Lehle Hartwig, Oettel Martin
Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jan;75(1 Pt 1):011602. doi: 10.1103/PhysRevE.75.011602. Epub 2007 Jan 12.
We calculate the effective fluctuation-induced force between spherical or disklike colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir-type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation-induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. Separating the colloid fluctuations from the fluctuations of the capillary wave field leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on a multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.
我们计算了由热激发毛细波介导的、被困在平坦流体界面处的球形或盘状胶体之间的有效涨落诱导力。这种卡西米尔型力由系统的配分函数决定，而配分函数又通过泛函积分方法计算得出，其中胶体对毛细波施加的限制通过辅助场来体现。在长程范围内，涨落诱导力被证明对胶体与两种流体相之间三相接触线处施加的边界条件敏感依赖。将胶体涨落与毛细波场涨落分开分别导致相互竞争的排斥和吸引贡献，这会导致主导项的抵消。在基于卡西米尔相互作用多极展开的第二种方法中，这些抵消可以从边界条件强制某些多极矩消失来理解。我们还讨论了不同类型边界条件与作用在胶体上的某些外部场的联系，这些外部场似乎可以通过诸如激光镊子法等实验技术来实现。
