Number 264, April 1, 1996 by Phillip F. Schewe and Ben Stein|
GRANULAR MATERIALS are all about us---sand, powders, nuts, sugar, and
coal. Nevertheless, they are unlike most other solid, liquid, and gaseous
states of matter. One reason for this is that temperature is unimportant.
Consider a pile of sand at rest. Applying heat to the sand has no effect
on the placement of the grains. The energy that really matters, the energy
it takes to lift one grain above another, is some 10**12 times larger than
the thermal energy of the system, kT (where k is Boltzmann's constant and
T is the temperature). Writing in the April issue of Physics Today, Heinrich
Jaeger, Sidney Nagel, and Robert Behringer draw out the implications of
this: "Temperature allows a system to explore phase space. The fact
that kT is negligible in a granular material precludes this. Unless perturbed
externally, each metastable configuration of the material will last indefinitely."
Consider sand contained in a tall cylinder. The pressure in the cylinder
does not increase indefinitely with depth, as it does in ordinary fluids.
Rather, the pressure does not exceed a certain maximum value because the
contact forces between grains and friction between grains and the walls
cause part of the weight of the overlying material to be imparted to the
walls. Another property which sets granular materials apart from other
fluids is the tendency (in a vibrated tank containing particles of differing
sizes) for the larger objects to float to the top regardless of their density.
Part of the reason for this is that the smaller particles fall into the
voids between the larger particles, making it difficult for the larger
ones to move downwards (especially along the walls) as part of a convective
flow. Aside from the technological importance of granular media in mixing,
sifting, mining, and erosion processes, the universe itself may exhibit
a sort of granular arrangement. One simulation of granular gases involving
a large sample of inelastically interacting hard disks resulted in the
"inelastic collapse" of the system into a foam of chainlike structures
roughly resembling the distribution of galaxies in the cosmos. The Physics
Today authors speculate that the role of gravity in shepherding galaxies
may be analogous to the role played by container walls in shaping granular
fluids into clusters. At the cosmological level, the "grains"
would be stars and galaxies. In another experiment, reported by Paul Umbanhowar
(Texas) at last month's APS meeting in St. Louis, the effects of air between
the grains and the interaction between the grains and the walls were minimized
by using a wide, shallow container. When the grain sample is vibrated,
numerous patterns form: stripes, hexagons, and baseball stitches. At a
layer thickness of exactly 17 particles, novel localized structures appear.
According to Umbanhowar, these "oscillons" are like ripples in
a pond but with an important difference; they do not spread out and they
can form bound states. (A lay language writeup on this subject can be found
at this Website: http://www.aps.org/mar96/vpr/Q5.02.html)
HOW MANY GRADUATING HIGH SCHOOL SENIORS TAKE PHYSICS? In 1987 the fraction
was 20%, while in 1993 it was 24%. During that period the number of high
school teachers with physics assignments rose about 1% per year. The total
number of students enrolled in physics in 1993 was 697,000. (From "High
School Physics in the 1990's," an AIP report; contact Michael Neuschatz