Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf

26 Hard problems with hard spheres
Could the electromagnetic properties of space be somehow akin to the mechanical
properties of sand Reynolds somehow convinced himself of this, asserting
the ‘ordinary electrical machine’ then in use as a generator ‘resembles in
all essential particulars the machines used by seedsmen for separating two kinds
of seed, trefoil and rye grass, which grow together (...)’.
So inspired was he by this notion that his last paper was entitled ‘The Submechanics
of the Universe’. But he hedged his bets by saying that his work also
offered ‘a new field for philosophical and mathematical research quite independent
of the ether’. Most of his readers probably agreed with J J Thomson that
this ‘was the most obscure of his writings, as at this time his mind was beginning
to fail’. Oliver Lodge diplomatically wrote that ‘Osborne Reynolds was a genius
whose ideas are not to be despised, and until we know more about the ether it is
just as well to bear this heroic speculation in mind’.
In his speech at the British Association Meeting (Aberdeen 1885) 7 Reynolds
explained that a granular material in a dense state must expand in order to flow or
deform
As the foot presses upon the sand when the falling tide leaves it firm,
that portion of it immediately surrounding the foot becomes momentarilydry(...).
Thepressure of the foot causes dilatation of the sand, and
so more water is (drawn) through the interstices of the surrounding sand
(...) leaving it dry....
Lord Kelvin spoke admiringly of this observation:
Of all the two hundred thousand million men, women, and children
who, from the beginning of the world, have ever walked on wet sand,
how many, prior to the British Association Meeting in Aberdeen in
1885, if asked, ‘Is the sand compressed under your foot’ would have
answered otherwise than ‘Yes’ 8
What Reynolds observed he called dilatancy, since the sand dilates. An
expansion is required to allow any deformation (typically the distance between
grains increases by about 1%).
In public lectures he dramatically demonstrated dilatancy (his ‘paradoxical
or anti-sponge property’) by filling a bag with sand and showing that if only just
enough water was added to fill the interstices, the sealed bag became rigid.
Reynolds was remembered thereafter for his contributions to the dynamics of
fluids (including the Reynolds number) but his work on granular materials enjoys
belated celebrity today. It has become a fashionable field of physics, one in which
fundamental explanations are sought for phenomena long known to engineers.
In one practical example, dry cement is stocked in large hoppers from which
it is dispensed at the bottom. Normally, the cement comes out with a constant
Reynolds O 1885 British Association Report Aberdeen p 897; 1885 On the dilatancy of media
composed of rigid particles in contact. With experimental illustrations Phil. Mag. 20 223.
Lord Kelvin 1904 Baltimore Lectures p 625.