Key Lesson: Diffusion. The rate of many culinary processes, such as cooking and brining, is limited by diffusion, in which the distance travelled is proportional to the square root of time.

Timing is one of the essential aspects of good cooking, and the approximate times needed for different culinary techniques can be estimated based on the diffusion constant of water. Raül Balam Ruscalleda explains the role of time and temperature, among many other variables, in creating the perfect paella.

Overview of the Science

Heat is limited by random collisions between the molecules in the food, a process called diffusion.

Faster moving molecules transfer their energy to slower moving molecules, so differences in temperature are decreased.

Foods cook faster if the external temperature is higher.

The temperature rise is fastest at the start of cooking, then slows down as the temperature of the food approaches the final temperature.

Equation of the Week

How fast does heat flow into food?

The cooking times of most foods are limited by the diffusion constant, D, of water.

The average distance, L, traveled by diffusing molecules (or heat), is related to the time, t, by:

$$ L = \sqrt{D t} $$

In theory, if the size of a food is doubled, then the cooking time increases by closer to a factor of four. Heat travels faster than other types of diffusion, so brining or soaking is often the most time-consuming step in a recipe:

Making perfect caramelized onions takes several hours

Below is a series of photos of onions at different stages of browning:

You can find out more about browning reactions in Week XX

Beyond the Lecture

The mathematics of sous vide cooking

Applied mathematician and sous vide expert Douglas Baldwin gives a nice introduction into the mathematics of sous vide in his book.