High-velocity coating flows and other related problems

Abstract

In most studies devoted to dynamic wetting, the viscosity of ambient air is classically neglected in comparison with that of the liquid. However, air entrainment is clearly the limiting factor in high-velocity coating processes (for instance coating of magnetic suspensions). In this context, the three-phase region, i.e. the air wedge in the vicinity of the “triple line”, is investigated. The novel approach of the dynamic wetting problem proposed here consists in taking into account the bearing force created in the air wedge in the dynamic balance of the meniscus. The free surface is such that the triple line is rejected to infinity and the amount of air entrained is predicted in so doing. Due to the form of the problem, the method of matched asymptotic expansions is applied, in the spirit of Park and Homsy's analysis. The analytical results are compared with the corresponding ones obtained by a numerical scheme specifically adapted. The agreement is excellent and we conclude that both methods are relevant to evaluate the amount of air entrained. The form of the results confirms that the problem is of the same nature as that of (i) the motion of a flexible web over a spindle (foil-bearing theory) or of (ii) the drag of a liquid by a moving plate (Landau and Levich problem).