Reversibility, Path-Dependence, and Memory of a Creeping Triple-Phase Contact Line.

The contact line around 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 the contact line has a detailed memory of its history of motion on the surface. To form a memory, we start with an initial volume of water and “train” the contact line with slow imbibition and drainage cycles at constant volume amplitude until its motion becomes periodic. Reducing the volume amplitude drastically changes the shape of the contact line when it returns to its starting volume, but when driven again with only one cycle at the training amplitude, it transitions back to its steady state. Driving above the training amplitude erases the memory making the steady state inaccessible. This behavior is reminiscent of return-point memory, a phenomenon best known in ferromagnets. Return-point memory, and the evolution to steady state, can give insight on how contact line hysteresis and the memory of its motion arise, offer a framework to study its reversible-irreversible transitions, and provide a comparison of this system to others that are far from equilibrium.