Dynamics of a climbing surfactant-laden film II: Stability

► We examine the spanwise stability of a surfactant-laden film climbing up a plane. ► Small-amplitude disturbances are introduced in the linearised base-state equations. ► In the constant-flux case the thinnest region is unstable to finger formation. ► For finite-volume spreading, the gravity-force-induced capillary ridge is unstable. ► Increasing the initial micellar concentration leads to stabilising effects.