  This paper is dedicated to the analysis of a mesoscopic model which describes
sedimentation of inertialess suspensions in a viscous flow at mesoscopic
scaling. The paper is divided into two parts, the first part concerns the
analysis of the transport-Stokes model including a global existence and
uniqueness result for $L^1\cap L^\infty$ initial densities with finite first
moment. We investigate in particular the case where the initial condition is
the characteristic function of the unit ball and show that we recover
Hadamard-Rybczynski result, that is, the spherical shape of the droplet is
preserved in time. In the second part of this paper, we derive a surface
evolution model in the case where the initial shape of the droplet is
axisymmetric. We obtain a 1D hyperbolic equation including non local operators
that are linked to the convolution formula with respect to the singular Green
function of the Stokes equation. We present a local existence and uniqueness
result and show that we recover the Hadamard-Rybczynski result as long as the
modelling is well defined and finish with numerical simulations in the
spherical case.
