Dip-Coating: Levelling the Contact Line Using Corner Rounding and Surface Roughening

If a rectangular object is dipped into a liquid, the contact line normally rises up the surface and dips near the corner, often an undesirable outcome in an industrial dip-coating context. Is it possible to round the corners of the object in such a way that the contact line curve becomes horizontal? We find that just rounding the corner is not sufficient to accomplish this, but by additionally roughening the surface in a prescribed way, one can indeed achieve the desired horizontal contact line.