Asymptotic methods yield an efficient leading-order model of flow along a thin curved duct. The flow consists of a primary axial component along the duct and, because of the curvature, a secondary “Dean flow” in the cross section. Such flows are used in microfluidics to sort suspended particles by size; an important application is “liquid biopsy”, the isolation of a particular cell type within a (dilute) cell suspension. A description of the background flow, in the absence of particles, is pre-requisite to modelling the perturbation caused by a particle and the migration of the particle within the duct cross-section. I will discuss the suitability of a thin-film model for this purpose. Time permitting, I will also discuss the use of asymptotic methods for modelling of particle migration.