Modelling Diffusion

Abstract

One of the clearest indications that there is human habitation on this planet is the presence of artificially produced material in the world’s oceans. For mankind, this is of course of central importance, also of more immediate concern is the presence of such material in coastal seas and estuaries. Sadly, much of this material is often poisonous to some degree as has already been mentioned in the first chapter of this book. The name pollution has been coined to describe foreign often toxic material in the sea. Once pollution is present, it does not remain unchanged but is pulled and pushed around by the currents and waves of the sea, spreading and (usually) diluting. This spreading takes place even if the sea were to be quiescent. The name of this process is diffusion. Molecular diffusion can be observed if a grain of potassium permanganate (purple) is placed in still water. A purple patch gradually grows. Of course this growth is enhanced if there are currents present. The school experiment that demonstrates convection by dropping a crystal of KMnO ₄ (potassium permanganate) in a beaker of water being heated from beneath by a bunsen burner clearly shows enhanced spreading. Similarly in the environment pollution can be made to spread effectively by the action of strong and usually variable currents. A word must be said here about the use of the word dispersion. Quite rightly dispersion is used as a synonym for diffusion. However, dispersion has come to have a special meaning for physicists and applied mathematicians, it means the change (increase) in the wavelength of a wave or group of waves as it propagates (see Chapter 6). This spreading of the waves is dictated by the dispersion relation that gives the relation between wavelength, frequency and other relevant physical parameters. In view of this and subsequent possible confusion the word dispersion will not be used as meaning general diffusion.