The levelling of paint films

Using a brush to apply paint to a flat surface almost inevitably means that the bristles of the brush leave behind an uneven paint surface. As the paint dries out, these non-uniformities tend to flatten out to leave a protective and aesthetically pleasing even coating; however, experiments have shown that some solvent-based high-gloss alkyd paints can exhibit more unusual behaviour as they dry. In these experiments the initial rate of levelling was faster than that expected simply due to constant surface tension effects, and, much more unexpectedly, over a timescale of a few minutes the peaks of the original disturbance became troughs and vice versa. In this paper the author presents a mathematical model for the drying of a layer of solvent-based high-gloss alkyd paint and analyses the linear stability of a uniform layer of paint subject to an initial perturbation representing the marks left by a paint brush. Investigating the model highlights the crucial role played by solvent evaporation and leads to a plausible physical explanation of the observed phenomena. Furthermore, the analytical and numerical predictions of the model are found to be in good quantitative agreement with the experimenta