Diffusion at Small Scale

Diffusion is a random movement of molecules due to collision with water molecules which leads to a net displacement over time, a random walk . When a large number of molecules is considered, the mean deviation, L (more precisely the root mean square of deviations), from the starting position is described by a simple but very important equation, which holds the secret of diffusion  

These are very counter-intuitive relations which have some surprising consequences. From Eq. 5.7 one can calculate the diffusion velocity , which is distance divided by time  

This leads to the curious conclusion that the shorter the period over which we measure diffusion, the larger is its velocity and vice versa. This is critical to keep in mind when working with diagenetic models, because the different chemical species have time and length scales of diffusion and reaction which vary over many orders of magnitude and which are therefore correspondingly difficult to compare. 

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