Rolling droplets

When a rigid circular cylinder or sphere is placed on a rough inclined plane it will roll down the plane. When the experiment is repeated with a rigid cube it will slide down the plane. If the object is deformable a variety of motions become possible; the motion of elastic bodies and fluid drops depends on the interfacial energies of the materials, the roughness of the interfaces, the size of the objects, etc. This is because a deformable body maintains contact with the surface over a finite area. For a viscous fluid droplet, two possible motions may ensue. If the droplet partially wets the surface it slides along it, while if the droplet is nonwetting, it can roll on the surface, much like an elastic body when viewed from the exterior. Here we consider the motion of a small nonwetting droplet forced by a weak gravitational field. A classic example of this motion is exhibited by a droplet of mercury on an inclined plane and is probably the origin of the name quicksilver, after the Latin Argentum Vivum for the swiftly moving droplet of the silvery liquid. For such motions to be observable, we must have liquids with high surface tension moving on very clean hydrophobic surfaces. Until recently, only chemically treated surfaces were amenable to such experiments that allowed for large contact angles; however, these surfaces were easily contaminated. Recently it has become possible to vary the surface roughness to achieve contact angles very close to 180° thus making robust experiments in the high contact angle regime more accessible. A small droplet rolling down such an incline then would reach a steady velocity determined by the balance between the rate of energy dissipation due to internal viscous motions and the rate of change of gravitational potential energy.