Drag on a colloid straddling a fluid interface

We analyze the dynamics of an active colloid moving along the interface between two immiscible fluids with similar viscosity. Under the assumption of a constant three-phase contact angle, we analytically obtain the interfacial deformation around a single particle and numerically the two-particle deformation. Applying the Lorentz reciprocal theorem to the zeroth-order approximation for spherical particles at a flat interface and to the first correction in Capillary number allows us to obtain explicit analytical expressions for the hydrodynamic drag in terms of the zeroth-order approximations and the correction deformations. The drag coefficients are computed as a function of the three-phase contact angle, the viscosity ratio of the two fluids, the Bond number, and the separation distance between the particles.