surface tension, and various faces may be present at the surface.
This will generally be the case at a solid fat surface.
The water added maydissolve some of the substances, for instance the
sugar crystals at the surface of a chocolate or a biscuit.
The surface may be rough(uneven) at a scale clearly larger than
molecular sizes. The contact angle with respect to the average plane
through the surface may then be very different at various places,
even if the true contact angle is the same. This is illustrated in Figure
10.26a. It should be understood that the figure depicts a two-
dimensional situation, whereas in three dimensions the relations are
far more intricate.These phenomena give rise to contact angle hysteresis, which is
illustrated in Figure 10.26b. If a drop of water is applied to a solid and the
contact angle is acute (0<y< 908 ), the water tends to spread over the
surface. In other words, the contact line advances over the solid. If water is
removed from the drop, for instance by means of a small syringe, the
contact line will recede. On a sloping surface, a drop will often slide
downwards, exhibiting an advancing and a receding edge. It is invariably
observed that theadvancingcontact angle is larger than therecedingone.
The hysteresis is generally between 1 and 60 8 ; 10–20 8 C is quite common. The
cause must be found in the three complications just mentioned. A
satisfactory quantitative theory has not been developed. By adding
FIGURE10.26 Contact angles of aqueous solutions (W) on solid surfaces (S) in air
(A). (a) Effect of surface roughness. Contact angles given with respect to the true
solid surface (inner ones) and to the apparent or average surface (depicted by —?—
?—?—?). (b) Illustration of the difference between an advancing and a receding
contact angle.