Force balance of particles trapped at fluid interfaces
Force balance of particles trapped at fluid interfaces
复制标题
DOI：
10.1063/1.2890035
复制
发表时间：
2008-03-21
影响因子：
4.4
通讯作者：
Dietrich, S.
中科院分区：
文献类型：
--
作者：
Dominguez, Alvaro;Oettel, Martin;Dietrich, S.
我们研究了捕获在流体界面上的胶体颗粒之间作用的有效力，该流体界面本身暴露于压力场。为此，我们应用所谓的“力方法”，该方法仅依赖于机械平衡条件，并且在某种意义上比更常用的“能量方法”限制更少，后者基于自由能泛函的最小化。目标是（i）阐明力方法与能量方法相比的优点和缺点，以及（ii）理清界面变形和颗粒之间毛细管诱导力的哪些特征仅遵循机械平衡的总体特征，而不是取决于细节的特征，例如界面与颗粒或系统边界的相互作用。首先，我们推导出界面处力的一般应力张量公式。在此基础上，我们在界面相对于其平面结构发生小变形的特殊情况下，与二维静电学进行了有用的类比。我们应用这种类比来计算流体界面处捕获的粒子之间有效力的渐近衰减，扩展了先前结果的有效性，并揭示了力方法与能量方法相比的优点和局限性。它遵循将力方法应用于非平坦界面变形的情况。在这种情况下，我们首先计算球形液滴由于其表面捕获的带电粒子的电场而产生的变形，并得出结论，颗粒间毛细管力不太可能解释这种配置中最近的某些实验观察结果。最后，我们讨论了我们的方法在一般弯曲界面上的应用，并作为说明性示例展示了沉积在形成最小表面的界面上的非球形颗粒被拉向较大曲率的区域。
We study the effective forces acting between colloidal particles trapped at a fluid interface which itself is exposed to a pressure field. To this end, we apply what we call the "force approach," which relies solely on the condition of mechanical equilibrium and turns to be in a certain sense less restrictive than the more frequently used "energy approach," which is based on the minimization of a free energy functional. The goals are (i) to elucidate the advantages and disadvantages of the force approach as compared to the energy approach, and (ii) to disentangle which features of the interfacial deformation and of the capillary-induced forces between the particles follow from the gross feature of mechanical equilibrium alone, as opposed to features which depend on the details of, e.g., the interaction of the interface with the particles or the boundaries of the system. First, we derive a general stress-tensor formulation of the forces at the interface. On that basis we work out a useful analogy with two-dimensional electrostatics in the particular case of small deformations of the interface relative to its flat configuration. We apply this analogy in order to compute the asymptotic decay of the effective force between particles trapped at a fluid interface, extending the validity of the previous results and revealing the advantages and limitations of the force approach compared to the energy approach. It follows the application of the force approach to the case of deformations of a nonflat interface. In this context, we first compute the deformation of a spherical droplet due to the electric field of a charged particle trapped at its surface and conclude that the interparticle capillary force is unlikely to explain certain recent experimental observations within such a configuration. We finally discuss the application of our approach to a generally curved interface and show as an illustrative example that a nonspherical particle deposited on an interface forming a minimal surface is pulled to regions of larger curvature.