Following the application of a Liquid coating to a curved substrate, surface tension forces will act to redistribute the coating layer. The coating will thin at outside corners and thicken at inside earners as the free surface contracts to minimize the surface energy. If the coating is a multicomponent liquid with a volatile component, the dynamics of the thinning process may be quite complex. Compositional changes in the bulk liquid during drying and convection of surfactant may cause surface tension gradient or Marangoni effects. In addition there may be viscosity variations due to concentration changes and the liquid may exhibit shear-thinning theology. A numerical model has been developed, based on the lubrication approximations, for predicting the time-evolution of the coating layer thickness of a complex liquid on a curved substrate. Substrate geometry is modeled as a time-independent overpressure distribution and the model. includes such effects as evaporation, convection, and diffusion of solvent in the bulk liquid, and convection and diffusion of a soluble surfactant. For a given starting profile and substrate geometry, the temporal and spatial evolution of the free surface, bulk composition, surfactant concentration, surface tension, and layer-averaged viscosity are calculated until the drying process is complete. We show that convection of surfactant away from outside corners may slow the thinning in these regions. In addition, solvent evaporation may lead to Marangoni forces in the corner region, causing a "rebound" effect. Surface tension forces will initially displace liquid from corner regions, but the thinning will produce surface tension gradients which act to pull liquid back to the corner region. If the evaporation time scale is suitably matched to the time scale for flow induced by surface tension gradients, corner defects in the final dry coating layer can be substantially mitigated.