标题： 毛细力作用于液气界面处的小粒子：理论与模拟 显示英文标题

标题： Capillary Forces on a Small Particle at a Liquid-Vapor Interface: Theory and Simulation

摘要： 我们研究了半径为$R$的小球形粒子在外侧的弯月面。 液体被限制在一个有限半径为$L$的圆柱形容器中，并在容器表面具有接触角$\pi/2$。 粒子的中心位于容器中心轴的不同高度上。 通过改变$L$，我们可以系统地研究弯月面从纳米尺度到宏观尺度的转变。 颗粒上的弯月面升高或下降被发现随着$\ln (2L/R)$增长，当$R\ll L\ll \kappa^{-1}$时，$\kappa^{-1}$为毛细管长度，并在$R \ll \kappa^{-1} \ll L$时达到由 Derjaguin-James 公式预测的值。 当位移较小时，颗粒上的毛细力与颗粒在界面处平衡位置的位移呈线性关系。 与之相关的弹簧常数为$2\pi\gamma\ln^{-1} (2L/R)$对于$L\ll \kappa^{-1}$并且对于$L\gg \kappa^{-1}$饱和到$2\pi\gamma\ln^{-1} (3.7\kappa^{-1}/R)$。 在纳米尺度上，我们对所述几何结构进行分子动力学模拟，结果与毛细管宏观理论的预测相符。 在微米到宏观尺度上，与 Anachkov\textit{等人}[Soft Matter{\bf 12}, 7632 (2016)] 的实验比较表明，为了解释使用$L \sim \kappa^{-1}$收集的实验数据，需要考虑液-气或液-液界面的有限跨度。 显示英文摘要

摘要： We study the meniscus on the outside of a small spherical particle with radius $R$ at a liquid-vapor interface. The liquid is confined in a cylindrical container with a finite radius $L$ and has a contact angle $\pi/2$ at the container surface. The center of the particle is placed at various heights along the central axis of the container. By varying $L$, we are able to systematically study the crossover of the meniscus from nanometer to macroscopic scales. The meniscus rise or depression on the particle is found to grow as $\ln (2L/R)$ when $R\ll L\ll \kappa^{-1}$ with $\kappa^{-1}$ being the capillary length and saturate to a value predicted by the Derjaguin-James formula when $R \ll \kappa^{-1} \ll L$. The capillary force on the particle exhibits a linear dependence on the particle's displacement from its equilibrium position at the interface when the displacement is small. The associated spring constant is found to be $2\pi\gamma\ln^{-1} (2L/R)$ for $L\ll \kappa^{-1}$ and saturates to $2\pi\gamma\ln^{-1} (3.7\kappa^{-1}/R)$ for $L\gg \kappa^{-1}$. At nanometer scales, we perform molecular dynamics simulations of the described geometry and the results agree well with the predictions of the macroscopic theory of capillarity. At micrometer to macroscopic scales, comparison to experiments by Anachkov \textit{et al.} [Soft Matter {\bf 12}, 7632 (2016)] shows that the finite span of a liquid-vapor or liquid-liquid interface needs to be considered to interpret experimental data collected with $L \sim \kappa^{-1}$.