Dynamics of a climbing surfactant-laden film - I: Base-state flow

► We model the dynamics of a surfactant-laden film climbing up an inclined plane. ► Using lubrication theory we obtain a 2-D evolution equation for the film height. ► The base flow is examined by carrying out a parametric study on the 1-D solutions. ► Competition between 2 forces is observed: Marangoni forces and gravity effects. ► The spreading of the surface-tension-induced ridges exhibits a power-law relation.