We study the time evolution and driven motion of thin liquid films lying on top of chemical patterns on a substrate. Lattice-Boltzmann and molecular dynamics methods are used for simulations of the flow of microscopic and nanoscopic films, respectively. Minimization of the fluid surface area is used to examine the corresponding equilibrium free energy landscapes. The focus is on motion across patterns containing diverging and converging flow junctions, with an eye towards applications to lab-on-a-chip devices. Both open liquid–vapor systems driven by body forces and confined liquid–liquid systems driven by boundary motion are considered. As in earlier studies of flow on a linear chemical channel, we observe continuous motion of a connected liquid film across repeated copies of the pattern, despite the appearance of pearling instabilities of the interface. Provided that the strength of the driving force and the volume of the liquid are not too large, the liquid is confined to the chemical channels and its motion can be directed by small variations in the geometry of the pattern.