  We present an analytical calculation of the hydrodynamic interaction between
two spherical particles near an elastic interface such as a cell membrane. The
theory predicts the frequency dependent self- and pair-mobilities accounting
for the finite particle size up to the 5th order in the ratio between particle
diameter and wall distance as well as between diameter and interparticle
distance. We find that particle motion towards a membrane with pure bending
resistance always leads to mutual repulsion similar as in the well-known case
of a hard-wall. In the vicinity of a membrane with shearing resistance,
however, we observe an attractive interaction in a certain parameter range
which is in contrast to the behavior near a hard wall. This attraction might
facilitate surface chemical reactions. Furthermore, we show that there exists a
frequency range in which the pair-mobility for perpendicular motion exceeds its
bulk value, leading to short-lived superdiffusive behavior. Using the
analytical particle mobilities we compute collective and relative diffusion
coefficients. The appropriateness of the approximations in our analytical
results is demonstrated by corresponding boundary integral simulations which
are in excellent agreement with the theoretical predictions.
