A Simple Model of Grinding

When I think of what a grinder does to coffee beans, the simplest idea that comes to mind is that it breaks the beans into uniform chunks whose size is determined by the grinder setting. This process is illustrated below.

When the ground coffee is put into a portafilter basket and tamped, it forms a packed bed, with individual grains separated by the intergranular space. An important characteristic of packed beds like this is packing density, which tells us how much of the total volume is occupied by the grains, and how much forms the gaps between grains, where water will flow.

Packing density does not depend on the size of the grains—if you make the grains bigger, the gaps between them get bigger in proportion. Because of this, the density of the packed bed also does not depend on the size of the individual grains.

So, if our ground coffee follows this model, we would expect density to stay the same when we change the grind setting. However, this is not what we see if we plot the density of the tamped puck over a range of grind settings:

Puck density vs. grind setting

It’s tempting just to fit this with an exponential curve, but I think it’s better to follow a process like this:

  1. Start with a hypothetical physical model for the system.
  2. Make a prediction, based on the model, of what the plot should look like.
  3. Compare the prediction to the actual data.

This keeps us a little more honest about the physical basis for the curve we’re fitting, and down the road it might also allow us to infer some hidden physical attributes from our data.

In the next post, I will develop an improved model of the grinding process and compare its predictions to our density measurements.

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