A Method for Predicting Shell-Thickness Inspired by Candy!

Inspired by videos of chocolatiers, a team of engineers has developed a theory that accurately predicts the final thickness of a shell given the rheological properties of the shell material and the geometry of the mold used for coating.

Pedro Reis and his team wondered whether there was a precise way to predict the final thickness of chocolate and other shells that start as a liquid film. (Image courtesy of MIT.)

The secrets to producing even, perfectly smooth chocolaty shells have been passed down since the 1600s, but this new theory enabled the team to create a rapid fabrication technique that simplifies the coating process and makes thickness adjustments easier.

Knowing just a few key variables, engineers can now predict the mechanical response of many types of shells, from pharmaceutical capsules to airplane and rocket bodies.

The Shell-Thickness Formulation

The research technique involved quickly creating thin, rubbery shells by drizzling liquid polymer over dome-shaped molds like ping pong balls. After coating each mold and curing the polymer, the researchers peeled off the shells and found them to be perfectly smooth with almost no defects.

Once the polymer shells were removed from each mold, the research team cut the shells in half and found that shell thickness was almost the same throughout.

In order to determine why, they systematically characterized the coating dynamics in each of their experiments, including the physical properties of the polymer, the size of the mold, how fast the fluid flows down a mold and the time it takes for the polymer to cure.

Based on their analysis, a simple formula was developed to estimate the final thickness of a shell:

Thickness equals the square root of the fluid’s viscosity times the mold’s radius, divided by the curing time of the polymer times the polymer’s density and the acceleration of gravity as the polymer flows down the mold.

With a larger mold radius, the time it takes fluid to flow to the bottom increases. The result is a thicker shell. In contrast, longer curing times mean the fluid drains faster to the bottom, creating a thinner shell.

After developing a numerical model, the team was able to explore configurations that could not be performed in the lab using simulations of complex coating patterns and the effects of changing a polymer’s curing time.

The team was able to control shell thickness by shortening the polymer’s curing time. By waiting for the polymer to thicken before pouring it onto the mold, curing time was reduced and more polymer ended up on the mold instead of running off. As a result, the thickness of the shell increased by a factor of 11.

“This flexibility of waiting gives us a simple parameter we can tune, depending on what we want for our final goal,” said Pedro Reis, mechanical engineering professor at MIT. “So I think ‘rapid fabrication’ is how we can describe this technique. Usually that term means 3-D printing and other expensive tools, but it could describe something as simple as pouring chocolate over a mold.”

Reis and his team have published their findings in the journal Nature Communications.