On the transition to dripping of an inverted liquid film

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on periodic domain assuming either fixed fluid volume or rate for hierarchy models: two lubrication models with linearised curvature full (the LCM and FCM, respectively), equations Stokes flow. Of particular interest breakdown travelling-wave solutions as inclination angle increased. For any reaches horizontal state where it attains cosine-shaped profile. sufficiently small volume, FCM attain weak Young-Laplace equilibrium profile, approach which described by asymptotic analysis generalising that Kalliadasis & Chang (1994) LCM. large volumes, bifurcation curves model have turning point so fully inverted never reached. blows up critical well predicted analysis. curve has else surface profile infinite slope singularity, indicating onset multi-valuedness. latter confirmed can be continued obtain overturning profiles. Overall thin-film provide accurate prediction supply upper bound angle.