The science behind molten chocolate cake

On page 53 of our April 2021 issue, Boston University’s Rama Bansil reviewed the book Science and Cooking: Physics Meets Food, from Homemade to Haute Cuisine (2020) by Michael Brenner, Pia Sörensen, and David Weitz. Physics Today’s Ryan Dahn spoke with two of the book’s authors about the Harvard University class they teach that inspired the book. In this recipe for molten chocolate cake, adapted from Science and Cooking, Brenner, Sörensen, and Weitz explain the science, from solubility to heat diffusion, that goes into a perfect recipe.

Molten chocolate cake

Ingredients^A

130 g dark chocolate chips

120 g unsalted butter (1 stick)

2 whole eggs plus 2 egg yolks

100 g sugar

60 g all-purpose flour^B

Pinch salt

Directions

1. Preheat the oven to 350 °F (177 °C). Spray 8 ramekins with nonstick baking spray.
2. In a small saucepan, melt the chocolate and butter^C together over low heat, stirring constantly.
3. In a medium bowl, whisk together the eggs, egg yolks, and sugar.^D
4. In another bowl, whisk together the flour and salt.
5. Slowly add the chocolate^E mixture to the egg mixture, whisking constantly.
6. Little by little, add the flour mixture to the wet ingredients and whisk well.^F Make sure the flour is completely incorporated.
7. Fill the prepared ramekins with batter so that they are a little more than half full (1.5 cm to 2 cm from the top).
8. Place the ramekins on the middle rack of the oven and bake^G for 12 minutes.^H
9. Serve warm, preferably topped with ice cream!

Notes

1. Moles. By estimating the number of molecules of each ingredient, we can create a mental picture of what the mixture will look like on a microscopic scale. A pinch of salt contains about as many, or potentially even more, molecules as a cup of flour, because flour molecules are a couple thousand to a couple million times as large as salt molecules.
2. Packing. Flour and sugar particles can pack more or less densely, so cooks prefer measuring quantities by weight rather than by volume. In our class, every student weighs a cup of flour, and we compile the results; they can vary by 30% or more. In addition, the actual temperature of ovens set to 350 ˚F can vary by 80 ˚F or more, or over 20%! For some recipes, precise oven temperatures and exact measurements are critical, but molten chocolate cake is a fairly robust recipe that tends to work regardless.
3. Phase transitions. The exact temperatures at which chocolate and butter melt are determined by the length, saturation, and internal arrangement of their fatty acids. Chocolate, for example, can have six different crystalline phases, each of which melts at a different temperature.
4. Solubility. Sugar will begin to dissolve in the water contained in the egg white. Sugar is highly soluble in water—at room temperature, a given quantity of sugar can dissolve in half the amount of water by weight.
5. Protein denaturation. Adding the hot chocolate–butter mixture to the eggs too quickly will cause the egg proteins to denature and “cook.” To avoid that outcome, add a little of the mixture at a time while constantly whisking.
6. Viscosity, polymers, emulsions, and foams. The final batter’s viscosity is determined by the various ingredients. Whisking causes the starch particles in the flour to swell and leak polymers. The polymers entangle and form a network that, together with the swollen starch particles, increases the viscosity of the batter. Whisking also incorporates air and creates a foam. The result is an emulsion of fat (butter) and water (egg white). The final viscosity depends on the volume fraction of air bubbles and fat droplets along with the packing density of starch particles and the network of polymers.
7. Solubility of gases and foams. When heated in the oven, the cakes rise because the air in the batter expands. Moreover, the solubility of carbon dioxide decreases with higher temperatures, so the CO₂ diffuses out of the batter and helps form the bubbles in the cake.
8. Heat diffusion. How far does heat diffuse in 12 minutes? To answer that question, measure the thickness of the cooked layer. As the cake bakes, the batter around the edges reaches the temperature at which it solidifies and forms a “crumb front” that moves toward the center of the cake. The characteristic molten center consists of batter that is heated but not cooked. By measuring the thickness of the solidified layer L and keeping track of how long you baked the cake t you can estimate an important physical constant—namely, the diffusion coefficient of heat in water—from the heat diffusion coefficient of the batter D = L²/4t, because cake batter is mostly water. See if you can get within an order of magnitude of the value in the literature, 0.0014 cm²/s. Congrats, you’ve calculated a physical constant with molten chocolate cake!