© 2019 by the authors. The evolution of a thin liquid film subject to a volatile solvent source and an air-blow effect which modifies locally the surface tension and leads to Marangoni-induced flow is shown to be governed by a degenerate fourth order nonlinear parabolic h-evolution equation of the type given by ∂th = -divx - M1 (h) ∂3 xh +M2 (h) ∂xh +M3 (h) ) , where the mobility termsM1 (h) and M2 (h) result from the presence of the source andM3 (h) results from the air-blow effect. Various authors assumeM2 (h) ≈ 0 and exclude the air-blow effect intoM3 (h). In this paper, the authors show that such assumption is not necessarily correct, and the inclusion of such effect does disturb the dynamics of the thin film. These emphasize the importance of the full definition→t ≈ grad (γ) = gradx (γ)+∂xh grady (γ) of the surface tension gradient at the free surface in contrast to the truncated expression→t grad (γ) ≈ gradx (g) employed by those authors and the effect of the air-blow flowing over the surface.