Giving Statistical Mechanics The Shakes: Analogies Between Ideal Gases and Granular Systems

Justin Mitchell, Aaron Coyner, Matthew Olson, Rebecca Ragar, Jeffery Wagner, Adrienne McVey, Justin Eskridge, Erin Lewallen, Ian Zedalis, Shawn Jackson, Michael Wilson*

The University of Tulsa*Currently at National Research Council

Granular Systems?

We know systems of 1023 or 2 particles. This neglects dunes, avalanches and

other systems. Granular systems involve dust, sand,

powder, and grains. We investigate statistics of driven

systems.

Inelastic Collapse

Each inelastic collision will remove energy.

Many collisions will cause system to collapse.

Energy in and out will define our granular phase.

Project Description Goals

Look for definitive inelastic collapse of a 3-d granular system in zero gravity.

Determine parameters necessary for a granular gas, the precursor to collapse.

* É. Falcon et al. , Phys. Rev. Lett. 80. 440 (1999).

Methods Preliminary testing

on NASA KC-135A low gravity aircraft

Future flight on Space Shuttle

Testing on sounding rocket*

Why Investigate Granular Gases?

Large granular systems, such as planets, are not well understood.

Asteroids, planetary rings, etc. are not fully explained by gravity because sizes are too small for gravity to act alone.

Inelastic collapse models provide plausible method for formation of these smaller objects.

Small scale granular gas studies allow for lab testing of the models on reasonable time scales.

Experimental Description Box set: 8 sapphire

walled cubes, 1 in3 each.

Box set mechanically shaken sinusoidally along body diagonal.

Each cube has one free wall attached to a piezoelectric sensor.

Video cameras view 3 orthogonal box set faces.

Box Set as Flown on KC-135A

System Acceleration

Shaking direction is perpendicular to mean effective gravity.

In “microgravity” the residual acceleration is ~0.03 gearth.

Residual acceleration is usually pointed up.

shaking

gearth

Residual acceleration

Granular Phases

SolidGrains pack in one corner

FluidGrains slosh around box walls

Gas~uniform distribution of kinetic grains

gresidual

Phase Diagram

0 10 20 30 40 50G

gasfluidsolid

G=A2/gresidual

G is the ratio of wall acceleration to gresidual

G diverges as gresidual goes to zero.

o Wall acceleration, density and gresidual define the phase.

Recent Work

Second KC-135 flight Free floating experiment.

No system accelerations until bumped.Lower shaking accelerations.

Further testing before shuttle flight.

Clustering Into Lattice

Lattice Random

Conclusion

Clusters are stable and keep a lattice. Clusters only exist in slow shaking

(~4Hz). Gases form for all shaking parameters. Only solid for non-shaking system. Partial proof of concept. Experiment is ready for a shuttle flight.