Post-Tanner stages of droplet spreading: the energy balance approach revisited

Abstract

The spreading of a circular liquid drop on a solid substrate canbe described in terms of the time evolution of its base radiusR(t). In complete wetting, the quasistationary regime (far away from initialand final transients) typically obeys the so-called Tanner law, withR∼tαT,αT = 1/10. Late-time spreading may differ significantly from the Tanner law: in some cases the dropdoes not thin down to a molecular film and instead reaches an equilibrium pancake-likeshape; in other situations, as revealed by recent experiments with spontaneously spreadingnematic crystals, the growth of the base radius accelerates after the Tanner stage. Here wedemonstrate that these two seemingly conflicting trends can be reconciled within a suitablyrevisited energy balance approach, by taking into account the line tension contribution tothe driving force of spreading: a positive line tension is responsible for the formation ofpancake-like structures, whereas a negative line tension tends to lengthen the contactline and induces an accelerated spreading (a transition to a faster power law forR(t) than in the Tanner stage).