Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent that is close to its critical consolute point T_c. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent that is at the critical concentration and close to T_c, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the two cylinders, while capillary forces originating from the extension of the liquid bridge turn out to be more important at large separations. In addition, we are able to infer from the wetting characteristics of the individual colloids the first-order transition of the liquid bridge connecting two colloidal particles to the ruptured state. While specific to cylindrical colloids, the results presented here also provide an outline for identifying critical Casimir forces acting on bridged colloidal particles as such and for analyzing the bridging transition between them.

中文翻译：

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圆柱形胶体在近临界溶剂中的液相桥联

在平均场理论内，我们研究了浸入作为溶剂的二元液体混合物中的一对平行圆柱状胶体之间的桥接转变，该溶剂接近其临界溶质点T _c。我们确定有效势和胶体之间力的通用缩放函数。对于临界浓度且接近T _c的溶剂，我们发现关键的卡西米尔力是紧密分离时的主要相互作用。这与两个气缸之间有效相互作用的相应Derjaguin近似非常吻合，而源自液桥延伸的毛细作用力在较大的分离距离中显得更为重要。另外，我们能够从各个胶体的润湿特性推断出将两个胶体颗粒连接到破裂状态的液桥的一级转变。尽管特定于圆柱状胶体，但此处给出的结果也为确定作用在桥接胶体颗粒上的关键卡西米尔力以及分析它们之间的桥接过渡提供了一个轮廓。