  The migration of a Brownian fluid droplet in a parallel-plate microchannel
was investigated using dissipative particle dynamics computer simulations. In a
Newtonian solvent, the droplet migrated toward the channel walls due to
inertial effects at the studied flow conditions, in agreement with theoretical
predictions and recent simulations. However, the droplet focused onto the
channel centerline when polymer chains were added to the solvent. Focusing was
typically enhanced for longer polymers and higher polymer concentrations with a
nontrivial flow-rate dependence due to droplet and polymer deformability.
Brownian motion caused the droplet position to fluctuate with a distribution
that primarily depended on the balance between inertial lift forces pushing the
droplet outward and elastic forces from the polymers driving it inward. The
droplet shape was controlled by the local shear rate, and so its average shape
depended on the droplet distribution.
