  The dynamics of particles attached to an interface separating two immiscible
fluids are encountered in a wide variety of applications. Here we present a
combined asymptotic and numerical investigation of the fluid motion past
spherical particles attached to a deformable interface undergoing uniform
creeping flows in the limit of small Capillary number and small deviation of
the contact angle from 90 degrees. Under the assumption of a constant
three-phase contact angle, we calculate the interfacial deformation around an
isolated particle and a particle pair. Applying the Lorentz reciprocal theorem
to the zeroth-order approximation corresponding to spherical particles at a
flat interface and the first correction in Capillary number and correction
contact angle 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. In addition, the
capillary force acting on the particles due to the interfacial deformation is
calculated.
