Droplet Friction and Adhesion: The Solid-Liquid Amontons' Laws

The empirical laws of dry friction between two solid bodies date back to the work of Amontons in 1699 and are pre-dated by the work of Leonardo da Vinci. Fundamental to those laws are the concepts of static and kinetic coefficients of friction relating the pinning and sliding friction forces along a surface to the normal load force. Here, we show how surface free energy arguments can be used to derive and define coefficients of static and kinetic friction for three-phase contact lines and droplets on solids. We provide a droplet analogy of Amontons' first and second laws, but with the normal load force of a solid replaced by the normal component of the surface tension force of the liquid. In the static regime the coefficient of static friction is proportional to the contact angle hysteresis. In the kinetic regime the coefficient of kinetic friction is proportional to the difference in dynamic advancing and receding contact angles. Our Amontons' laws provide a direct link between droplet friction and work of adhesion. We show literature data can be fitted to provide numerical values for droplet-on-solid coefficients of friction.