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Tree-like structure in chocolate

Today I let some melted chocolate solidify in a smooth bowl in my fridge. When it had settled, I gently heated the outside of the bowl with warm water to unstick the chocolate. It caught my attention that the remaining chocolate (both in the bowl and on the larger piece I removed) formed a beautiful, fractal tree-structure of sorts. I noticed that the various branches in the tree do not seem to intersect each other.

After re-heating chocolate that had solidified in a smooth bowl a complex, tree-like structure emerged.

Next it occured to me that I had seen a similar thing happen to soft butter on a cold knife. I suspect the effect emerges because the fatty compounds in chocolate/butter try to minimize their surface tension (like water forming droplets), but why is the minimum-energy-configuration a non-self-intersecting, fractal branch structure, and not simply droplets? Could it be some tradeoff between surface tension, viscosity and density?

The same thing happens with soft butter on a cold knife.

EDIT User, Bert Hickman, suggested the effect might be an example of a "Hele-Shaw cell". This apparatus is used to demonstrate "Hele-Shaw flow" of a liquid between two plates: enter image description here

This explanation makes sense considering what I did to the chocolate. When re-heating it the chocolate between the bowl and the upper layer is liquified. Once I remove the upper layer air rushes in and creates the peculiar flow. I found this nice video demonstrating the effect with water and oil.

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    $\begingroup$ Similar observations have been made about the fracture surfaces of metals. There's a paper titled "Fractal character of fracture surfaces of metals" by none other than Benoit Mandelbrot, et. al., in Nature, v. 308, 721 (1984). Unfortunately, one needs a subscription to access it. $\endgroup$ – user93237 May 28 '18 at 0:47
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    $\begingroup$ It looks like you may have inadvertently created a Hele-Shaw cell. Hele-Shaw flow occurs when a thin viscous fluid layer exists between two flat solid plates that are then separated. See: rspa.royalsocietypublishing.org/content/245/1242/312.short $\endgroup$ – Bert Hickman May 29 '18 at 20:54
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    $\begingroup$ Agree with @berthickman. very similar pattern seen upon pulling apart samples of splat-frozen amorphous metal alloys. Same trick can be done pulling apart glass plates stuck together with vaseline. $\endgroup$ – niels nielsen Jul 18 '18 at 6:53
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That is the microstructure of fat crystal networks.

Source: "Nanostructured Fat Crystal Systems" (Nov 2014), by Acevedo, Nuria & Marangoni, Alejandro. Annual review of food science and technology. 6.10.1146/annurev-food-030713-092400.

Figure 3 depicts the mesoscale of a fat crystal network at two different magnifications. Crystals and polycrystal aggregates in the micrometer range, as well as the fractal distribution of crystalline mass in the network, can be observed clearly. The formation of these polycrystals is influenced strongly by external fields (such as temperature gradients and shear fields) experienced during nucleation and crystal growth.

Superimposed PLM and PCM micrographs showing fat crystal mesostructure at two different magnifications.

Figure 3. Polarized light microscopy (PLM) and phase contrast microscopy (PCM) micrographs showing fat crystal mesostructure at two different magnifications. The images were created by superimposing PLM and PCM micrographs. Polycrystals and polycrystal agglomerates of several micrometers in size can be observed. (The data are unpublished.)

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The new experimental results on the nanoscale of fats set the stage for the updated depiction of the structure of TAG crystal networks at different length scales (Figure 9). The complex combination of the structural properties along all length scales, from TAG molecules, primary nanoplatelets, and mesocrystals to a colloidal network of polycrystals, determines the macroscopic properties of a fat, such as its mechanical strength, oil-binding capacity, and sensory properties.

Structural levels present in a triacylglycerol (TAG) crystal network.

Figure 9. Structural levels present in a triacylglycerol (TAG) crystal network. The crystalline unit is a platelet with sizes within the range of several nanometers; in turn, nanoplatelets are composed of stacks of TAG lamellae. At the mesoscale (several micrometers), spherulites can be observed that then self-assemble to constitute a three-dimensional network. Adapted from Marangoni et al. (2012) with permission from the Royal Society of Chemistry.

The mathematics behind this are explained in: "Confectionery and Chocolate Engineering: Principles and Applications" by Ferenc A. Mohos.

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  • $\begingroup$ I am not sure the "crystal-explanation" is correct. The effect was visible while the chocolate was still liquid, so no crystal structures should be present at that point. If it had to do with crystalization, surely one would see it whenever chocolate melts or solidifies under normal circumstances? It seems to be a bulk-effect, rather than one on the micro-scale. I think the Hele-Shaw model explains the situation better. Your figure 3 states that shear stress (which should be present in the HS model) can affect the crystal structure, so maybe there is some connection there? $\endgroup$ – Ole Krarup Aug 20 '18 at 5:26
  • $\begingroup$ HS requires thin non-porous plates, and Darcy's Law uses a porous medium relating to homogenization - Unfortunately Samuel, Bert and Niels haven't had time to provide an answer, and we only have Ferenc's expertise. $\endgroup$ – Rob Aug 20 '18 at 6:34

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