Theory of capillary-induced interactions beyond the superposition approximation

Abstract

Within a general theoretical framework we study the effective, deformation-induced interaction between two colloidal particles trapped at a fluid interface in the regime of small deformations. In many studies, this interaction has been computed with the ansatz that the actual interface configuration for the pair is given by the linear superposition of the interface deformations around the single particles. Here we assess the validity of this approach and compute the leading term of the effective interaction for large interparticle separation beyond this so-called superposition approximation. As an application, we consider the experimentally relevant case of interface deformations owing to the electrostatic field emanating from charged colloidal particles. In mechanical isolation, i.e., if the net force acting on the total system consisting of the particles plus the interface vanishes, the superposition approximation is actually invalid. The effective capillary interaction is governed by contributions beyond this approximation and turns out to be attractive. For sufficiently small surface charges on the colloids, such that linearization is strictly valid, and at asymptotically large separations, the effective interaction does not overcome the direct electrostatic repulsion between the colloidal particles.

Minor typos corrected

References in corpus (5)

• Effective capillary interaction of spherical particles at fluid interfaces
• Charge renormalization for effective interactions of colloids at water interfaces
• Electric-field induced capillary interaction of charged particles at a polar interface
• Attractions between charged colloids at water interfaces
• Capillary-induced interactions between colloids at an interface

Cited by in corpus (6)

• Force balance of particles trapped at fluid interfaces
• Interaction of Charged Colloidal Particles at the Air-Water Interface
• Multipolar expansion of the electrostatic interaction between charged colloids at interfaces
• Effective interactions of colloids on nematic films
• Free energy of colloidal particles at the surface of sessile drops
• Electrostatic interaction between colloidal particles trapped at an electrolyte interface