Capillary interactions among spherical particles at curved liquid interfaces

Abstract

We study the effect of interfacial curvature on the binding energy and forces exerted on small spherical particles that adsorb on an interface between two immiscible liquids. When the interface has anisotropic curvature, the constant-contact-angle condition at the particle-fluid boundary requires a deformation of the interface. Focusing on the case of an initially cylindrical interface, we predict the shape after a spherical particle binds. We then calculate the energy of adsorption and find that it depends on the shape of the interface very far from the binding site. Turning to the problem of two adsorbed spherical particles, we predict a capillary interaction that arises purely from the deformations caused by the contact-angle condition. An analogy is made between these curvature-induced capillary forces and electrostatic forces between quadrupoles in two dimensions. We conclude with a conjectured general form for the interaction of a single spherical particle with the Gaussian curvature of the underlying fluid interface, which we compare to previous work.

Capillarity-induced ordering of spherical colloids on an interface with anisotropic curvature

“…In this case, it is no longer possible for an adsorbed particle to satisfy a uniform contact angle along the contact line without distorting the interface. Although it has been predicted that the distortion of an anisotropically curved interface leads to anisotropic capillary interactions between otherwise isotropic colloidal particles (24,25), this has not been rigorously investigated experimentally. Here, we investigate how these interactions govern the self-assembly of particles adsorbed to interfaces of various different shapes.…”

The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations

“…A widely used approach to calculate a minimum energy surface is by means of the Surface Evolver program. 42 But several other approaches, both theoretical and numerical, have been used for studying the fluid-fluid interface shape in different physical problems, e.g., menisci shapes and capillary interactions, [43][44][45][46][47][48][49][50][51][52] droplet shapes, [53][54][55][56][57] diffuse interfaces, [58][59][60] or fluid-fluid interfaces in contact with deformable solids. [61][62][63] In this article, we introduce a new numerical method to obtain the minimum-energy shape of a fluid-fluid interface.…”

General framework for adsorption processes on dynamic interfaces

“…Our formulation incorporates the characterization of the particles by the contact angle and captures the coupled-nonlinear dynamics between particle density and the interfacial location and geometry. The generality of our framework also enables to model surfactants, the incorporation of particles with non-local interactions [12,31] or even of free energies obtained from first principles, such as density functional theory for instance, e.g. [32,33,34,35], while of particular interest would be the extension of the framework to wetting problems, e.g.…”