Theory of the forced wetting transition

We consider a solid plate being withdrawn from a bath of liquid which it does not wet. At low speeds, the meniscus rises below a moving contact line, leaving the rest of the plate dry. At a critical speed of withdrawal, this solution bifurcates into another branch via a saddle-node bifurcation: two branches exist below the critical speed, the lower branch is stable, the upper branch is unstable. The upper branch eventually leads to a solution corresponding to film deposition. We add the local analysis of the upper branch of the bifurcation to a previous analysis of the lower branch. We thus provide a complete description of the dynamical wetting transition in terms of matched asymptotic expansions