**Decompression During Scuba Diving**

Colin Please

School of Mathematics, University of Southampton

When a diver enters the water he needs to breath air at a pressure very close to that of the surrounding water. Hence a pressure of many atmospheres is easily attained at reasonable diving depths. At this elevated pressure the gas goes into solution within the diver's body and, by taking care that the concentrations of certain gases do not get too large, this allows divers to work at great depths for long times. However, when a diver wants to return to the water surface he must be extremely careful. If he returns to the surface rapidly then bubbles of gas will form in his tissue and cause damage commonly referred to as Òthe bendsÓ or Òdecompression sicknessÓ (DCS). An extreme example of this type of phenomena can be seen by quickly removing the cap from a bottle of carbonated soda.

The task for the student team working on this problem will
be to develop and examine mathematical models of how gas dissolves in tissue,
how it may form bubbles, and how tissue reacts to gas and bubbles. The aim will be to construct a
reasonable mathematical model of the processes and then to see how to use this
model to determine how a diver should return to the surface in some Òoptimal
mannerÓ to avoid any DCS problems.

There are a number of companies that produce small dive computers to assist divers in calculating how to avoid DCS, and these are based on various types of models with a lot of empirical data fitting. For an example of such a product try the web link:

http://www.technologyindepth.com/vrxvgm.html

At this site, you can download code that will allow you to
see the sorts of predictions that are made.