Chiral symmetry avoidance through a cascade of wrinkles

We describe how a line initially dividing the plane spontaneously breaks its chiral symmetry by actively sustaining a cascade of successive wrinkles of ever smaller sizes. The line is an oil thread deposited at the surface of a still water bath, interacting with its environment by Marangoni stresses.

The thread surface tension is lower than that of the underlying bath by an amount $\Delta\sigma$. This driving force directed from the thread core to the outer environment first thickens the thread by spreading the oil concentration gradient over a length scale $\ell$. 

This chiral left/right (-/+) symmetry soon breaks into a meandering motion, any small displacement of the thread centerline being amplified by the difference of the surface tension gradients on each side of the thread $\Delta\sigma/\ell\vert_- \neq \Delta\sigma/\ell\vert_+$, a difference further increasing as the thread deforms. 

We provide a detailed description of this newly reported instability, of its most unstable wavelength and associated growth rate. We also explain why and how this destabilization process repeats iteratively, leading to an accelerated cascade of fractal wrinkles, which ends-up in a finite time when molecular diffusion finally erases the driving force concentration gradients.