Making a deposit: the role of substrate adsorption in coffee-ring formation in sessile evaporating droplets

A thin, evaporating sessile droplet with a pinned contact line containing inert particles is considered. In the limit in which the liquid flow decouples from the particle transport, we discuss the interplay between particle advection, diffusion and adsorption onto the solid substrate on which the droplet sits. We perform an asymptotic analysis in the physically relevant regime in which the Péclet number is large, i.e. ${\textit{Pe}}\gg 1$ , so that advection dominates diffusion in the droplet except in a boundary layer near the contact line, and in which the ratio of the particle velocities due to substrate adsorption and diffusion is at most of order unity as ${\textit{Pe}}\rightarrow \infty$ . We use the asymptotic model alongside numerical simulations to demonstrate that substrate adsorption leads to a different leading-order distribution of particle mass compared with cases with negligible substrate adsorption, with a significant reduction of the mass in the suspension – the nascent coffee ring reported in Moore et al. ( J. Fluid Mech. , vol. 920, 2021, A54). The redistribution leads to an extension of the validity of the dilute suspension assumption, albeit at the cost of breakdown due to the growth of the deposited layer, which are important considerations for future models that seek to accurately model the porous deposit regions.