标题： 向列液晶液滴的后Tanner扩展 显示英文标题

标题： Post-Tanner spreading of nematic droplets

摘要： 准稳态圆形液滴在固体基底上的铺展通常遵循所谓的Tanner定律，瞬时基底半径 \$R(t)\$ 随时间增长表现为 \$R \sim t^\{{1/10}\}\$——这是由于小尺寸液滴中毛细力起主导作用的效果。 然而，对于向列型液晶液滴，在长时间尺度下会表现出更快的铺展规律，使得 \$R \sim t^\alpha\$ 其中 \$\alpha\$ 显著大于Tanner指数1/10。 在薄膜模型（或润滑近似）框架内，我们将这种“加速”描述为一种由向列型特有的强烈基底-液体相互作用驱动的不同铺展模式转变（界面处的对抗性锚定）。 薄膜方程的数值解与向列型液晶的现有实验数据吻合得很好，尽管非牛顿流变学尚未被考虑进去。 因此，我们在Tanner阶段之后补充了铺展理论，指出铺展过程可能会从通常由毛细力主导的阶段过渡到Derjaguin意义下的整个储层成为扩散膜的阶段。 显示英文摘要

摘要： The quasistationary spreading of a circular liquid drop on a solid substrate typically obeys the so-called Tanner law, with the instantaneous base radius R(t) growing with time as R ~ t^{1/10} -- an effect of the dominant role of capillary forces for a small-sized droplet. However, for droplets of nematic liquid crystals, a faster spreading law sets in at long times, so that R ~ t^alpha with alpha significantly larger than the Tanner exponent 1/10. In the framework of the thin film model (or lubrication approximation), we describe this "acceleration" as a transition to a qualitatively different spreading regime driven by a strong substrate-liquid interaction specific to nematics (antagonistic anchoring at the interfaces). The numerical solution of the thin film equation agrees well with the available experimental data for nematics, even though the non-Newtonian rheology has yet to be taken into account. Thus we complement the theory of spreading with a post-Tanner stage, noting that the spreading process can be expected to cross over from the usual capillarity-dominated stage to a regime where the whole reservoir becomes a diffusive film in the sense of Derjaguin.