The asymptotic description of the moving contact line as a textbook singular perturbation problem: cracking an old nut

We revisit the classical matched asymptotic analysis of the moving contact line, a problem that has received considerable attention for several decades. The prevalent solution to the problem, considered classical now, involves a three-region asymptotic structure with an intermediate region deemed necessary as the inner and outer regions do not directly match. In this work, we describe why this classical solution is not the end of the story. In fact, we show that the textbook singular perturbation method of matching overlapping outer and boundary layer regions directly applies even to the moving contact line problem, thus correcting a several decades misconception.