Chocolate cake

The science behind melted chocolate cake

On page 53 of our April 2021 issue, Rama Bansil of Boston University reviewed the book Science and cooking: physics meets food, from homemade to haute cuisine (2020) by Michael Brenner, Pia Sörensen and David Weitz. Physics todayRyan Dahn spoke to two of the book’s authors about the course they teach at Harvard University that inspired the book. In this chocolate fondant recipe, adapted from Science and cooking, Brenner, Sörensen and Weitz explain the science, from solubility to heat diffusion, which goes into a perfect recipe.

Melted chocolate cake

Credit: Pia Sörensen

IngredientsA

130g dark chocolate chips

120 g unsalted butter (1 stick)

2 whole eggs and 2 egg yolks

100g of sugar

60g all-purpose flourB

Pinch of salt

directions

  1. Preheat the oven to 350 ° F (177 ° C). Spray 8 ramekins with nonstick cooking spray.
  2. In a small saucepan, melt the chocolate and butterVS together over low heat, stirring constantly.
  3. In a medium bowl, whisk together the eggs, egg yolks and sugar.D
  4. In another bowl, combine the flour and salt.
  5. Slowly add the chocolateE mix with egg mixture, whisking constantly.
  6. Gradually 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 dough so that they are a little more than halfway (1.5 cm to 2 cm from the top).
  8. Place the ramekins on the middle rack of the oven and bakeg for 12 minutes.H
  9. Serve hot, preferably topped with ice cream!

Remarks

  1. Moles. By estimating the number of molecules in 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, if not more, molecules than a cup of flour, because flour molecules are a few thousand to a few million times larger than salt molecules.
  2. Packaging. The particles of flour and sugar can pile up more or less densely, so cooks prefer to measure amounts by weight rather than volume. In our class, each 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 at 350 F can vary by 80 F or more, or more than 20%! For some recipes, precise oven temperatures and exact measurements are essential, but melted 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 crystal phases, each melting at a different temperature.
  4. Solubility. The sugar will begin to dissolve in the water contained in the egg white. Sugar is very soluble in water: at room temperature, a given amount of sugar can dissolve in half the amount of water by weight.
  5. Denaturation of proteins. Adding the hot chocolate-butter mixture to the eggs too quickly will cause the protein in the egg to denature and “cook”. To avoid this result, add a little of the mixture at a time while whisking constantly.
  6. Viscosity, polymers, emulsions and foams. The viscosity of the final dough is determined by the different ingredients. The whisk swells the starch particles in the flour and releases polymers. The polymers intermingle and form a network which, together with the swollen starch particles, increases the viscosity of the dough. Whipping 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 as well as the packing density of the starch particles and the polymer network.
  7. Solubility of gases and foams. When heated in the oven, cakes rise because the air in the dough expands. In addition, the solubility of carbon dioxide decreases with higher temperatures, so that CO2 diffuses out of the dough and helps to form bubbles in the cake.
  8. Heat diffusion. How far does heat spread in 12 minutes? To answer this question, measure the thickness of the baked layer. As the cake bakes, the dough 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 melted center consists of a heated but uncooked dough. By measuring the thickness of the solidified layer L and keep track of how long you baked the cake t you can estimate an important physical constant, namely the heat diffusion coefficient in water, from the heat diffusion coefficient of the dough D = L2/ 4t, because the cake batter is mostly water. See if you can get in an order of magnitude of the value in the literature, 0.0014 cm2/ s. Congratulations, you have calculated a physical constant with a melted chocolate cake!
    Melted chocolate cake
    Credit: Pia Sörensen


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