Osmosis in a 2-dimensional gas solution

Kostas Papamichalis Dr of Theoretical Physics

To download the Theoretical Model and the Activities click here: The Theoretical Model

Summary

In the plane orthogonal container shown in the window of the simulation, the user can see a 2-dimensional gas consisted of N/3 red and 2N/3 blue particles (ps). The container is seperated in two departments D1 and D2 by a semi-permeable barrier. The red ps cannot pass through the barrier but the blues can. The red ps are confined in the left department D1. The number of the blue ps passing from D1 to D2 in the time interval [t,t+Dt] is proportional to the number of the blue ps located in D1 at the time t, though the number of the blue ps passing from D2 to D1 in the same interval is proportional to the number of the blue ps in D2.

The pressure in every department is caused by the elastic collisions of the ps to the walls of the container. Initially, in D1 and D2 there is the same number of ps and the pressures in them are equal. During any p-p interaction the total linear momentum and the energy of the interacting couple are conserved. The particles can ocverlap in space, but the distance of their centers is always greater than r (the particles' radius).

The system is driven to an equilibrium state, where the number of the blue ps in D1 and D2 are equal, but the pressures in them are different. The difference of the pressures in the two departments at the equilibrium state is called "osmotic" pressure.

The initial velocity distribution of the gas is "near" the Maxwell-Boltzmann (M-B) distribution but it converges to it, according to the Boltzmann H-theorem. The "nearness" between the actual distribution and the M-B one, is estimated by comparing the mean absolute x-velocity measured in a sequence of time moments, with the corresponding value obtained when the gas state is determined by the M-B distribution. The user can watch these values at the appropriate measuring tools in the virtual environment of the simulation.

Return to the original page