How many licks to finish a lollipop? Formula models how water currents shape and dissolve solids

"How flowing fluids generate unique shapes through erosion or dissolution is complex and fascinating," says Leif Ristroph, an assistant professor at NYU's Courant Institute and the paper's senior author.

The researchers studied this effect by immersing hard candy in a water current. They found that a peculiar but consistent shape emerges and then persists before eventually vanishing. This same 'sculpture' results regardless of the candy's initial form and the speed of the water flow.

The authors were also surprised to find that their work offers a long-sought answer to a question from childhood: How many licks does it take to reach the center of a lollipop? By formulating a theory for how flows cause dissolving and shrinking, the researchers calculated an estimate of about 1,000 licks.

But the work addresses some serious science, too. Understanding how materials dissolve is at the heart of the chemical and pharmaceutical industries -- their products rely on the incorporation of solid compounds into solutions within reactors and within the human body.

The work also has relevance in geology -- the research links the morphology of eroding and dissolving surfaces to the flows present, which could offer a way to explain the unusual but consistent shapes of landscapes and landforms.

Conducted in NYU's Applied Math Lab, the study involved experiments using pieces of hard candy, cooked up by the researchers and measuring about two inches. Simple shapes, such as spheres or cylinders, were then placed in a water tunnel, which allows for washing of these bodies by well-controlled flows. The researchers captured the change of candy's shape using time-lapse photography and used these measurements to formulate a theory for how flows affect dissolving.

The study was led by Jinzi Huang, a doctoral student at the Courant Institute, and also includes Professor Nicholas Moore of Florida State's Department of Mathematics.