Physics for Geologists, Second edition

1 14 Fluids and fluid flow
Figure 12.3 The contact angle 9.
fluids (water being wetting on most materials and we then refer to them as
being water-wet). We are mostly concerned with wetting fluids.
Returning to the capillary aspects of water in tubes, the water rises in the
tube until the upward component of capillary force is equal to the weight of
the elevated fluid:
and
pgh,n? = o2nr cos cp
h, = (g ) cos cp,
where o is the surface tension [MT-2], y the weight density, r the radius of
the capillary tube, and cp is the contact angle (Figure 12.3) (cos cp 1 for
water on quartz).
If you fill a pipe with sand and stand it in a pan of water, water rises in
the sand above the level in the pan, just as it did in the capillary tubes. It
is essential for proper understanding to realize that this water in the sand is
immobile. If it were not, we could drill a hole in the side of the pipe, let the
water flow out and do work as it falls, and so have perpetual motion. This
point was made by Pierre Perrault in 1674, and is just as true today.
If you put a measured quantity of water into a beaker, then put glass
beads in up to the water level and hold them with a filter gauze, you will find
that you cannot drain the same quantity of water from the beaker. Some is
retained, and you can see it around the points of contact between the beads.
This is called pendular water, and it is in pendular rings (Figure 12.4). It
is also the wetting phase. Clearly this water is immobile, not in hydraulic
continuity, or it would not be there; and we presume that it is at a pressure
rather less than that of the air in the pore space (because of the shape of
the interface). It is held there by interfacial tension, and it would require
energy to remove it - more energy than that required for the removal of the
Copyright 2002 by Richard E. Chapman