File:Osmosis computer simulation.jpg

Summary

This is a shot from a three dimensional computer simulation of the process of <a href="https://en.wikipedia.org/wiki/osmosis" class="extiw" title="en:osmosis">en:osmosis</a>. The blue <a href="https://en.wikipedia.org/wiki/mesh" class="extiw" title="en:mesh">en:mesh</a> is impermeable to the larger balls, whereas all of the balls are (in the animated version) bouncing about according to the rules of physical simulation of the kinetics of an ideal gas. Averaged over long period of time, each ball has has the same kinetic energy as each of the other balls, even though at any given moment the velocities are distributed according to the appropriate <a href="https://en.wikipedia.org/wiki/Boltzmann" class="extiw" title="en:Boltzmann">en:Boltzmann</a> functions. Likewise, each species (in this case color) of balls (as a group) exerts time averaged force (due to the bouncing) upon the walls of the box, which corresponds to the partial <a href="https://en.wikipedia.org/wiki/pressure" class="extiw" title="en:pressure">en:pressure</a> contribution associated with that group. These properties emerge even though the collision function used in the simulation is trivial, to wit:

void Mass::collide (Mass *X)
{
  vector v_cm;
  v_cm = (velocity*mass+X->velocity*X->mass)/(mass+X->mass);
  velocity = v_cm*2 - velocity;
  X->velocity = v_cm*2 - X->velocity;
  m_bCollision = true;
  X->m_bCollision = true;
}

Accordingly, one can make theoretical assumtions about the behaviour of such mixtures according to the application of <a href="https://en.wikipedia.org/wiki/Dalton%27s_law" class="extiw" title="en:Dalton's law"> Dalton's law </a> of partial pressures, and so on, and thereby gain some insights into how certain physical processes really work.

Licensing

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