  Building on the recent theoretical work of Wray, Duffy and Wilson [J. Fluid
Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation
of multiple thin sessile droplets in proximity to each other, we obtain
theoretical predictions for the spatially non-uniform densities of the
contact-line deposits (often referred to as "coffee stains" or "ring stains")
left on the substrate after droplets containing dispersed solid particles have
completely evaporated. Neighbouring droplets interact via their vapour fields,
which results in a spatially non-uniform "shielding" effect. We give
predictions for the deposits from a pair of identical droplets, which show that
the deposit is reduced the most where the droplets are closest together, and
demonstrate excellent quantitative agreement with experimental results of
Pradhan and Panigrahi [Coll. Surf. A 482, 562-567 (2015)]. We also give
corresponding predictions for a triplet of identical droplets arranged in an
equilateral triangle, which show that the effect of shielding on the deposit is
more subtle in this case.
