{"title":"液滴碰撞的临界电荷","authors":"A. Dubey, G. P. Bewley, K. Gustavsson, B. Mehlig","doi":"10.1103/physrevfluids.9.074302","DOIUrl":null,"url":null,"abstract":"Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>20</mn><mspace width=\"0.16em\"></mspace><mi>µ</mi><mi mathvariant=\"normal\">m</mi></mrow></math>, we observe that the transition occurs at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>∼</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></math> elementary charges <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>e</mi></math>. For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Kn</mi></math>, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Kn</mi></math>. For droplets charged with the same polarity, we find the critical charge to be substantially larger (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>∼</mo><msup><mn>10</mn><mn>4</mn></msup><mspace width=\"0.16em\"></mspace><mi>e</mi></mrow></math> for the above radii) for reasons that we discuss.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Critical charges for droplet collisions\",\"authors\":\"A. Dubey, G. P. Bewley, K. Gustavsson, B. Mehlig\",\"doi\":\"10.1103/physrevfluids.9.074302\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mn>20</mn><mspace width=\\\"0.16em\\\"></mspace><mi>µ</mi><mi mathvariant=\\\"normal\\\">m</mi></mrow></math>, we observe that the transition occurs at <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mo>∼</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></math> elementary charges <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>e</mi></math>. For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>Kn</mi></math>, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>Kn</mi></math>. For droplets charged with the same polarity, we find the critical charge to be substantially larger (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mo>∼</mo><msup><mn>10</mn><mn>4</mn></msup><mspace width=\\\"0.16em\\\"></mspace><mi>e</mi></mrow></math> for the above radii) for reasons that we discuss.\",\"PeriodicalId\":20160,\"journal\":{\"name\":\"Physical Review Fluids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review Fluids\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevfluids.9.074302\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review Fluids","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevfluids.9.074302","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and , we observe that the transition occurs at elementary charges . For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number (, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon . For droplets charged with the same polarity, we find the critical charge to be substantially larger ( for the above radii) for reasons that we discuss.
期刊介绍:
Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.