  We investigate the motion of a suspended non-Brownian sphere past a fixed
cylindrical or spherical obstacle in the limit of zero Reynolds number for
arbitrary particle-obstacle aspect ratios. We consider both a suspended sphere
moving in a quiescent fluid under the action of a uniform force as well as a
uniform ambient velocity field driving a freely suspended particle. We
determine the distribution of particles around a single obstacle and solve for
the individual particle trajectories to comment on the transport of dilute
suspensions past an array of fixed obstacles. First, we obtain an expression
for the probability density function governing the distribution of a dilute
suspension of particles around an isolated obstacle, and we show that it is
isotropic. We then present an analytical expression -- derived using both
Eulerian and Lagrangian approaches -- for the minimum particle-obstacle
separation attained during the motion, as a function of the incoming impact
parameter, i.e. the initial offset between the line of motion far from the
obstacle and the coordinate axis parallel to the driving field. Further, we
derive the asymptotic behaviour for small initial offsets and show that the
minimum separation decays exponentially. Finally we use this analytical
expression to define an effective hydrodynamic surface roughness based on the
net lateral displacement experienced by a suspended sphere moving past an
obstacle.
