Growth of a fluid-infused patch from droplet drainage into a thin porous layer

Abstract

Growth of a fluid-infused patch on a thin porous layer, e.g. on a piece of paper or cloth, is related to the transmission of virus particles through exhaled droplets and aerosols. We present a theoretical model to describe how a wet patch develops gradually through imbibition, once a sessile droplet attaches at a permeable surface and drains gradually into a thin porous layer. Two limiting cases are considered based on different assumptions on the motion of the contact line during the coupled process of drop drainage and patch growth: (i) the apparent contact angle remains unchanged, so the radius of a sessile droplet decreases with time; and (ii) the location of the contact line remains pinned, so the contact angle decreases as time progresses. The model leads to evolution pathways for both the droplet and the fluid film within the porous layer, without introducing arbitrary fitting parameters. Potential implications of the model and its solutions are also discussed briefly in the context of the outspread of COVID-19, employing physical parameters for exhaled droplets, paper and cloth.