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In particular, the growth of cloud droplets across the size gap from 10 to 50 \u03bcm in radius has not been fully explained. In this paper, the authors investigate the growth of cloud droplets by collision\u2013coalescence, taking into account both the gravitational mechanism and several enhancements of the collision\u2013coalescence rate due to air turbulence. The kinetic collection equation (KCE) is solved with an accurate bin integral method and a newly developed parameterization of turbulent collection kernel derived from direct numerical simulation of droplet-laden turbulent flows. Three other formulations of the turbulent collection kernel are also considered so as to assess the dependence of the rain initiation time on the nature of the collection kernel. The results are compared to the base case using the Hall hydrodynamical\u2013gravitational collection kernel. Under liquid water content and eddy dissipation rate values typical of small cumulus clouds, it is found that air turbulence has a significant impact on the collection kernel and thus on the time required to form drizzle drops. With the most realistic turbulent kernel, the air turbulence can shorten the time for the formation of drizzle drops by about 40% relative to the base case, applying measures based on either the radar reflectivity or the mass-weighted drop size. A methodology is also developed to unambiguously identify the three phases of droplet growth, namely, the autoconversion phase, the accretion phase, and the larger hydrometeor self-collection phase. The important observation is that even a moderate enhancement of collection kernel by turbulence can have a significant impact on the autoconversion phase of the growth.<\/jats:p>","DOI":"10.1175\/2007jas2406.1","type":"journal-article","created":{"date-parts":[[2008,2,19]],"date-time":"2008-02-19T20:01:12Z","timestamp":1203451272000},"page":"331-356","source":"Crossref","is-referenced-by-count":88,"title":["Growth of Cloud Droplets by Turbulent Collision\u2013Coalescence"],"prefix":"10.1175","volume":"65","author":[{"given":"Yan","family":"Xue","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, Delaware"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lian-Ping","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, Delaware"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wojciech W.","family":"Grabowski","sequence":"additional","affiliation":[{"name":"Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research,* Boulder, Colorado"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"12","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"2020061122464151100_i1520-0469-65-2-331-Arenberg1","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1175\/1520-0477-20.10.444","article-title":"Turbulence as a major factor in the growth of cloud droplets.","volume":"20","author":"Arenberg","year":"1939","journal-title":"Bull. 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The impact parameters for collision and disruption of 300 and 60 \u03bc radius droplets over a charge range from 10\u221215 to 10\u221212 C per droplet, and with impact velocity from 1 to 8 m\/sec are reported. It is found that for droplets in this size and velocity range, electric charge on the droplets has no appreciable effect on the collision and coalescence process. However, the impact velocity and the impact parameter of the droplets dramatically affect the stability of the coalesced droplet. For 60 \u03bc droplets, all collisions coalesce and form one droplet if the impact velocity is less than 2.2 m\/sec. As the impact velocity is increased, the impact parameter for which only one droplet is produced after collision decreases and the all other collisions disrupt into several droplet fragments. 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Although it is well known that surface charge can affect coalescence rates of Brownian particles in a quiescent medium, no studies have been found in the literature which explicitly examine charge effects on larger drops in turbulent media.<\/jats:p><jats:p>Results demonstate that drop charge can substantially inhibit coalescence between drops in agitated dispersions. Moreover, this effect can arise solely from latent drop charges, which are attributed to the preferential adsorption of hydroxide ions onto the water\u2010organic phase interface. Ionic strength and pH thus are shown to play a major role in determining coalescence rates between agitated drops.<\/jats:p><jats:p>Results also demonstrate that reliance on measurement of average drop sizes for the purpose of determining coalescence rate dependencies is a precarious practice. Strong size\u2010dependent effects such as obtained here have the potential to suggest erroneous conclusions when conclusions are based on measurements of average drop sizes rather than of drop\u2010size distributions.<\/jats:p>","DOI":"10.1002\/aic.690380807","type":"journal-article","created":{"date-parts":[[2004,6,23]],"date-time":"2004-06-23T03:16:25Z","timestamp":1087960585000},"page":"1199-1205","source":"Crossref","is-referenced-by-count":35,"title":["Coalescence of charged droplets in agitated liquid\u2010liquid dispersions"],"prefix":"10.1002","volume":"38","author":[{"given":"T.","family":"Tobin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Ramkrishna","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2004,6,17]]},"reference":[{"key":"e_1_2_1_2_1","volume-title":"Principles of Colloid and Surface Chemistry","author":"Hiemenz P. 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Recent experimental findings have demonstrated that an elevation in ambient pressure initially facilitates the bouncing behavior of colliding water droplets, and this facilitative effect essentially plateaus as the ambient pressure continues to rise. In this work, we extended the experimental working fluid from water to glycerol aqueous solutions with different Ohnesorge (Oh) number and verified the universality of this phenomenon in the collision processes of different types of droplets. Furthermore, based on high-resolution droplet collision images, we clarified the variation law of the shape factor \u03d5 (which characterizes the degree of droplet deformation in Estrade et al.'s model) with the impact parameter B. By introducing empirical coefficients, we completed the fitting of the droplet deformation shape factor with ambient pressure under head-on collision conditions \u03d5B=0. 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All rights reserved.","name":"copyright","label":"Copyright"}]},{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T21:06:10Z","timestamp":1765487170649,"version":"3.41.2"},"reference-count":32,"publisher":"AIP Publishing","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52207158"],"award-info":[{"award-number":["52207158"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"published-print":{"date-parts":[[2025,1,1]]},"abstract":"<jats:p>Droplet collision and growth are common phenomena. While charge and electric fields can promote the droplet collision process, the impact of field intensity and high charge on droplet collision characteristics, as in thunderclouds, is not well understood. This paper presents a trajectory model to study the collision characteristics of a neutral droplet and a charged droplet with varying amounts of charge under various electric field intensities. The findings reveal a transition stage in collision efficiency as the electric field E increases, related to droplet size variation. During this transition stage (about E\u2009=\u20097.5\u2009\u00d7\u2009102 V\u22c5m\u22121 to 7.5\u2009\u00d7\u2009104 V\u22c5m\u22121), there is a peak in the collision efficiency of highly charged and neutral droplets as the neutral droplet size increases. Conversely, at other electric fields (near 102 V\u22c5m\u22121 and between 7.5\u2009\u00d7\u2009104 V\u22c5m\u22121 and 107 V\u22c5m\u22121), a larger neutral droplet is advantageous for enhancing the collision efficiency, increasing the collision probability. Throughout the range from 102 V\u22c5m\u22121 to 107 V\u22c5m\u22121, a larger neutral droplet is beneficial for enhancing the collision kernel, raising the collision frequency. An increase in charge significantly enhances both collision efficiency and kernel. For a micrometer-sized charged-neutral droplet pair, collision efficiency initially decreases (disturbance effect) and then slightly rises to about 1.0 (inertial effect) with the electric field at a constant droplet size ratio. In addition, the impact of droplet size on collision characteristics was investigated, and the collision characteristics of two neutral droplets were compared. 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Here, we unveil the surfactant mass transport mechanism and report on several major differences in the coalescence of surfactant-laden droplets as compared to pure water droplets by means of molecular dynamics simulation of a coarse-grained model. Large-scale changes to bridge growth dynamics are identified, such as the lack of multiple thermally excited precursors, attenuated collective excitations after contact, slowing down in the inertial regime due to aggregate-induced rigidity and reduced water flow, and a slowing down in the coalescence rate (deceleration) when surfactant concentration increases, while at the same time, we also confirm the existence of an initial thermal, and a power-law, inertial, regime of the bridge growth dynamics in both the pure and the surfactant-laden droplets. 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