  A micro-hydrodynamics model based on elastic collisions of light point
solvent particles with a heavy solute particle is investigated in the setting
where the light particles have velocity distribution corresponding to a
background flow. Considering a range of stationary background flows and
distributions for the solvent particle velocities, the macroscopic
Langevin-type description of the behaviour of the heavy particle is derived in
the form of a generalized Ornstein-Uhlenbeck process. At leading order, the
drift term in this process depends upon both the geometric structure of the
background flow and the size of the heavy particle, while both drift and
diffusion terms scale with moments of the light particle velocity distribution.
Computational methods for simulating the micro-hydrodynamics model are then
designed to confirm the theoretical results. To enable long-time stochastic
simulations, simulations are performed in a frame co-moving with the heavy
particle. Efficient methods for sampling the position and velocity
distributions of incoming solvent particles at the boundaries of the co-moving
frame are derived for a range of distributions of solvent particles. The
simulations show good agreement with the theoretical results.
