by which the liquid pulls at the plate and divides it by the perimeter of the
plate in a plane parallel to the liquid surface. A prerequisite is that the plate
is fully wetted by the (lower) liquid, since otherwise the interfacial force on
the plate does not act in the downward direction. To obtain the net force,
the weight of the plate has to be taken into account. The apparatus of
Figure 10.2a can be used to measure surface tension, i.e., the tension acting
at a surface between a liquid and air (or another gas), or interfacial tension,
i.e., the tension between two liquids. In the latter case, one has to correct for
the buoyancy of the plate caused by the upper liquid.
Over whatrangecan surface tension forces be sensed? Figure 10.3
shows a water drop hanging on a horizontal solid surface. For the sake of
simplicity, it is assumed that the drop is a half sphere and that its surface
thus meets the solid at a right angle. If such a drop is very large, it would fall
off, but a small drop can be kept suspended by surface tension. How large
can the radius of the drop be before it would fall off? At a level just below
the solid, the surface tensiongpulls the drop upwards. The total upward
force then equals circumference (2pR) timesg. The downwards force is given
by the volume of the half sphere ((2/3)pR^3 ) times mass density (r& 103
kg?m^3 ) times gravitational acceleration (g&9.8 m?s^2 ). According to
Table 10.1, water hasg¼0.072 N?m^1 , and we calculate for the maximum
possible radiusR¼0.0047 m. This then means that surface forces can affect
the shape of a system over several millimeters.
For amolecular explanationof surface tension, we refer to Chapter 3,
where it is stated that attractive forces act between all molecules, i.e., the van
der Waals forces; for some molecules, also other attractive forces act.
Consider a horizontal surface between a liquid, say oil, and air. Oil
molecules present in the surface sense the attractive forces due to the oil
molecules below, and hardly any attractive forces due to the air molecules
above, because there are so few air molecules per unit volume. This does not
mean that the molecules in the surface are subject to a net downward force,
since that would imply that these molecules immediately move downwards;
FIGURE10.3 Drop of surface tensionghanging on a horizontal solid surface.