Physicists Ask: How Many Licks Does It Take to Get to the Center of a Lollipop?

Physicists at New York University have measured and modeled how a lollipop dissolves in flowing water, and they can now address the age-long question: “How many licks does it take to get to the center of a lollipop?” Their answer is about 1000 licks.

The research, supervised by Leif Ristroph, appears in this month’s issue of the Journal of Fluid Mechanics.

Flowing fluids dissolve things faster, as is clear from watching rivers and wind erode stone on geological timescales. “How flowing fluids generate unique shapes through erosion or dissolution is complex and fascinating, and our research at NYU’s Applied Math Lab uses laboratory experiments to carefully witness and speed along these geologically-slow processes,” said Ristroph in an email.

The goal is to better understand how the dissolving shape of a body in turn alters the flow patterns around the body and its further dissolution. And a candy lollipop is the perfect simple shape to experimentally measure this feedback process.

Jinzi Mac Huang, NYU graduate student in applied mathematics and lead author on the work, prepared homemade lollipops out of a simple solution of boiled sugar, corn syrup, and water, which he set into molds of various shapes.

The researchers immersed the lollipops in a keyboard-sized “water tunnel” (analogous to a wind tunnel) with water speeds ranging from 0.2 to 2 miles per hour and watched them dissolve. The video above (courtesy of Leif Ristroph) shows the full time-lapse disappearance of the originally-spherical lollipop.

Lollipop after 60 minutes dissolving in a 30 cm/s flow of water. The lollipop was originally spherical.
Image courtesy of Jinzi Mac Huang, Applied Mathematics Laboratory, NYU

The above image shows a partially-dissolved lollipop with a smooth rounded front, a beveled facet in the middle, and a flat back side, a shape which the researchers saw emerge again and again.

“A peculiar shape emerges and then persists as the body vanishes, and this same final sculpture is unveiled regardless of the initial form and imposed flow speed,” said Ristroph.

The team also dissolved cylindrical lollipops and surprisingly found the same unique shape emerge as for the spherical lollipop. This indicates that there is a preferred shape for general objects dissolving in a flow, which has potential applications in both geology and in medicine, such as how pills dissolve in the human body.

“Much more than a curiosity, understanding how materials dissolve is critical to the chemical and pharmaceutical industries,” said Ristroph. “Geologically, our studies link the morphology of eroding and dissolving surfaces to the flows present, which could offer a way to infer past environmental conditions from the shapes of landforms.”

Along with the experimental data, the team theoretically modeled how the lollipop dissolves over time and how the rate depends on flow speed. For example, they predicted that if the flow speed was 4 mph instead of 1 mph, then the lollipop would completely dissolve in half the time. This prediction was exactly matched by the real data.

Theoretical models in hand, Huang and his colleagues end their paper with a fun application of their work. They write,

“this scaling allows us to address the following long-standing question: ‘How many licks does it take to get to the centre of a lollipop?’ For candy of size a ~ 1 cm licked at a speed of U0 ~ 1 cm s-1, we estimate a total of U0/vn ~ 1000 licks, a prediction that is notoriously difficult to test experimentally.”

By Tamela Maciel, also known as “pendulum”
Top image credit: Jinzi Mac Huang, Applied Mathematics Laboratory, New York University

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