Double-peaked edge-bead in drying film of solvent-resin mixtures

A thick ridge of a film arising along the periphery of a substrate, which is the so-called edge-bead, is investigated experimentally and numerically for the case where the bead becomes double-peaked shape in direction away from the periphery of the substrate. It is clarified, by the optical measurement of thickness variations, that the double-peaked bead is separated from a single bead during the drying process, and after the separation, the inner bead moves inward. This motion of the bead is modeled by a lubrication-approximated flow equation, where the Laplace pressure and the solutocapillary effect are taken into account, coupled with the convective and diffusive mass transfer. The numerically simulated motion of the bead shows a good agreement with that obtained by the experiment, and it is revealed that the mechanism how the double-peaked edge-bead is formed. At the early stage of the drying process, a single bead is formed by the Laplace pressure due to the curvature along the substrate periphery. Along this single bead, the concentration gradient is caused by both the spatial distribution of the evaporation rate and the thickness effect on the change rate of the concentration, due to the fact that the resin concentration increases at a faster rate in the thin region. Consequently, the concentration distribution has a local minimum in the middle of the single bead, which drives oppositely directed solutocapillary flows and separates the bead. After the separation, the inner bead moves inward by a kind of a feed-forward mechanism, until the viscosity of the film becomes large enough to suppress the flow.