Tea Time

I was making a cup of tea this morning, and started thinking about the various rules I've learned for how to make a good cup.  One of these is that you should never dunk a teabag in and out of the water.  I've certainly found this to be true, but I started wondering why.  My guess is that it causes the solids contained in the tea leaves to dissolve too quickly, and in the wrong proportions.  Dissolution is governed by the equation

where dm/dt is the rate of dissolution, A is the surface area of the dissolving solid, D is the diffusion coefficient, d is the thickness of the boundary between liquid and solid, Cs is the concentration of material on the surface of the solid, and Cb is the concentration of material in the bulk of the liquid.

By dunking the teabag, or otherwise mixing things, you lower Cb near the teabag, causing the rate of dissolution to increase.  Normally, it would take time for the concentration near the teabag to diffuse outward to the rest of the cup, but instead you're doing the diffusion work yourself, speeding things up.

Thinking about this reminded me of an essay by one of my favorite authors, Douglas Adams.  He theorized that "the Americans are all mystified about why the English make such a big thing out of tea because most Americans HAVE NEVER HAD A GOOD CUP OF TEA."  He doesn't mention the dunking issue, but he does give excellent instructions for making good tea.