Multipolar expansion of the electrostatic interaction between charged colloids at interfaces

Abstract

The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic interaction terms arise only for higher powers $d^{-n}$ with $n\ge 4$.

6 pages, mathematical details added

References in corpus (6)

• Effective capillary interaction of spherical particles at fluid interfaces
• Long-range electrostatic interactions between like-charged colloids: steric and confinement effects
• 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
• Theory of capillary-induced interactions beyond the superposition approximation

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• Phase coexistence in a monolayer of active particles induced by Marangoni flows
• Signature of the time-dependent hydrodynamic interactions on the collective diffusion in colloidal monolayers
• Electrostatic pair-interaction of nearby metal or metal-coated colloids at fluid interfaces
• Ionic self-phoresis maps onto correlation-induced self-phoresis