Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(9): 096803    DOI: 10.1088/1674-1056/ab8ac7

The drying of liquid droplets

Zechao Jiang(姜泽超)1,2, Xiuyuan Yang(杨修远)1,2, Mengmeng Wu(吴萌萌)1,2, Xingkun Man(满兴坤)1,2
1 Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China;
2 School of Physics, Beihang University, Beijing 100191, China
Abstract  The drying of liquid droplets is a common phenomenon in daily life, and has long attracted special interest in scientific research. We propose a simple model to quantify the shape evolution of drying droplets. The model takes into account the friction constant between the contact line (CL) and the substrate, the capillary forces, and the evaporation rate. Two typical evaporation processes observed in experiments, i.e., the constant contact radius (CCR) and the constant contact angle (CCA), are demonstrated by the model. Moreover, the simple model shows complicated evaporation dynamics, for example, the CL first spreads and then recedes during evaporation. Analytical models of no evaporation, CCR, and CCA cases are given, respectively. The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model, and they are all subjected to experimental tests. The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.
Keywords:  evaporation      droplets      Onsager variational principle      contact line motion  
Received:  12 March 2020      Revised:  13 April 2020      Accepted manuscript online:  18 April 2020
PACS:  68.03.Fg (Evaporation and condensation of liquids)  
  45.10.Db (Variational and optimization methods)  
  82.20.Wt (Computational modeling; simulation)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 21822302), the joint NSFC-ISF Research Program, China (Grant No. 21961142020), the Fundamental Research Funds for the Central Universities, China, and the National College Students' Innovative and Entrepreneurial Training Plan Program, China (Grant No. 201910006142).
Corresponding Authors:  Xingkun Man     E-mail:

Cite this article: 

Zechao Jiang(姜泽超), Xiuyuan Yang(杨修远), Mengmeng Wu(吴萌萌), Xingkun Man(满兴坤) The drying of liquid droplets 2020 Chin. Phys. B 29 096803

[1] Deegan R D 2000 Phys. Rev. E 61 475
[2] Bonn D, Eggers J, Indekeu J, Meunier J and Rolley E 2009 Rev. Mod. Phys. 81 739
[3] Deegan R D, Bakajin O, Dupont T F, Huber G, Nagel S R and Witten T A 1997 Nature 389 827
[4] Marín Á G, Gelderblom H, Lohse D and Snoeijer J H 2011 Phys. Rev. Lett. 107 085502
[5] Willmer D, Baldwin K A, Kwartnik C and Fairhurst D J 2010 Phys. Chem. Chem. Phys. 12 3998
[6] Li Y F, Sheng Y J and Tsao H K 2013 Langmuir 29 7802
[7] Li Y F, Sheng Y J and Tsao H K 2014 Langmuir 30 7716
[8] Kajiya T, Monteux C, Narita T, Lequeux F and Doi M 2009 Langmuir 25 6934
[9] Fukuda K, Sekine T, Kumaki D and Tokito S 2013 ACS Appl. Mater. Interfaces 5 3916
[10] Wu M M, Man X K and Doi M 2018 Langmuir 34 9572
[11] Shrikanth V, Archana S and Bobji M S 2019 Meas. Sci. Technol. 30 075002
[12] Yu Y, Zhu H, Frantz J M, Reding M E, Chan K C, Ozkan H E 2009 Biosyst. Eng. 104 324
[13] Li H Y, Tee B C-K, Cha J J, Cui Y, Chung J W, Lee S Y and Bao Z N 2012 J. Am. Chem. Soc. 134 2760
[14] Picknett R G and Bexon R 1977 J. Colloid Interface Sci. 61 336
[15] Bourg'es-Monnier C B and Shanahan M E R 1995 Langmuir 11 2820
[16] Erbil H Y, McHale G and Newton M I 2002 Langmuir 18 2636
[17] Kim J H, Ahn S I and Zin W C 2007 Langmuir 23 6163
[18] Shrikanth V, Archana S and Bobji M S 2019 Meas. Sci. Technol. 30 075002
[19] Wang F C and Wu H A 2013 Soft Matter 9 5703
[20] Liu Y and Zhang X 2013 Phys. Rev. E 88 012404
[21] Sun Y J, Huang T, Zhao J F, Chen Y 2017 Front. Phys. 12 126401
[22] Deegan R D, Bakajin O, Dupont T F, Huber G, Nagel S R and Witten T A 2000 Phys. Rev. E 62 756
[23] Hu H and Larson R G 2002 J. Phys. Chem. B 106 1334
[24] Hu H and Larson R G 2005 Langmuir 21 3963
[25] Freed-Brown J 2014 Soft Matter 10 9506
[26] Mouat A P, Wood C E, Pye J E and Burton J C 2020 Phys. Rev. Lett. 124 064502
[27] Frastia L, Archer A J and Thiele U 2011 Phys. Rev. Lett. 106 077801
[28] Thampi S P, Pagonabarraga I, Adhikaric R and Govindarajan R 2016 Soft Matter 12 6073
[29] Doi M 2011 J. Phys.: Condens. Matter 23 284118
[30] Doi M 2013 Soft Matter Physics (New York: Oxford University Press) pp. 114-135
[31] Doi M 2015 Chin. Phys. B 24 020505
[32] Onsager L 1931 Phys. Rev. 37 405
[33] Onsager L 1931 Phys. Rev. 38 2265
[34] Onuki A 2002 Phase Transition Dynamics (Cambridge: Cambridge University Press)
[35] Doi M 2009 J. Phys. Soc. Jpn. 78 052001
[36] Parisse F and Allain C 1997 Langmuir 13 3598
[37] Kobayashi M, Makino M, Okuzono T and Doi M 2010 J. Phys. Soc. Jpn. 79 044802
[38] Snoeijer J H and Andreotti B 2013 Annu. Rev. Fluid Mech. 45 269
[39] Ding H and Spelt P D M 2007 J. Fluid Mech 576 287
[40] Erbil H Y, McHale G and Newton M I 2002 Langmuir 18 2636
[41] Pan Z H, Dash S, Weibel J A, and Garimella S V 2013 Langmuir 29 15831
[42] Duan F, He B, and Wei T 2015 J. Nanosci. Nanotechnol. 15 3011
[1] Low-dimensional phases engineering for improving the emission efficiency and stability of quasi-2D perovskite films
Yue Wang(王月), Zhuang-Zhuang Ma(马壮壮), Ying Li(李营), Fei Zhang(张飞), Xu Chen(陈旭), and Zhi-Feng Shi (史志锋). Chin. Phys. B, 2021, 30(6): 067802.
[2] Influences of annealing temperature on properties of Fe2+: ZnSe thin films deposited by electron beam evaporation and their applications to Q-switched fiber laser
Du-Xin Qing(卿杜鑫), Shu-Tong Wang(王树同), Shou-Gui Ning(宁守贵), Wei Zhang(张伟), Xiao-Xu Chen(陈晓旭), Hong Zhang(张弘), Guo-Ying Feng(冯国英), Shou-Huan Zhou(周寿桓). Chin. Phys. B, 2020, 29(5): 054208.
[3] Evaporation of nanoscale water on solid surfaces
Rongzheng Wan(万荣正) and Haiping Fang(方海平). Chin. Phys. B, 2020, 29(12): 126601.
[4] Evaporation of saline colloidal droplet and deposition pattern
Hong-Hui Sun(孙弘辉), Wei-Bin Li(李伟斌), Wen-Jie Ji(纪文杰), Guo-Liang Dai(戴国亮), Yong Huan(郇勇), Yu-Ren Wang(王育人), Ding Lan(蓝鼎). Chin. Phys. B, 2020, 29(1): 014701.
[5] Direct simulation Monte Carlo study of metal evaporation with collimator in e-beam physical vapor deposition
Xiaoyong Lu(卢肖勇), Junjie Chai(柴俊杰). Chin. Phys. B, 2019, 28(7): 074702.
[6] Cryogenic amplifier with low input-referred voltage noise calibrated by shot noise measurement
Wuhao Yang(杨伍昊), Jian Wei(危健). Chin. Phys. B, 2018, 27(6): 060702.
[7] Numerical simulation of metal evaporation based on the kinetic model equation and the direct simulation Monte Carlo method
Xiaoyong Lu(卢肖勇), Xiaozhang Zhang(张小章), Zhizhong Zhang(张志忠). Chin. Phys. B, 2018, 27(12): 124702.
[8] Key parameters of two typical intercalation reactions to prepare hybrid inorganic-organic perovskite films
Biao Shi(石标), Sheng Guo(郭升), Changchun Wei(魏长春), Baozhang Li(李宝璋), Yi Ding(丁毅), Yuelong Li(李跃龙), Qing Wan(万青), Ying Zhao(赵颖), Xiaodan Zhang(张晓丹). Chin. Phys. B, 2018, 27(1): 018807.
[9] Influence of Ag and Sn incorporation in In2S3 thin films
Lin Ling-Yan, Yu Jin-Ling, Cheng Shu-Ying, Lu Pei-Min. Chin. Phys. B, 2015, 24(7): 078103.
[10] Influence of obstacle on electromagnetic wave propagation in evaporation duct with experiment verification
Shi Yang, Yang Kun-De, Yang Yi-Xin, Ma Yuan-Liang. Chin. Phys. B, 2015, 24(5): 054101.
[11] Experimental verification of effect of horizontal inhomogeneity of evaporation duct on electromagnetic wave propagation
Shi Yang, Yang Kun-De, Yang Yi-Xin, Ma Yuan-Liang. Chin. Phys. B, 2015, 24(4): 044102.
[12] Electrical properties of zinc-oxide-based thin-film transistors using strontium-oxide-doped semiconductors
Wu Shao-Hang, Zhang Nan, Hu Yong-Sheng, Chen Hong, Jiang Da-Peng, Liu Xing-Yuan. Chin. Phys. B, 2015, 24(10): 108504.
[13] Effects of thermal annealing on the properties of N-implanted ZnS films
Xue Shu-Wen, Zhang Jun, Quan Jun. Chin. Phys. B, 2014, 23(5): 057803.
[14] Optical and electrical characterizations of nanoparticle Cu2S thin films
M. Saadeldin, H. S. Soliman, H. A. M. Ali, K. Sawaby. Chin. Phys. B, 2014, 23(4): 046803.
[15] Influences of anionic and cationic dopants on the morphology andoptical properties of PbS nanostructures
Ramin Yousefi, Mohsen Cheragizade, Farid Jamali-Sheini, M. R. Mahmoudian, Abdolhossein Saaédi, Nay Ming Huang. Chin. Phys. B, 2014, 23(10): 108101.
No Suggested Reading articles found!