Wetton Numbers

When modelling physical processes (that is, writing down mathematical equations that describe a physical system, at least approximately), many parameters can enter the model. If you consider idealized fluid flow, the parameters are the density, viscosity and speed of the fluid, and the size of the object it is flowing around. Actually, the behaviour of the fluid does not depend on all four of these parameters separately, but just a single combination of them called the Reynolds number (usually abbreviated Re). A situation changed to a fluid twice the viscosity of the original and with flow speed also twice as fast will behave exactly the same (at least, the same to the level that the Navier Stokes equations can accurately describe the flow). The Reynolds number is dimensionless and in words represents the ratio of inertial to viscous forces in the fluid. Flows with a high enough Reynolds number are turbulent. Small Reynolds number flows are laminar.

Around 10 years ago, as I was approaching my fortieth birthday, I was working on a project modelling fuel cell behaviour. Specifically, I was looking at models of how unit fuel cells in a stack affected each other due to electrical coupling through currents in shared current collecting plates (bipolar plates, which sounds kind of funny now that I look at it years later).  I identified a dimensionless parameter in this stetting that is the ratio of bipolar plate electrical resistance to equivalent resistance in the local electrochemical reaction. It could be used to estimate the number of adjacent cells that would be affected by an anomalous cell in the stack through this electrical coupling. In the paper I wrote up, I labelled this parameter W. I hoped that people would refer to it as the Wetton number. This was a bit egotistical, I admit, but it was an important birthday coming up for me. However, while the paper was in draft, I discovered that a very related idea was known in the literature since the 1940s as the Wagner number. Not only did that bastard Wagner steal my number (well OK, he did get there first by quite a large margin), but his number was the inverse of mine, and I had to do the work to change this everywhere that it occurred in my draft.

While working with Jean St Pierre at the Hawaii Natural Energy Institute earlier this year, I identified another candidate for the Wetton number, W1. It is the solubility of a trace gas component (possibly a contaminant) in air, scaled to the fuel cell setting. A high W1 means that the trace component will be almost completely scavenged by the water by fuel cell outlet. You see the "1" on the W1, so you can guess that there is a W2. The second parameter describes a possible, generic first order ionization of the dissolved component. The formation of these ions effectively allows more of the component to enter the water. It is more significant at low concentration levels. Not all gases will ionize significantly in water but there are some interesting ones that do, like sulphur dioxide. The ionization lowers the pH of the water (this effect is one of the contributors to acid rain). Maybe these new candidates will actually be known as Wetton numbers. This would be a nice fiftieth birthday present!