Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces

Abstract

We develop the scattering formalism to calculate the interaction between colloidal particles trapped at a fluid interface. Since, in addition to the interface, the colloids may also fluctuate in this system, we implement the fluctuation of the boundaries into the scattering formalism and investigate how the interaction between colloids is modified by their fluctuations. This general method can be applied to any number of colloids with various geometries at an interface. We apply the formalism derived in this work to a system of spherical colloids at the interface between two fluid phases. For two spherical colloids, this method very effectively reproduces the previous known results. For three particles we find analytical expressions for the large separation asymptotic energies and numerically calculate the Casimir interaction at all separations. Our results show an interesting three body effect for fixed and fluctuating colloids. While the three body effect strengthens the attractive interaction between fluctuating colloids, it diminishes the attractive force between colloids fixed at an interface.

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Cited by in corpus (9)

• A Materials Perspective on Casimir and van der Waals Interactions
• Critical Casimir Effect: Exact Results
• Conformal Field Theory of Critical Casimir Interactions in 2D
• Three-body critical Casimir forces
• Fluctuation-induced Interactions in Micro- and Nano-systems: Survey of Some Basic Results
• Classification of the sign of the critical Casimir force in two dimensional systems at asymptotically large separations
• Fluctuation-induced forces between rings threaded around a polymer chain under tension
• Reversing the Critical Casimir force by shape deformation
• Casimir Interaction between Polydisperse Colloids Trapped at a Fluid Interface