Evaporation-induced flow near a contact line: Consequences on coating and contact angle

We propose a simple model of the dynamics of a contact line under evaporation and partial wetting conditions, taking into account the divergent nature of evaporation near the contact line, as evidenced by Deegan et al. (Nature, 389 (1997) 827). We show that evaporation can induce a non-negligible change of the contact angle together with modification of the flow near the contact line. We apply our results to dip-coating of a substrate with non volatile solutes. We show that at small velocities the coating thickness increases and scales like the inverse of the square of the velocity which implies a minimum of the coating thickness at the cross-over with the more familiar Landau-Levich regime