Unravelling the physics of curling

By Hamish Johnston

Apologies to our many Canadian readers, because this blog entry is not about that kind of curling – you can read about the physics of the winter sport here.

Instead, I’m blogging about how things like hair, plant tendrils and even red blood cells curl and uncurl. Despite these processes being all around us, it turns out that physicists have a relatively poor understanding of the dynamics of curling.

That’s why Andrew Callan-Jones of the University of Montpellier, France, and colleagues at the University of Paris have made a theoretical and experimental study of how a steel strip curls.

The experiment begins with a piece of steel that is 635 mm long, 9.5 mm wide and 0.13 mm thick. The strip is in a naturally curled state and is secured to a flat surface at one end. The strip is then flattened onto the surface and released so that it curls up again – a process that takes about 30 ms. The curling is captured by a fast camera at a rate of 7000 frames per second (above right).

The photographs reveal that the process begins at the free end of the strip, which lifts up and then bends over to complete the first few loops of the spiral. Then, a circular “spool” forms and some of the strip wraps tightly around this structure. Finally, the last few loops of the curl are wrapped very loosely round the spool.

One interesting observation by the team is that the radius of curvature of the spool is about twice that of the natural radius of curvature of the strip itself. This is illustrated by the fact that the free end of the strip forms a tighter curve inside the spool, with a radius of curvature that matches the material itself.

The physicists believe that the tight spool is formed as the curl spins rapidly – and this affects the radial forces that define the size of the spool.

This behaviour was successfully described by a mathematical model created by the team. These insights were then incorporated into a computer simulation of how a much longer strip would curl. This identified a third structure that emerges towards the end of the curling process – a large loosely wound region.

The researchers are now applying their new-found knowledge of curling to the bursting of red blood cells – which is caused by certain nasty bacteria and involves the curling back of the cell membrane.

The research is described in Physical Review Letters 108 174302 and you can find the paper here.