We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect.

中文翻译：

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单个和多个浸没的固着液滴的对流主导溶解

我们对单个和多个液滴的溶解进行了数值研究，其中液滴由溶解在密度较大的宿主液体中的较轻液体组成。浮力的重要性由瑞利数 Ra 量化，瑞利数 Ra 是浮力超过粘性阻尼力。在这项研究中，Ra 跨越了从 0.1 到 400 的近四个十年。我们关注质量通量（以舍伍德数 Sh 为特征）和流动形态如何依赖于 Ra。对于单液滴溶解，我们首先展示了 Sh(Ra) 标度从恒定值到 $Sh\sim Ra^{1/4}$ 的转变，这证实了 Dietrich 等人的实验结果。（J. Fluid Mech.，第 794 卷，2016 年，第 45--67 页）。两种不同的状态，即扩散主导和对流主导的状态，表现出不同的流动形态：当 Ra>=10 时，清晰可见的漂浮羽流与低 Ra 下的纯扩散情况形成鲜明对比。对于多液滴溶解，众所周知的屏蔽效应在低 Ra 时发挥作用，因此与单液滴情况相比，溶解速度更慢。然而，在高 Ra 下，对流变得越来越占优势，因此集体羽流增强了质量通量，并且多个液滴的溶解速度明显快于单个液滴。Laghezza 等人的实验也发现了这一点。（软物质，第 12 卷，2016 年，第 5787--5796 页）。我们通过形成单个更大的羽流而不是几个单独的羽流来解释这种增强。此外，存在一个使增强最大化的最佳 Ra，因为单个羽流在 Ra 较大时更窄，从而阻碍了增强。