question about particle-wall collision simulation

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maarten - 17 Nov 2005 14:58 GMT

Hi,

I am programming a simulation (java) with particle-particle collisions and
particle-wall collisions. All entities are 2D.
The particles are modelled as hard spheres. Internal energy is not modelled.
This work nice. You can see the particles moving with a brownian motion.
The problem occurs when I want to model a correct particle wall collision:
- what is the direction vector after the collision?
- what is the energy (=temperature) of the particle after the collision?

I tried the following:
1) The direction of the particle after the collision is completely random.
The energy is such that the temperature is equal to the temperature of the
wall.
2) The direction of the particle after the collsion is straight from the
wall. The energy is such that the temperature is equal to the temperature
of the wall.
3) The direction of the particle is such that alpha_in=alpha_out. The energy
is such that the temperature is equal to the temperature of the wall.

All seem to work OK, with the exception that the 2nd option requires enough
particles for introducing enough chaos.

Does sombody know whether it is good physics to simulate a particle-wall
collision this way? Or a website where I can find theory about this topic?

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PD - 18 Nov 2005 17:18 GMT

> Hi,
>
[quoted text clipped - 5 lines]
> - what is the direction vector after the collision?
> - what is the energy (=temperature) of the particle after the collision?

A 2D model of a gas (which is what you have) simply has to require
conservation of momentum (in both x and y directions) and conservation
of kinetic energy in every collision.

The same thing is true for a wall.

What this will yield, for example, for a y-wall (parallel to y-axis) at
x=L/2, is that
v_x(before) = -v_x(after)
v_y(before) = v_y(after)

This is for a case where the wall does not transact energy with the
particle. This isn't perfect, even in the case where the gas is in
thermal equilibrium with the wall, but it's close. If you want to add
thermal transactions with the wall, then the easiest thing to do is to
treat every wall collision like the collision with another particle
having kinetic energy equal to the average kinetic energy of the
particles in the gas.

PD

> I tried the following:
> 1) The direction of the particle after the collision is completely random.
[quoted text clipped - 11 lines]
> Does sombody know whether it is good physics to simulate a particle-wall
> collision this way? Or a website where I can find theory about this topic?

Reply to this Message

maarten - 19 Nov 2005 10:05 GMT

> A 2D model of a gas (which is what you have) simply has to require
> conservation of momentum (in both x and y directions) and conservation
> of kinetic energy in every collision.

That is what I do.

> The same thing is true for a wall.
>
> What this will yield, for example, for a y-wall (parallel to y-axis) at
> x=L/2, is that
> v_x(before) = -v_x(after)
> v_y(before) = v_y(after)

This is what I do for the walls that should not be there but are the
boundery of the simulation.

> This is for a case where the wall does not transact energy with the
> particle. This isn't perfect, even in the case where the gas is in
> thermal equilibrium with the wall, but it's close.

What's the difference? I assume there is a chaos element in the direction
and the energy?

> If you want to add
> thermal transactions with the wall, then the easiest thing to do is to
> treat every wall collision like the collision with another particle
> having kinetic energy equal to the average kinetic energy of the
> particles in the gas.

Sounds logical. I will try that.
I assume the avarage kinetic energy of the particles of a gas:
Ekin = 3/2*k*T
In which T is the temperature of the wall.
I will assume the the wall has that kinetic energy in the direction straight
from the wall. The the energy of the gas-particle after the collision can
be calculated considering conservation of momentum and energy. Then the
delta E for the wall can be seen as a delta Q which can be translated in a
delta Twall.

I will try that. Meanwhile, I put the application on the web using webstart:
http://maarten.dootingh.nl/professioneel/heatConductionSimulation/hcsim.jnlp
HeatConductionOfGas.jar
Or you can download it: http://maarten.dootingh.nl/professioneel
heatConductionSimulation/HeatConductionOfGas.jar
This version uses an incorrect collision energy formula. You can see that
the molecules get a lower temprature than the walls when molecule-molecule
collsions occur. I hope this will be corrected once I implement the above
molecule-wall collsion formula.

Thanks

> PD
>
[quoted text clipped - 15 lines]
>> collision this way? Or a website where I can find theory about this
>> topic?

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Natural Science Forum / Physics / Particle Physics / November 2005

question about particle-wall collision simulation