In this paper, we investigate the dynamics of spherical droplets in the presence of a source–sink pair flow field. The dynamics of the droplets is governed by the Maxey–Riley equation with the Basset–Boussinesq history term neglected. We find that, in the absence of gravity, there are two distinct behaviors for the droplets: small droplets cannot go further than a specific distance, which we determine analytically, from the source before getting pulled into the sink. Larger droplets can travel further from the source before getting pulled into the sink by virtue of their larger inertia, and their maximum traveled distance is determined analytically. We investigate the effects of gravity, and we find that there are three distinct droplet behaviors categorized by their relative sizes: small, intermediate-sized, and large. Counterintuitively, we find that the droplets with a minimum horizontal range are neither small nor large, but of intermediate size. Furthermore, we show that in conditions of regular human respiration, these intermediate-sized droplets range in size from a few μm to a few hundred μm. The result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion.

中文翻译：

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球形液滴在源汇流中的分散及其与 COVID-19 大流行的相关性

在本文中，我们研究了在源-汇对流场存在下球形液滴的动力学。液滴的动力学由 Maxey-Riley 方程控制，忽略 Basset-Boussinesq 历史项。我们发现，在没有重力的情况下，液滴有两种不同的行为：小液滴在被拉入水槽之前，距离源头的距离不能超过我们通过分析确定的特定距离。由于惯性较大，较大的液滴在被拉入水槽之前可以从源头移动得更远，并且它们的最大移动距离是通过分析确定的。我们研究了重力的影响，我们发现有三种不同的液滴行为，按它们的相对大小分类：小、中、大。与直觉相反，我们发现具有最小水平范围的液滴既不小也不大，而是中等大小。此外，我们表明，在人类正常呼吸的条件下，这些中等大小的液滴的大小从几微米到几百微米不等。这种液滴的射程非常短的结果可能对解释有关液滴分散的现有数据具有重要意义。