{"title":"两个蒸发小水滴的引力相互作用","authors":"Michael Rother","doi":"10.1007/s41810-024-00243-7","DOIUrl":null,"url":null,"abstract":"<div><p>The effect of evaporation on relative trajectories of two spherical drops sedimenting due to gravity in air is investigated. Theoretical analysis and numerical simulation of the interactions are used to obtain results. Several assumptions are made in the model. The drops remain small enough that the Reynolds number, which is linear in the density of the surrounding fluid, is negligible. However, the Stokes number, which is proportional to droplet mass and is a measure of drop inertia, can be much larger than one. Another restriction is that evaporation is dominated by diffusion and that convection of mass is insignificant. In analyzing evaporation when two drops are present, it is noted that the loss of mass is not the same at each point on a droplet surface. That is, evaporation is non-uniform in a spatial sense. In order to maintain the required spherical drop shape, three approaches, involving the isolated droplet and bispherical coordinate solutions, were taken to determine the mass flux due to evaporation and subsequently the drop position at each time step. For a pair of water drops with radii between 2 and 30 <span>\\(\\upmu\\)</span>m, the following conclusions were obtained. In all three methods, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. Most importantly, in comparing critical horizontal offsets, when both attractive molecular forces and Maxwell slip are considered, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential.</p></div>","PeriodicalId":36991,"journal":{"name":"Aerosol Science and Engineering","volume":"9 1","pages":"52 - 66"},"PeriodicalIF":1.6000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gravitational Interactions of Two Small Evaporating Drops\",\"authors\":\"Michael Rother\",\"doi\":\"10.1007/s41810-024-00243-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The effect of evaporation on relative trajectories of two spherical drops sedimenting due to gravity in air is investigated. Theoretical analysis and numerical simulation of the interactions are used to obtain results. Several assumptions are made in the model. The drops remain small enough that the Reynolds number, which is linear in the density of the surrounding fluid, is negligible. However, the Stokes number, which is proportional to droplet mass and is a measure of drop inertia, can be much larger than one. Another restriction is that evaporation is dominated by diffusion and that convection of mass is insignificant. In analyzing evaporation when two drops are present, it is noted that the loss of mass is not the same at each point on a droplet surface. That is, evaporation is non-uniform in a spatial sense. In order to maintain the required spherical drop shape, three approaches, involving the isolated droplet and bispherical coordinate solutions, were taken to determine the mass flux due to evaporation and subsequently the drop position at each time step. For a pair of water drops with radii between 2 and 30 <span>\\\\(\\\\upmu\\\\)</span>m, the following conclusions were obtained. In all three methods, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. Most importantly, in comparing critical horizontal offsets, when both attractive molecular forces and Maxwell slip are considered, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential.</p></div>\",\"PeriodicalId\":36991,\"journal\":{\"name\":\"Aerosol Science and Engineering\",\"volume\":\"9 1\",\"pages\":\"52 - 66\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aerosol Science and Engineering\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s41810-024-00243-7\",\"RegionNum\":4,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ENVIRONMENTAL SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aerosol Science and Engineering","FirstCategoryId":"93","ListUrlMain":"https://link.springer.com/article/10.1007/s41810-024-00243-7","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
Gravitational Interactions of Two Small Evaporating Drops
The effect of evaporation on relative trajectories of two spherical drops sedimenting due to gravity in air is investigated. Theoretical analysis and numerical simulation of the interactions are used to obtain results. Several assumptions are made in the model. The drops remain small enough that the Reynolds number, which is linear in the density of the surrounding fluid, is negligible. However, the Stokes number, which is proportional to droplet mass and is a measure of drop inertia, can be much larger than one. Another restriction is that evaporation is dominated by diffusion and that convection of mass is insignificant. In analyzing evaporation when two drops are present, it is noted that the loss of mass is not the same at each point on a droplet surface. That is, evaporation is non-uniform in a spatial sense. In order to maintain the required spherical drop shape, three approaches, involving the isolated droplet and bispherical coordinate solutions, were taken to determine the mass flux due to evaporation and subsequently the drop position at each time step. For a pair of water drops with radii between 2 and 30 \(\upmu\)m, the following conclusions were obtained. In all three methods, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. Most importantly, in comparing critical horizontal offsets, when both attractive molecular forces and Maxwell slip are considered, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential.
期刊介绍:
ASE is an international journal that publishes high-quality papers, communications, and discussion that advance aerosol science and engineering. Acceptable article forms include original research papers, review articles, letters, commentaries, news and views, research highlights, editorials, correspondence, and new-direction columns. ASE emphasizes the application of aerosol technology to both environmental and technical issues, and it provides a platform not only for basic research but also for industrial interests. We encourage scientists and researchers to submit papers that will advance our knowledge of aerosols and highlight new approaches for aerosol studies and new technologies for pollution control. ASE promotes cutting-edge studies of aerosol science and state-of-art instrumentation, but it is not limited to academic topics and instead aims to bridge the gap between basic science and industrial applications. ASE accepts papers covering a broad range of aerosol-related topics, including aerosol physical and chemical properties, composition, formation, transport and deposition, numerical simulation of air pollution incidents, chemical processes in the atmosphere, aerosol control technologies and industrial applications. In addition, ASE welcomes papers involving new and advanced methods and technologies that focus on aerosol pollution, sampling and analysis, including the invention and development of instrumentation, nanoparticle formation, nano technology, indoor and outdoor air quality monitoring, air pollution control, and air pollution remediation and feasibility assessments.