A new study published in the new issue of the journal Nature could have ramifications for your next pint of beer. Well, maybe not your next, but at some point in the future it may change the way brewers think about brewing their beer.
The article, by mathematician Robert D. MacPherson of Princeton’s Institute for Advanced Study and physicist David J. Srolovitz of Yeshiva University, is saddled with the indecipherable jargon-laden title, “The von Neumann relation generalized to coarsening of three-dimensional microstructures.” What that means essentially for the bubbles in your beer, is that they’ve found a mathematical formula that can be used to accurately predict and map out the dissipation of the head. It also describes the growth patterns of the beer bubbles, or any cell with boundaries. As co-author Srolovitz tells it. “What the theory does is it tells you how the size of every single bubble will evolve in time.”
Here’s the abstract:
Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure (using the relation between wall velocity and mean curvature, the fact that three domain walls meet at 120° and basic topology). This forms the basis of modern grain growth theory. Here we present an exact and much-sought extension of this result into three (and higher) dimensions. The present results may lead to the development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios—such as the heat treatment of metals, or even controlling the ‘head’ on a pint of beer.
It’s pretty heady stuff — yes, pun intended — although it will likely be many years before it can be applied directly to brewing beer, if it ever really can be used in that way. It certainly seems plausible that it may be restricted to analysis after the fact, though even that may yield insights on what to tweak in the process for the next batch in the search for the ideal head.