Tiramisu

September 30th, 2020

Making the Tiramisu

For this Tiramisu, I followed this recipe, which claims to be the best Tiramisu I will ever make. To start, I prepared the cooked mixture of egg and sugar, apparently called a sabayon. As I stirred the mixture over simmering water, it went through a couple of interesting rheological transitions. Initially, the mixture was just wet sugar, a cohesive granular material with a very high yield stress. Then, as the sugar melted, it became a low-medium viscosity liquid. Finally, over the course of ten minutes of stirring and cooking, the viscosity steadily increased until it became quite thick. Presumably this viscosity increase was primarily due to the formation of microgel particles, but there was also a slight entrainment of air bubbles due to the mixing that would also increase the viscosity. A fun coincidence that I found when measuring out the egg yolks for this mixture was that in the ½ cup they visually resemble the exact schematic of a common microgel microstructure that I and others have often used.

After cooling the sabayon slightly, I added the milk product, mascarpone, which is very similar to cream cheese but with higher fat content. Then I folded in a cream whipped into medium-stiff peaks. Because of how many ingredients and microstructures went into this cream, it’s difficult to guess at what the final structure looks like and what aspects contribute most to the rheology. There are the microgels from the cooked egg, air bubbles from the whipped cream foam, and the mascarpone is likely some type of oil-in-water emulsion or even a gel. Ultimately, the mixture does have a slight yield stress as evidenced by the persistence of a rough surface, and has significant temperature-dependence which I’ll elaborate on later.

Next, I laid down the coffee-dipped ladyfingers into a layer. I didn’t have a large square pan which would have made packing them easier, but I think it worked out fine. It took a couple of tries to figure out that I only needed to very quickly wet the biscuits in the coffee; my first couple were left too long and disintegrated shockingly fast. I’d never had ladyfingers on their own before and it was interesting how porous and sponge-like they were.

As I spread the last of the cream over the second layer of ladyfingers, it struck me that due to the gaps between biscuits, the yield-stress of the material needed to be low enough to spread and fill these gaps. Weighing a teaspoon of the cream mixture, I found it had a density of around 0.6 g/cm^3, about 60% the density of water. This low density is due to the incorporation of air bubbles via folding in of the whipped cream. To figure out approximately what stress the material was experiencing at the interface of the ladyfinger and cream layers, we can use the equation that stress that a layer of material experiences is equal to the density multiplied by the height of the layer and the gravitational constant (approximately 10 m/s^2). Here we’re neglecting the fact that there are the confining pan walls. As the layer becomes thicker, the weight of material pressing down on the bottom surface increases linearly with the height. The top layer was approximately 1.5 cm thick and thus the stress that the bottom of the top layer experienced was about 90 Pa. Thus, the mixture must have a yield stress below 90 Pa in order to fill the gaps around the ladyfingers. We still want the cream to be a yield-stress fluid though so that it can trap the air bubbles of the foam within it. Indeed, tasting the room temperature cream mixture, I estimate the yield stress to be around 10 to 50 Pa which would be sufficient to hold the rough surface structures that we can observe.

After the assembly was completed, I refrigerated the cake overnight to allow it to stiffen. I sprinkled cocoa powder on top and the final result came out pretty well. I made it in my spring-form pan and was able to briefly remove the sides to take some pictures. Here it seems as though there is an apparent contradiction: despite our calculation and my estimate of a yield stress less than 90 Pa, the entire cake is able to hold its shape without the bottommost layer getting pressed out. I believe the resolution to this is to consider the temperature at which we assembled the cake. Just after being pulled out of the fridge, the cream is at approximately 4 degrees Celsius. Considering the difference between the consistency at a cold temperature versus room temperature of a high-fat content product like butter as an example, it is not that surprising that the cake is able to hold its shape given how much fat is contained in the cream layers. I believe that the fat content is the most likely explanation for the significant temperature dependence; perhaps the need to incorporate a sufficient amount of fat is one of the reasons why mascarpone is preferred over normal cream cheese.

The significant temperature dependence does however make this particular cake more pressing to consume quickly in a hot place like Singapore. Indeed, within minutes of placing the cake on my plate, the bottom layer starts to get pressed out as the temperature rises. If I were to make this cake again, I don’t think that putting in an additive to increase the yield stress would be an appropriate solution. Though a higher yield stress would help the cake preserve its shape, we calculated that there is an upper limit on the yield stress in order to nicely fill the gaps in the middle layers of the cake; a higher yield stress would likely result in large voids. Rather, I would likely try to incorporate a gelling agent like gelatin into the cream to still allow it to spread at room temperature, but solidify more permanently after refrigeration.