The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Bouncing, coalescence, and separation in head-on collision of unequal-size droplets
Abstract
The dynamics of head-on collision of unequal-size droplets were experimentally and theoretically investigated, with emphasis on identifying distinct collision outcomes and interpreting the size-ratio dependence. A unified regime diagram in terms of bouncing, permanent coalescence, and separation after coalescence was identified for hydrocarbon and water droplets in the parameter space of the size ratio and a collision Weber number. Experimental results show that the transition Weber number, Web-c, that separates the bouncing and permanent coalescence regimes, weakly depends on the size ratio, while the transition Weber number, Wec-s, that separates permanent coalescence and separation regimes, significantly increases with the size ratio. A theoretical model based on energy balance and scaling analysis was developed to explain the size-ratio dependence of Wec-s. The theoretical results show good agreement with the experimental data for tetradecane and decane droplets, with a moderate discrepancy for water droplets.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“The results show that β = 0.7 for water droplets (α is not defined here because the bouncing outcome is absent for pure water droplet collision in the atmosphere environment), α = 0.25 and β = 0.8 for decane droplets, and α = 0.65 and β = 1.4 for tetradecane droplets.”
From Droplet collision of hypergolic propellants (2024) · cites this paper as [24]
Citations
Cites
Regimes of coalescence and separation in droplet collision
QIAN, J., & LAW, C. K. (1997) · Journal of Fluid Mechanics · doi:10.1017/s0022112096003722 · Cited by 841
Self-citationCoalescence and separation in binary collisions of liquid drops
Ashgriz, N., & Poo, J. Y. (1990) · Journal of Fluid Mechanics · doi:10.1017/s0022112090003536 · Cited by 753
Current status of droplet and liquid combustion
Faeth, G. M. (1977) · Progress in Energy and Combustion Science · doi:10.1016/0360-1285(77)90012-0 · Cited by 624
Formation and cycling of aerosols in the global troposphere
elisabeth, R. F. P., Dingenen, R. V., Vignati, E., Wilson, J., Putaud, J., Seinfeld, J. H., & Adams, P. J. (2000) · Atmospheric Environment · doi:10.1016/s1352-2310(00)00239-9 · Cited by 470
An experimental investigation on the collision behaviour of hydrocarbon droplets
Jiang, Y. J., Umemura, A., & Law, C. K. (1992) · Journal of Fluid Mechanics · doi:10.1017/s0022112092000740 · Cited by 433
Self-citationThe interaction of falling water drops: coalescence
Brazier-Smith, P. R., Jennings, S. G., & Latham, J. (1972) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1972.0016 · Cited by 340
Formation and Cycling of Aerosols in the Global Troposphere
Raes, F. (2002) · Springer eBooks · doi:10.1007/978-94-010-0082-6_3 · Cited by 286
Head-on collision of drops—A numerical investigation
Nobari, M. R. H., Jan, Y.-J., & Tryggvason, G. (1996) · Physics of Fluids · doi:10.1063/1.868812 · Cited by 219
The Collision, Coalescence, and Disruption of Water Droplets
Adam, J. R., Lindblad, N. R., & Hendricks, C. D. (1968) · Journal of Applied Physics · doi:10.1063/1.1655940 · Cited by 187
Raes, F., & Dingenen, R. V. (1992) · Journal of Geophysical Research Atmospheres · doi:10.1029/92jd00961 · Cited by 100
Flagged first, then by citations
Cited by
Sorted by citations
Items 101–164 of 164
An investigation on the impact of two vertically aligned drops on a liquid surface
Paul, A., Ray, B., Sahu, K. C., & Biswas, G. (2023) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2023.104588 · Cited by 7
Chang, X., Gao, J., Chen, Z., Wang, X., He, H., Wu, J., & Hu, E. (2025) · Journal of the Energy Institute · doi:10.1016/j.joei.2025.102396 · Cited by 6
Collision of two drops moving in the same direction
Pal, A. K., Sahu, K. C., De, S., & Biswas, G. (2024) · Physics of Fluids · doi:10.1063/5.0189168 · Cited by 6
Li, Y., Jiang, B., Yang, N., Xiao, X., Sun, Y., & Zhang, L. (2024) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.4c00338 · Cited by 6
Antuono, M., Marrone, S., & Colagrossi, A. (2025) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2025.118014 · Cited by 5
Dynamics of binary droplet collisions
He, C., Zhang, P., & Law, C. K. (2025) · Progress in Energy and Combustion Science · doi:10.1016/j.pecs.2025.101252 · Cited by 5
Self-citationXia, J., Zhang, Q., Wang, J., He, Z., Zhou, Q., Zhou, D., Qian, Y., & Lü, X. (2023) · International Journal of Engine Research · doi:10.1177/14680874231171230 · Cited by 5
Jena, A., & Ágarwal, A. K. (2023) · Physics of Fluids · doi:10.1063/5.0169203 · Cited by 5
Mulbah, C., Kang, C., Song, H., & Yin, J. (2024) · Physics of Fluids · doi:10.1063/5.0187008 · Cited by 5
He, C., He, Z., & Zhang, P. (2023) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2023.104548 · Cited by 5
Self-citationNew insights into impact-induced removal of the deposited droplet
Xie, F.-F., Xin, H., Liu, Q., Yang, Z., Shateri, A., Hong, W., & Liao, M. (2024) · Physics of Fluids · doi:10.1063/5.0240101 · Cited by 4
Bouncing dynamics of binary equal-sized high-viscosity molten glass droplets in head-on collisions
Hu, X., Yu, Z., Tao, L., Zhang, H., & Li, S. (2024) · Physics of Fluids · doi:10.1063/5.0235016 · Cited by 4
Kinetic study of head-on collisions of unequal-sized compound droplets
Zhao, Y., Wang, Z., Yang, Q., Zhang, B., Gao, Q., & Hong, S. (2025) · Physics of Fluids · doi:10.1063/5.0246229 · Cited by 5
Liu, Z., Liang, C., Ma, N., Wei, S., Li, T., & Sun, Q. (2025) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2025.108891 · Cited by 4
Quéré, D. (2012) · Journal of Fluid Mechanics · doi:10.1017/jfm.2012.208 · Cited by 5
Splashing impact of a falling liquid drop
Paul, A., Pal, A. K., Wang, A.-B., & Biswas, G. (2024) · Physics of Fluids · doi:10.1063/5.0230574 · Cited by 3
Leveling-off of droplet bouncing dynamics under high ambient gas pressures
Zhang, C., Zhang, Z., Zhang, P., Zhou, J., & Zhao, C. (2025) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2025.105468 · Cited by 3
Self-citationThermally induced motion, collision and mixing of levitated droplets
Davanlou, A. (2015) · Journal of International Crisis and Risk Communication Research · Cited by 3
Influences of Liquid Viscosity and Relative Velocity on the Head-On Collisions of Immiscible Drops
Chang, J., Xu, R., Cui, J., Song, Q., & Shen, T. (2022) · Energies · doi:10.3390/en15228544 · Cited by 4
Meniscus motion and drop formation in inkjet printing
M.P. Meulen, V. D. (2014) · doi:10.3990/1.9789036538282 · Cited by 3
Numerical study of two equal-sized miscible drops undergoing head-on collision
Singh, S., & Saha, A. (2024) · Physics of Fluids · doi:10.1063/5.0221949 · Cited by 2
Numerical analysis of binary molten glass microspheres droplets co-directional collision behavior
Hu, X., Tao, L., Li, W., Guo, J., Liu, Z., Xie, N., & Tong, B. (2025) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2025.105366 · Cited by 2
A machine learning-based approach to predict the outcome of binary droplet collision
Yu, W., & Chang, S. (2025) · Chemical Engineering Science · doi:10.1016/j.ces.2025.122349 · Cited by 3
Liang, X., Zhang, Z., Xu, Z., & Yue, H. (2025) · Physics of Fluids · doi:10.1063/5.0304464 · Cited by 2
Characterizing the spray under varying ambient pressures for internal-mixing gas-liquid injector
Qiao, W., Yang, X., Wang, S., Deng, Z., Yang, L., & Fu, Q. (2026) · International Journal of Multiphase Flow · doi:10.1016/j.ijmultiphaseflow.2026.105711 · Cited by 2
Dynamics of binary droplet collision in gaseous environment
He, C., & Zhang, P. (2017) · Zhongguo kexue. Wulixue Lixue Tianwenxue · doi:10.1360/sspma2017-00041 · Cited by 2
Self-citationRegimes and Breakup Model of Head-On Collisions of Unequal-Sized Water Nanodroplets
Yin, Z., & Zhang, C. (2025) · Langmuir · doi:10.1021/acs.langmuir.5c00566 · Cited by 2
Atomization and Droplet Dynamics Analysis of Air-assisted Spray under Different Gas-liquid Ratios
Wu, H., Zhang, Z., Xiao, W., & Zhang, F. (2021) · International Conference on Liquid Atomization and Spray Systems (ICLASS) · doi:10.2218/iclass.2021.5851 · Cited by 2
On the dynamics of head-on collision of sessile droplets on the traveling substrate
Li, W., Hu, L., Su, R., Liu, W., & Li, M. (2023) · Colloids and Surfaces A Physicochemical and Engineering Aspects · doi:10.1016/j.colsurfa.2023.132892 · Cited by 2
Coalescence Dynamics of Drops over a Hydrophobic Surface
Somwanshi, P. M., Muralidhar, K., & Khandekar, S. (2020) · Mechanical engineering series · doi:10.1007/978-3-030-48461-3_3 · Cited by 2
Chemically sensitive fluorescence imaging of colliding microdroplets
Quine, Z., Goun, A., Laforge, F. O., RABITZ, H. A., & Law, C. K. (2023) · Physics of Fluids · doi:10.1063/5.0143255 · Cited by 1
Self-citationImpact of Fluid Rheology and Density Ratio in Droplet Collision: A Numerical Investigation
Kant, K., Reddy, S. R., & Banerjee, R. (2024) · Journal of Fluids Engineering · doi:10.1115/1.4066928 · Cited by 1
Liquid flow and interface evolution near the contact line during droplet coalescence
Ma, T., Zhao, Y., Zhou, L., & Du, X. (2024) · International Journal of Heat and Fluid Flow · doi:10.1016/j.ijheatfluidflow.2024.109613 · Cited by 1
Yu, W., & Chang, S. (2024) · Physics of Fluids · doi:10.1063/5.0241247 · Cited by 1
Restrepo-Cano, J., Pérez, F. E. H., & Im, H. G. (2025) · Chemical Engineering Science · doi:10.1016/j.ces.2025.121502 · Cited by 1
Fang, C., Liu, Y., Wang, S., Liu, C., Mu, Y., & Xu, G. (2025) · Physics of Fluids · doi:10.1063/5.0277630 · Cited by 1
Direct numerical simulation of colliding droplets with intervening nonequilibrium gas film
Wang, N., Zhang, Z., Zhang, P., & Zhao, C. (2026) · Acta Mechanica Sinica · doi:10.1007/s10409-025-25492-x · Cited by 1
Self-citationContact Time of Double Unequal-Sized Droplets Simultaneously Impacting Superhydrophobic Surfaces
Gao, S., Shi, L.-K., Huang, X., Wang, Y.-X., Zheng, S.-F., Huang, C., Yang, Y.-R., Han, X., & Wang, X. (2026) · Langmuir · doi:10.1021/acs.langmuir.5c06659 · Cited by 1
Effect of radial fuel staging on atomization in lean-burn gas turbine swirl injectors
Sahu, V., Sampath, R., & Shanmugadas, K. P. (2026) · Aerospace Science and Technology · doi:10.1016/j.ast.2026.112159 · Cited by 1
Droplet breakup and collision dynamics in lean-burn multi-swirl injector sprays
Sahu, V., & Shanmugadas, K. P. (2026) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2026.131354 · Cited by 1
Yang, M., Hou, L.-T., Liu, S., & Xu, J. Q. (2026) · Separation and Purification Technology · doi:10.1016/j.seppur.2026.138796 · Cited by 1
Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision
Leng, Y., He, C., Wang, Q., He, Z., Simms, N. J., & Zhang, P. (2023) · Symmetry · doi:10.3390/sym16010047 · Cited by 1
Self-citationCollision of immiscible droplets on a solid surface
Moradi, M. (2025) · Physics of Fluids · doi:10.1063/5.0257622 · Cited by 1
Amani, A. (2019) · UPCommons institutional repository (Universitat Politècnica de Catalunya) · doi:10.5821/dissertation-2117-167836 · Cited by 1
Qu, Q., Ge, C., Liu, P., & Agarwal, R. K. (2017) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2017-1233
Observation of FRET in collision of droplets
Radhakrishnan, S., Alemán, A., Bhaskaran, P. T., & Hanstorp, D. (2019) · Optical Trapping and Optical Micromanipulation · doi:10.1117/12.2528390
Bu, J., Li, L., Zhang, F., Zhong, S., Liao, X., Liu, Z., Fan, L., & Du, Q. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4535917
A coupled LSVOF-adaptive mesh refinement-moving mesh technique to study complex multiphase problems
Amani, A., Segarra, C. D. P., & Oliva, A. (2023) · International Symposium on Turbulence, Heat and Mass Transfer (THMT) · doi:10.1615/ichmt.thmt-23.1080
A coupled LSVOF-adaptive mesh refinement-moving mesh technique to study complex multiphase problems
Amani, A., Segarra, C. D. P., & Oliva, A. (2023) · International Symposium on Turbulence, Heat and Mass Transfer (THMT) · doi:10.1615/thmt-23.1080
Numerical Investigation of Off-center Collision between Two Equal-sized Water Droplets
Yu, W., Chang, S., & Wang, S. (2024) · Atomization and Sprays · doi:10.1615/atomizspr.2024052913
Bu, J., Li, L., Zhang, F., Zhong, S., Liao, X., Liu, Z., Du, Q., Fan, L., & Jiao, K. (2024) · International Journal of Green Energy · doi:10.1080/15435075.2024.2399786
Schmidt, E. W. (2025) · De Gruyter eBooks · doi:10.1515/9783111331560-001
Zhang, C., Xu, Z., Zhou, J., & Zhang, Z. (2026) · Physics of Fluids · doi:10.1063/5.0310037
Transient self-similar jet evolution in inertial droplets
Senapati, A., Singh, G., & Atta, A. (2026) · Physics of Fluids · doi:10.1063/5.0306182
Dual roles of liquid viscosity in influencing bouncing and coalescence of two identical droplets
Zhang, C., Zhang, Z., Zhang, P., Zhou, J., & Zhao, C. (2026) · Chemical Engineering Science · doi:10.1016/j.ces.2026.123426 · Cited by 1
Self-citationHe, C., Chen, X., Chi, Y., He, Z., & Yue, L. (2026) · Physics of Fluids · doi:10.1063/5.0326178
Time-Resolved Imaging of Droplet Collision in Interacting Sprays
Ghosh, S., & Sahu, S. (2026) · Lecture notes in mechanical engineering · doi:10.1007/978-981-96-9600-0_14
Bounce or coalescence: A physical learning frame
Xu, J. H., & Wang, Z. L. (2026) · Physics of Fluids · doi:10.1063/5.0343886
Coalescence of droplets at microchannel junctions
Lian, H., Hou, X., & Liu, D. (2026) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2026.07.021
Numerical investigation on off-center pursuit collision dynamics of molten glass microbeads
Hu, X., Tao, L., ZHAO, Y., Liu, Z., Tong, B., & 谢能刚 (2026) · Physics of Fluids · doi:10.1063/5.0330712
Zhang, Z., Yang, J., & Fu, L. (2026) · Journal of Computational Physics · doi:10.1016/j.jcp.2026.115250
Sharp-interface level set simulations of binary coalescence dynamics in unequal-sized droplets
Hazourli, H., & Abdelouahab, M. (2026) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-026-08303-2
DNA-decorated phase-shift microdroplets enable programmable coalescence and gene transfection
Perilli, G., Ditri, A., Vitaliti, A., Toumia, Y., Porchetta, A., Paradossi, G., & Domenici, F. (2026) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2026.141646
Metadata
- Authors
- Tang, C., Zhang, P., & Law, C. K.
- Affiliations
- Princeton University (US)
- Venue
- Physics of Fluids
- Publisher
- AIP Publishing
- Published
- 2012-02-01
- Volume
- 24
- Issue
- 2
- ISSN
- 1070-6631 (ISSN-L)
- 1089-7666
- OpenAlex
- W2068744655
- Cited by
- 164
- References
- 15
- Citations by year
- 2026: 17 · 2025: 17 · 2024: 19 · 2023: 21 · 2022: 12 · 2021: 14 · 2020: 10 · 2019: 14 · 2018: 7 · 2017: 12 · 2016: 4 · 2015: 6 · 2014: 6 · 2013: 3 · 2012: 2
- FWCI
- 5.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physics of Fluids (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Heat Transfer
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Electrohydrodynamics and Fluid Dynamics
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Particle Dynamics in Fluid Flows
- Keywords
- droplet collision, head-on collisions, droplet bouncing, energy balance model, scaling analysis, hydrocarbon droplets, water droplets, tetradecane, n-decane
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review