On the theory for the arrest of an advancing molten contact line on a cold solid of the same material

We show that a conventional continuum formulation of the equations and boundary conditions for the spreading of a pure molten material over a cold, solid substrate of its own kind has no meaningful solution for the angle of attack theta(s) of the fusion front at the contact line, which is the quantity that determines contact-line arrest. theta(s) is determined by the heat flux just behind the contact line, and the heat flux in the mathematical model is singular at the contact line. The scale of the physical mechanism which limits the heat flux at the contact line and removes the singularity is estimated by computing the point where the continuum model must be cutoff in order to bring it into agreement with the experimental data for a microcrystalline wax. The cutoff scale is in the range 0.1-1 mu m, that is, much larger than molecular dimensions, but of order 10(-2)-10(-1) times the convective thermal length scale alpha/U. (C) 1997 American Institute of Physics.