The Irregular Motion of a Liquid Contact Line is a Memory

The contact line at the edge of a water drop on a horizontal surface has an irregular shape that does not relax to equilibrium, revealing the disorder of the solid substrate beneath. We show that a disordered contact line can store multiple nested memories of the magnitude of its past motion. To encode a memory, we ‘train’ the contact line to a steady state through slow, cyclic injections and withdrawals at a constant volume of liquid. Afterwards, further training only drives it through a hysteresis loop that returns the contact line to its steady state. Changing the volume amplitude results in a different shape but applying one cycle at the training amplitude returns the contact line to its steady state. If the amplitude ever exceeds the training amplitude, the memory is erased, and the steady state is lost. This behavior is reminiscent of return-point memory, a phenomenon best known in ferromagnets. Return-point memory, and the process of reaching a steady state, can give insight about the history dependence and reversibility of contact line motion, offer a new framework for manipulating its shape, and lets us compare this system to others that do not relax to equilibrium.