Chemical potential and banana waffles

The concept of chemical potential is one that seems almost deliberately obscure to many.  I’ve written about this here, and referenced this article.  What you may not realize is that the chemical potential, of water in particular, plays a crucial role in why my banana waffle recipe works so well.  

My waffle recipe starts with an old, peel-getting-brown banana, which I peel and put in a medium bowl with a couple of teaspoons of salt and a tablespoon of brown sugar.  With just a little mashing with a fork to mix with the salt and sugar, the banana basically liquefies in a couple of minutes.  That’s where the chemical potential comes in.  

Chemical potential, \(\mu\), describes how particles tend to diffuse, from regions of high chemical potential (more accurately, high \(\mu/T\)) to regions of low chemical potential \((\mu/T\)). The water molecules in the cells of the banana is already at a higher chemical potential than, e.g., the water vapor in the air around the banana.  That’s why if you let the banana sit around it would eventually dry out, and there is an “osmotic” pressure that pushes out against the cell membranes and cell walls.  Adding salt and sugar to the exterior of the cells lowers the chemical potential for water outside the cells even more (because there is an energetic benefit to the water molecules to form a solution with the salt and sugar - the polar water molecules have an attractive interaction with the ions from the salt, and an attractive interaction via hydrogen bonding with the sugar).  This increases the osmotic pressure, so that water leaks out of the cells (maybe even rupturing the cell membrane, though when people want to encourage that they throw in a little soap, not conducive to good waffles).  Wait a couple of minutes, stir, and then I have yummy banana goo that forms the beginning of my Sunday morning waffle batter.

This is a goofy example of the power of thermodynamics and statistical mechanics.  At room temperature, there are many more microscopic arrangements of the water molecules (in the presence of sugar and salt) with the banana forming liquefied goo than with the water sitting in the cells, and so the liquefaction happens spontaneously once the ingredients are put together.  (Osmosis can even be funny - I highly recommend reading this story of you can find a copy.)