In this study the authors consider a very old branch of fluid mechanic
s, namely that of Taylor dispersion, in a new light, using up-to-date
techniques from the theory of stochastic processes. The aim is to show
how these techniques not only help in deepening our understanding of
dispersion, but are in fact very useful for every-day calculations. So
me old and not-so-old problems in dispersion theory are considered in
order to demonstrate the new techniques, and so far as possible any hi
dden calculations are avoided, so a reader new to the probabilistic te
chniques can judge their effectiveness. A wider knowledge of probabili
stic techniques would be useful in many traditional areas of applied m
athematics, but dispersion theory is probably the most natural field f
or their introduction into fluid mechanics.