Department of Chemical Engineering, Faculty of Chemistry, University of Sofia, 1164 Sofia, Bulgaria.
Adv Colloid Interface Sci. 2010 Feb 26;154(1-2):91-103. doi: 10.1016/j.cis.2010.01.010. Epub 2010 Feb 6.
The liquid interface around an adsorbed colloidal particle can be undulated because of roughness or heterogeneity of the particle surface, or due to the fact that the particle has non-spherical (e.g. ellipsoidal or polyhedral) shape. In such case, the meniscus around the particle can be expanded in Fourier series, which is equivalent to a superposition of capillary multipoles, viz. capillary charges, dipoles, quadrupoles, etc. The capillary multipoles attract a growing interest because their interactions have been found to influence the self-assembly of particles at liquid interfaces, as well as the interfacial rheology and the properties of particle-stabilized emulsions and foams. As a rule, the interfacial deformation in the middle between two adsorbed colloidal particles is small. This fact is utilized for derivation of accurate asymptotic expressions for calculating the capillary forces by integration in the midplane, where the Young-Laplace equation can be linearized and the superposition approximation can be applied. Thus, we derived a general integral expression for the capillary force, which was further applied to obtain convenient asymptotic formulas for the force and energy of interaction between capillary multipoles of arbitrary orders. The new analytical expressions have a wider range of validity in comparison with the previously published ones. They are applicable not only for interparticle distances that are much smaller than the capillary length, but also for distances that are comparable or greater than the capillary length.
由于颗粒表面的粗糙度或不均匀性，或者由于颗粒具有非球形（例如椭球形或多面体形）形状，吸附胶体颗粒周围的液界面可能会起伏。在这种情况下，颗粒周围的弯月面可以用傅立叶级数展开，这等效于毛细多极的叠加，即毛细电荷、偶极子、四极子等。毛细多极子引起了越来越多的关注，因为它们的相互作用已被发现会影响颗粒在液界面处的自组装，以及界面流变学和颗粒稳定乳液和泡沫的性质。通常，两个吸附胶体颗粒之间中间的界面变形很小。这一事实被用于通过在中间平面进行积分来推导计算毛细力的精确渐近表达式，在中间平面中可以线性化 Young-Laplace 方程并应用叠加近似。因此，我们推导出了毛细力的一般积分表达式，进一步将其应用于获得任意阶毛细多极相互作用的力和能量的方便渐近公式。与之前发表的公式相比，新的解析表达式具有更广泛的有效性。它们不仅适用于比毛细长度小得多的颗粒间距离，也适用于可与毛细长度相比或大于毛细长度的距离。
