Post-Tanner stages of droplet spreading: the energy balance approach revisited
Post-Tanner stages of droplet spreading: the energy balance approach revisited
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DOI：
10.1088/0953-8984/21/46/464131
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
S. Mechkov;A. Cazabat;G. Oshanin
中科院分区：
文献类型：
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作者：
S. Mechkov;A. Cazabat;G. Oshanin
圆形液滴在固体衬底上的扩散可以用其基圆半径R(T)随时间的变化来描述。在完全润湿时，准稳态区域(远离初始和最终的瞬变)通常遵循所谓的坦纳定律，即R∼tαT，αT=1/10。后期扩散可能与坦纳定律显著不同：在某些情况下，液滴不会变薄为分子膜，而是达到平衡的煎饼状形状；在其他情况下，如最近自发扩展向列相晶体的实验所揭示的那样，在坦纳阶段之后，基半径的增长加速。在这里，我们证明，通过考虑线张力对扩散驱动力的贡献，这两个看似冲突的趋势可以在适当地重新审视的能量平衡方法中得到协调：正的线张力负责形成煎饼状结构，而负的线张力倾向于加长接触线并导致加速扩散(与Tanner阶段相比，向R(T)更快的幂定律的转变)。
The spreading of a circular liquid drop on a solid substrate can be described in terms of 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∼tαT, αT = 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).