Mathematical modelling can help keep the stuff that comes out of your taps clean and fresh

In July, my wife Avril and I celebrated our 40th wedding anniversary in Barbados. We joked with the hotel waiter that we only came for the tap water, which is amazingly good. We found out why when we visited Harrison’s cave. Barbados is mostly fossilised coral, which acts like a giant filter for rainwater. So the tap water is very clean, with a tangy mineral taste.

Several years ago we went to Slovenia, and were invited to join a group of Chinese karstologists visiting the spectacular caves there. Karst is rugged limestone, all jagged edges and collapsed holes. What’s all this geology got to do with maths? Well, I was idly reading a mathematics research journal and came across an article about karst.

Great stuff for mathematicians and geologists, to be sure, but why should anybody else care about karst?

The answer is: groundwater. Much of the water we drink, and the water that industries use, comes from groundwater.

Because we rely heavily on groundwater, contamination is a serious problem. Industrial waste, excess fertiliser running off fields, landfill sites for everyday rubbish, and dozens of other sources can cause undesirable chemicals to get into our groundwater. To some extent, karst aquifers can clean themselves, given time, but it’s not clear whether they can cope with the level of contamination that is common today. So scientists need to understand how water flows through the porous karst geology.

Traditionally, they use mathematical models of fluid flow through a porous substance. The usual models assume that the rock is equally porous everywhere, because until recently no one knew how to include more realistic effects, such as cracks in the rock, surface sinkholes, and springs. The sums were simply too difficult, even using powerful computers. But those cracks are more important than the porous rock when we want to know how contaminants move from place to place.

That’s where all the stuff about Beavers-Joseph interfaces comes in. It’s how the modellers deal with holes and cracks in porous rock. After many years of effort, the mathematicians who work in this area have discovered a good way to set up realistic models in a computer, and calculate how effective the rock is at filtering out chemical nasties and keeping itself clean.

The Economist

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