Monte Carlo Simulation of Individual Molecular Histories

1 Monte Carlo Simulation of Individual Molecular Histories 

When looking for a reasonable approximation of p(t] ), one can consult the equations of Sect. 2.2. They describe diffusional deposition in channels under various flow regimes, when the tracer is evenly distributed over the inlet area. The solutions for both hydrodynamically and diffusionally developing flow directly apply to the problem of the first jump down the column. It is the common experimental situation 

Reproduced from Radiochimica Acta, 38(2), Zvara I, Simulation of thermochromatographic processes by the Monte Carlo method, 95-101, 1985, with permission from Oldenbourg Wis-senschaftsverlag. 

In the meantime, the above semi-quantitative microscopic picture of the migrations suggests that p it, ) has a shape like in Fig. 4.5a, and that a reasonable two-term approximation to it, convenient for simulations, would be Fig. 4.5b. The first term considers that the mean of the short displacements must be close to zero hence, they can be all put equal zero through The other term accounts for the occasional intermittent, rather long, downstream jumps it does it through only one exponential distribution. Thus  

The quantity an is evidently the reciprocal of the average number of collisions of a molecule with a wall in a column section of the length r,. 

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