Size matters when it comes to making the ideal cup of coffee

The complex maths used to build aircraft and racing cars is being applied to produce the ultimate coffee maker. The mathematicians are developing a detailed theory of coffee brewing aimed at producing the ultimate morning brew. "We have got closer to the perfect cup of coffee, and we now know how to quantify that," says Dr William Lee, formerly of the University of Limerick and now based at the University of Portsmouth.

It can be a daily challenge getting that ideal cup of coffee, not too strong, not too weak. The UL researchers however have created mathematical models to study the magic that goes on when ground coffee and hot water join to make one of life's little treats.

The research got going after a get to know you meeting between mathematicians and industry people looking to set up joint projects. Researchers from the Philips company were there, looking to build a better coffee maker and a partnership was formed, Dr Lee said.

Kevin Moroney in UL's Macsi applied maths centre led the research and Dr Lee co-authored the work.

Basic fluid mechanics

The team started with the very basics, how hot water flowed around a single grain of ground coffee, Dr Lee said. “It is a basic fluid mechanics problem. We took a model from water trickling through the earth and used it to model water flow through coffee.”

They built new “hideously complicated” mathematical models and conducted experiments and discovered the absolute bottom line when it comes to making good coffee - the size of the grains.

“It is absolutely critical,” he said. “What surprised us is the coffee extraction was a two step process, the fast extraction from the grain surface and the slower extraction from inside the grain.”

This means that size does matter when grinding your coffee. Large grains have lower surface area so less coffee from the surface and the water is slower to penetrate the grain.

Smaller grains are better for the opposite reasons, more surface area and easier to extract the flavour from inside. Unfortunately there is more to worry about.

“There is an optimum amount of coffee you want to extract from the grain. If you have too much it will be bitter, if too little you end up with something like smokey water,” Dr Lee said.

The team has reached a key point however, with models and data proving these key points, details of which were published on Tuesday in the SIAM Journal on Applied Mathematics.

Next they will turn their attention to making a better coffee maker. Hot water flowing into the filter tends to make a hole in the “coffee bed”. Dr Lee wants to see whether they get better results if the water flows like a shower head.