Kitchen physics continued

Some further observations, and hints for readers who wish to try this at home
(or in the classroom).

I was, as you could probably tell, flushed with the success of making
cross-bedding in the comfort of my own kitchen, and eagerly awaiting the arrival
of colourful granular materials from the aquarium supplies place. I had, much to
my wife’s appreciation (and, indeed, mine, since, much as I like sand, grains in
your dinner are a step too far), removed my lab from the kitchen. The
substantial box of supplies was delivered and I set up to enthusiastically
scatter granular materials around a different room in our apartment. Not being
familiar with aquarium interior design and therefore not knowing quite what to
expect, I had ordered quite a variety of materials, both in terms of colour and
grain character; furthermore, I had happened upon a “buy one, get one free”
offer and so was surrounded by a rainbow of pots of grits. The variety and
volume available turned out to be a good thing.

Given that a simple mixture of sugar and play sand had immediately produced
such dramatic results, I had blithely assumed that, with a little thought as to
mixtures of grain size and angularity (with appropriately different angles of
repose), I would easily generate even more dramatic structures, the colour
variations picking out in fine detail the segregation and stratification in a
visually satisfying way. But this was not to be. Given even my qualitative
understanding of the unpredictability and fickleness of granular materials, I
should have anticipated that it would not be that simple to induce them to
cooperate. My first couple of mixtures essentially produced no internal
structure at all, and then I succeeded in producing segregation, but not
*stratification.*By this I mean that different families of grains would
spontaneously separate, with smaller grains at the top of the pile, larger ones
towards the base, as in the image at the top of this post; this was an
interesting demonstration but hardly what I was looking for.

I then had a brilliant idea: I would actually re-read the original paper by
Makse and his colleagues (available here);
this proved - surprise, surprise - to be be extremely informative. To begin
with, they used a combination of two grain types, initially white glass beads
(repose angle 26 degrees) and sugar crystals (roughly cubic and with an angle of
repose of 39 degrees); this produced spontaneous segregation andstratification. They then used a mixture of fine and coarse sand and
achieved the same result (indicating that grain density was not a critical
factor). They wrote:

In all the above experiments we used mixtures composed of two types of grain
with different shape, and therefore with different angles of repose. In
particular we obtain stratification (plus segregation) when we use larger cubic
grains and smaller spherical grains: the angle of repose of the large species is
then larger than the angle of repose of the small species. Otherwise we obtain
only segregation and not stratification when the large grains are less faceted
than the small grains, i.e., the large grains have smaller angle of repose than
the small grains.

They continued with further experimental variables and concluded:

These results suggest that the phenomenon of segregation is always expected
when pouring a granular mixture of grains of different sizes, no matter the
values of the angles of repose of the species. However, the phenomenon
of stratification is only expected when the large species have larger angle of
repose than the small species. Additionally, we performed a series of
experiments in which we find similar stratification by using different mixtures
of differing size ratio between large and small grains (1.66, 2.1, 2.25, 3.25,
and 6.66), suggesting that the phenomenon occurs for a broad regime of grain
size ratios. We find a similar stratification when we double the gap between the
vertical plates of the cell and simultaneously double the flow rate of
grains.

They then moved on to mixtures of three grain types (a close-up of this
stratification is shown at right):

The experiment results in stratification with three layers, with the finest
grains on the bottommost of each triplet of layers and the coarsest grains on
the topmost layer … Experiments using a continuum size distribution are
ongoing, since geological rock formations (which also display stratification)
generally occur in the presence of a continuum distribution of grain
size.

I was relieved that density was not a major factor (since, until I have a
look with a microscope, I have no idea exactly what my aquarium decor is made
of); I also followed their advice of cleaning the perspex with an anti-static
cleaner - electrostatic effects between the grains can be important (indeed, it
would seem to be influential in natural movement of sand by saltation, a
phenomenon known as triboelectrification - perhaps more on that another
time). I then repaired to, yes, the kitchen, and, on a series of plates, poured
out a selection of my materials into heaps to determine grain size versus angle
of repose. Selecting a coarse, black, angular, material (strictly more of a
gravel than sand) with a steep angle of repose and fine, golden, semi-rounded
grains (gloriously titled “imperial yellow”) that formed a distinctly more
gently sloping pile. I mixed up these materials, fully expecting to produce a
sort of dramatic bumblebee effect - but they refused to cooperate, segregating
somewhat but not really stratifying. As a result of this and my previous
experiments, I was now surrounded by pots, tupperware etc., stolen from the
kitchen and containing a wide variety of colourful, but non-performing mixtures.
I added some fine, almost spherical “diamonique green” and tried again: hints of
stratification. Becoming more desperate and, as if it were possible, less
analytical, and having great faith in natural sand, I then mixed in a large
proportion of the play sand (still, I believe, with some sugar) and poured. The
result was dramatic and not unlike the illustrations in Makse’s paper:

Both segregation and stratification appeared, and each stratified layer was
clearly beginning to show sorting by grain size:

So, what is it about natural sand that seems to make it self-stratify more
spontaneously than the artificial materials? Clearly, my “kitchen physics” is
not conducted under strict laboratory conditions, I have not quantitatively
evaluated the grain size, sorting, and shapes of my materials, and I have not
rigorously recorded the many permutations and combinations now occupying the
small army of tupperware containers on the floor; I am, in short, overwhelmed by
my variables. But here are my amateur conclusions:

1. Using an anti-static cleaner is probably important.
2. Artificially coloured materials are valuable in offering a range of grain
   types and in highlighting internal structure of the pile.
3. Natural sand is probably a key ingredient in most easily producing
   stratification.
4. Adding sugar is, pragmatically, likely to produce results.
5. Varying the rate of pouring produces different outcomes.

I shall continue (it is, after all, an excuse to play), but if anyone has
recommendations and further experiences to contribute, I would be delighted to
hear them. SIGNATURE

Originally published at: https://throughthesandglass.typepad.com/through_the_sandglass/2009/04/kitchen-physics-continued.html