Building on the recent theoretical work of Wray et al. [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 nonuniform densities of the contact-line deposits (often referred to as “coffee stains” or “ring stains”) left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighboring droplets interact via their vapour fields, which results in a spatially nonuniform “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 [Colloids Surf. A Physicochem. Eng. Asp. 482, 562 (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.

中文翻译：

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来自多个蒸发液滴的接触线沉积物

基于 Wray等人最近的理论工作。[ J. 流体机械。 884, A45 (2020)] 关于多个相互靠近的细小液滴的竞争性扩散限制蒸发，我们获得了接触线沉积物空间不均匀密度的理论预测（通常称为“咖啡渍”或“环状污渍”）在含有悬浮固体颗粒的液滴完全蒸发后留在基材上。相邻的液滴通过它们的蒸气场相互作用，导致空间不均匀的“屏蔽”效应。我们对来自一对相同液滴的沉积物进行预测，这表明在液滴最靠近的地方沉积物减少最多，并且与 Pradhan 和 Panigrahi [ Colloids Surf. 的 实验结果具有极好的定量一致性。物理化学。英。ASP 482, 562 (2015)]。我们还对排列在等边三角形中的三重相同液滴给出了相应的预测，这表明在这种情况下屏蔽对沉积物的影响更加微妙。