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Gaslab_Two_Color_Gas

by David Bowen (Submitted: 05/01/2007)

[screen shot]

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WHAT IS IT?

This model is one in a series of GasLab models. They use the same basic rules for simulating the behavior of gases. Each model integrates different features in order to highlight different aspects of gas behavior.

The basic principle of the models is that gas particles are assumed to have two elementary actions: they move and they collide - either with other particles or with any other objects such as walls.

This model has two gases, one with orange particles and the other with yellow, that are otherwise identical. The particles are moving and colliding with each other and with the container walls, but with no gravitational effects.. In this model, particles are modeled as perfectly elastic ones with no energy except their kinetic energy -- which is due to their motion. Collisions between particles are elastic. The pressure on the left or red container wall is calculated as the change in momentum of the particles colliding with it.

HOW IT WORKS

The basic principle of all GasLab models is the following algorithm (for more details, see the model "GasLab Gas in a Box"):

1) A particle moves in a straight line without changing its speed, unless it collides with another particle or bounces off the wall.
2) Two particles "collide" if they find themselves on the same patch (NetLogo's View is composed of a grid of small squares called patches). In this model, two particles are aimed so that they will collide at the origin.
3) An angle of collision for the particles is chosen, as if they were two solid balls that hit, and this angle describes the direction of the line connecting their centers.
4) The particles exchange momentum and energy only along this line, conforming to the conservation of momentum and energy for elastic collisions.
5) Each particle is assigned its new speed, heading and energy.

HOW TO USE IT

Initial settings:
- NUMBER-OF-PARTICLES: the number of gas particles.
- TRACE?: Draws the path of one individual particle.
- COLLIDE?: Turns collisions between particles on and off.
- INIT-PARTICLE-SPEED: the initial speed of each particle -- they all start with the same speed.
- ORANGE-STATIONARY?: If this is set to "Off," then the orange particles are initialized with the same speed as the yellow ones, to INIT-PARTICLE-SPEED. If this is set to "On," then the orange particles are initially stationary (not moving). The orange particles are only put into motion through collisions with the yellow particles.
- PARTICLE-MASS: the mass of each particle -- they all have the same mass.

As in most NetLogo models, the first step is to press SETUP. It puts in the initial conditions you have set with the sliders. Be sure to wait till the SETUP button stops before pushing GO.
The GO button runs the models again and again. This is a "forever" button.

Monitors:
- PERCENT FAST, PERCENT MEDIUM, PERCENT SLOW monitors: percent of particles with different speeds: fast (red), medium (green), and slow (blue).
- AVERAGE SPEED: average speed of the particles.
- AVERAGE ENERGY: average kinetic energy of the particles.
- % THAT ARE ORANGE: This does not change, but is not 50% because particles are colored orange or yellow based on their initial position, which varies statistically.
- % ON LEFT THAT ARE ORANGE: For the particles on the left hand of the box, what percent are orange.

Plots:
- SPEED COUNTS: plots the number of particles in each range of speed (fast, medium or slow).
- SPEED HISTOGRAM: speed distribution of all the particles, plotted separately for each color (orange / yellow). The displayed values for speed are ten times the actual values.
- ENERGY HISTOGRAM: the distribution of energies of all the particles, plotted separately for each color (orange / yellow).
- PRESSURE ON THE RED WALL: The average of the momentum change of particles colliding with the left or red wall, per unit wall length, over the last three clock ticks.

Initially, all the particles have the same speed but random directions. Therefore the first histogram plots of speed and energy should show only one column each. As the particles repeatedly collide, they exchange energy and head off in new directions, and the speeds are dispersed -- some particles get faster, some get slower, and the plot will show that change.

THINGS TO NOTICE

While all of the orange particles are initially on the left, and yellow on the right, the colors diffuse until they are evenly distributed. Initially, 100% of the particles on the left are orange, but this declines quickly to about the percent of all particles that are orange.

If ORANGE_STIONARY? is clicked to "On," how long does it take for the speed and energy distributions for the two colors to equalize? Compared to the initial speed, what speed to both colors come to?

What is happening to the numbers of particles of different speeds? Why are there more slow particles than fast ones?

Why does the average speed (avg-speed) drop? Does this violate conservation of energy?

Watch the particle whose path is traced in the drawing. Does the trace resemble Brownian motion? Can you recognize when a collision happens? What factors affect the frequency of collisions? What about the "angularity" of the path? Could you get it to stay "local" or travel all over the world?

In what ways is this model an "idealization" of the real world?

THINGS TO TRY

Both the fluctuations in the percent of the particles on the left that are orange and the fluctuations in pressure get larger for a lower number of particles. These are statistical effects.

Set all the particles in part of the world, or with the same heading -- what happens? Does this correspond to a physical possibility?

Try different settings, especially the extremes. Are the histograms different? Does the trace pattern change?

Are there other interesting quantities to keep track of?

Look up or calculate the REAL number, size, mass and speed of particles in a typical gas. When you compare those numbers to the ones in the model, are you surprised this model works as well as it does? What physical phenomena might be observed if there really were a small number of big particles in the space around us?

We often say outer space is a vacuum. Is that really true? How many particles would there be in a space the size of this computer?

EXTENDING THE MODEL

Could you find a way to measure or express the "temperature" of this imaginary gas? Try to construct a thermometer.

What happens if there are particles of different masses? (See "GasLab Two Gas" model.)

How would you define and calculate pressure in this "boundless" space?

What happens if the gas is inside a container instead of a boundless space? (See "Gas in a Box" model.)

What happens if the collisions are non-elastic?

How does this 2-D model differ from the 3-D model?

Set up only two particles to collide head-on. This may help to show how the collision rule works. Remember that the axis of collision is being randomly chosen each time.

What if some of the particles had a "drift" tendency -- a force pulling them in one direction? Could you develop a model of a centrifuge, or charged particles in an electric field?

Find a way to monitor how often particles collide, and how far they go, on average, between collisions. The latter is called the "mean free path". What factors affect its value?

In what ways is this idealization different from the one used to derive the Maxwell-Boltzmann distribution? Specifically, what other code could be used to represent the two-body collisions of particles?

If MORE than two particles arrive on the same patch, the current code says they don't collide. Is this a mistake? How does it affect the results?

Is this model valid for fluids in any aspect? How could it be made to be fluid-like?

NETLOGO FEATURES

Notice the use of the histogram primitive.

Notice how collisions are detected by the turtles and how the code guarantees that the same two particles do not collide twice. What happens if we let the patches detect them?

CREDITS AND REFERENCES

This model was written by David Bowen at Wayne State University, and is based on the GasLab models (a) Free Gas, (b) Gas in a Box, and (c) Pressure Box.

To refer to Free Gas, Gas in a Box, or Pressure Box models in academic publications, please use: Wilensky, U. (1997). NetLogo GasLab Free Gas (or other) model. http://ccl.northwestern.edu/netlogo/models/GasLabFreeGas (or other). Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1997 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/GasLabFreeGas (or other) for terms of use.

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