Slip-induced suppression of Marangoni film thickening in surfactant-retarded Landau-Levich-Bretherton flows

We report that the well-known Marangoni film thickening in surfactant-laden Landau-Levich-Bretherton coating flow can be completely suppressed by wall slip. The analysis is made by mainly looking at how the deposited film thickness varies with the capillary number and the dimensionless slip length in the presence of a trace amount of insoluble surfactant, where is the slip length and is the radius of the meniscus. When slip effects are weak at sufficiently large (but still ) such that , the film thickness can still vary as and be thickened by surfactant as if wall slip were absent. However, when slip effects become strong by lowering to , the film, especially when surface diffusion of surfactant is negligible, does not get thinner according to the strong-slip quadratic law reported previously (Liao et al., Phys. Rev. Lett., vol. 111, 2013, 136001; Li et al., J. Fluid Mech., vol. 741, 2014, pp. 200-227). Instead, the film behaves as if both surfactant and wall slip were absent, precisely following the no-slip law without surfactant. Effects of surface diffusion are also examined, revealing three distinct regimes as is varied from small to large values: the strong-slip quadratic scaling without surfactant, the no-slip scaling without surfactant and the film thickening along the no-slip scaling with surfactant. An experiment is also suggested to test the above findings.