One of the biggest challenges when
trying to model granular material flow
is its ability to appear to pass through the regular phases
of matter very easily.
Those are solid, liquid, and gas.
For example, if you look at the top section of the hourglass,
you'll see that the grains are pretty much just sitting there.
Just about all the grains you're looking at
are not moving apparently at all.
And that kind of resembles what we
might think of as a solid, where the material is sort of locked
in place.
But closer to the bottom of the top section--
we're getting close to the nozzle--
you have to think that the grains are now
starting to flow.
And in fact as they pass through the nozzle,
they seem to be pouring much like we'd expect of a liquid.
Then they can move to the bottom compartment.
You'll see that when they land the grains form
something like a cone.
What this is telling us is that the material
can support its own weight a little bit differently
than a standard liquid can.
In fact, if you look at where the stream hits
the top of the cone, you might be
able to see that the grains are actually colliding and bouncing
around a lot, much like you'd expect in a gas.
So, lo and behold, in this one geometry
you're seeing what appears to be granular solid, liquid, and gas
coexisting at the same time.
Granular materials are extremely ubiquitous.
They're all over the place.
And especially in industry, where
they are second only to water as the most handled material type.
Food industry-- things like manipulating grains, corn,
through silos, conveyors, hoppers, chutes.
Pharmaceutical industry must deal with pills and powders
on a daily basis.
They lose millions of dollars in handling processes alone.
You also have to think that granular materials compose
simple geological materials like, of course, sand,
but also soil, dirt, gravel.
Help us answer questions like, how does a landslide start?
What's the flow like in a landslide?
It has been estimated that we waste about 40%
of the capacity of most industrial plants
due to inefficiencies in handling granular materials.
And because they are so common, they account for about 10%
of the energy consumed in the world.
So we hope that in understanding how grains flow,
we can start to optimize these processes better.
Because for the most part they've
been based on rules of thumb-- just empirical rules that
have been passed down.
Another important application would be applications
involving traction.
The Mars Rover, Spirit, was intermittently
stuck in the sand on a number of occasions for months at a time.
May 1, 2009 it got stuck in the sand for good.
It is currently still stuck in the sand up on Mars.
And it's interesting to think that such
an expensive and well-thought-out operation
could be foiled by sand, which is just so simple in our day
to day lives.
Existing continuum models for granular materials
are sort of shut off from the way
that we do continuum modeling of simpler materials like fluids
or linearly elastic solids, where the idea kind of goes
as follows.
I think of a granular flow by imagining that the entire flow
environment is split up into tiny little cubes for example.
And I try to figure out how the grains flow
by doing a bunch of experiments on a single cube.
When I'm done I then apply the rule
that I got from those experiments
to all the cubes in the patchwork
and let the material flow accordingly.
This type of modeling can take you pretty far,
but for granular materials you get--
you run into some pitfalls.
Unlike a fluid for example, where
the smallest parts of the flow is something
on the atomic scale, whereas the cup that you're
trying to predict the flow in is extremely big in comparison,
the grains themselves are small, but not all that small
compared to the geometry you're trying to flow them through.
For example, it's not uncommon to be
able to look at the whole flow geometry
and still make out the individual grains.
As a result, you don't get quite a clean breakdown
of this continuum argument like I just gave you.
And in fact, the size of the grains
start to have cascading effects.
And you can think of it like the properties of one deforming
cube are now influencing the other cube.
The recent work that we've done has
tried to factor the size of the grain itself
into the continuum law.
As a result, you can think of it like small little cubes,
or continuum elements, are now sort
of chattering with each other and influencing
each other's deformation.
And as a result, we were able to get much better results
with flow.