后退浮膜中多分散颗粒的分级
Fractionation of polydisperse particles in a receding floating film
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中文总结 AI 辅助
本文通过深度积分处理组分输运求解润滑问题，发现后退浮膜的前沿可作为色谱仪实现多分散颗粒分级，利用扩散率差异决定分级方向，为几纳米级纳米颗粒分级提供了新途径。
中文摘要 AI 辅助
在深的不混溶液体下相上，承载N种不同尺寸颗粒的薄挥发性薄膜蒸发。铺展系数为正，因此无钉扎现象。薄膜终止于后退前沿，其运动超出薄膜方程的范畴；未施加接触线定律。我们通过保守的深度积分处理组分输运来求解润滑问题，结果表明该前沿相当于一台色谱仪。每种组分都会在前沿处堆积成浓度峰，且各组分的滞留比例与其佩克莱数（Péclet number）成正比。尺寸更小、扩散性更强的组分会持续泄漏到前沿通过后留存的流体中；尺寸更大的组分则会沉积在扫过路径上。干燥后的沉积物是该扫过过程的时间积分记录，且按尺寸分级：富含小颗粒的中心区、富含大颗粒的中间环带。钉扎的双分散液滴的分级方向相反。固体上的未钉扎液滴按此方式分级，但依据的是力平衡；此处仅扩散率差异就能决定方向。尺寸仅通过佩克莱数进入输运问题，因此扩散率差异是唯一可用于选择方向的对称性破缺因素：马兰戈尼应力、胶体相互作用和润湿效应仅作用于大小，且根据输运算子的对称性，无法设定方向。相邻组分的带分离度与有效佩克莱数倒数的差值成比例，这是本文推导并测量的规律：即该色谱仪的分辨率。该缩放关系为几纳米范围内多分散纳米颗粒的尺寸分级提供了一条途径，而这正是标准方法难以应对的区域。
英文摘要
A thin volatile film carrying N particle species of different sizes evaporates on a deep immiscible liquid subphase. The spreading coefficient is positive, so nothing pins. The film ends at a receding front whose motion falls out of the film equations; no contact-line law is imposed. We solve the lubrication problem with a conservative depth-integrated treatment of species transport, and the front turns out to be a chromatograph. Every species piles into a concentration spike at the front, each held there in proportion to its Péclet number. The smaller, more diffusive species leaks continuously into the fluid that survives the front's passage; the larger species is laid down along the sweep path. The dried deposit is the time-integrated record of that sweep, and it is sorted by size: small-rich centre, large-rich mid-annulus. Pinned bidisperse droplets sort the other way. Depinned droplets on solids sort this way, but by a force balance; here, diffusivity contrast alone picks the direction. Size enters the transport problem only through the Péclet number, so diffusivity contrast is the only symmetry-breaking available to choose a direction: Marangoni stresses, colloidal interactions and wetting effects act on the magnitude and, by the symmetry of the transport operator, cannot set the direction. Adjacent-species band separations scale with the difference in inverse effective Péclet number, a law derived and measured here: the resolution of the chromatograph. That scaling points to a route to size fractionation of polydisperse nanoparticles in the few-nanometre regime, exactly where standard methods struggle.
