液滴扩散的后Tanner阶段：能量平衡方法的再讨论
Post-Tanner stages of droplet spreading: the energy balance approach revisited
摘要：
圆形液滴在固体基底上的铺展可以用其基半径R（t）的时间演化来描述。在完全润湿中，准稳态状态（远离初始和最终瞬态）通常遵守所谓的坦纳定律，其中Rt ^alpha_T，alpha_T=1/10。后期的扩展可能与坦纳定律有很大的不同：在某些情况下，液滴不会变薄成分子膜，而是达到平衡的煎饼状形状;在其他情况下，如最近的实验所揭示的自发扩展的晶体，基底半径的增长加速后坦纳阶段。在这里，我们证明了这两个看似矛盾的趋势可以在一个适当的重新审视的能量平衡方法中得到调和，通过考虑线张力对扩展驱动力的贡献：正的线张力是形成薄饼状结构的原因，而负的线张力倾向于延长接触线（过渡到比Tanner阶段更快的R（t）幂律）。
英文摘要：
The spreading of a circular liquid drop on a solid substrate can be described by the time evolution of its base radius R(t). In complete wetting the quasistationary regime (far away from initial and final transients) typically obeys the so-called Tanner law, with R t^alpha_T, alpha_T=1/10. Late-time spreading may differ significantly from the Tanner law: in some cases the drop does not thin down to a molecular film and instead reaches an equilibrium pancake-like shape; in other situations, as revealed by recent experiments with spontaneously spreading nematic crystals, the growth of the base radius accelerates after the Tanner stage. Here we demonstrate that these two seemingly conflicting trends can be reconciled within a suitably revisited energy balance approach, by taking into account the line tension contribution to the driving force of spreading: a positive line tension is responsible for the formation of pancake-like structures, whereas a negative line tension tends to lengthen the contact line and induces an accelerated spreading (a transition to a faster power law for R(t) than in the Tanner stage).
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