A theoretical study on coalescence-induced jumping of partially wetted condensed droplets on nano-textured surfaces

Liu Tian-Qing; Sun Wei; Li Xiang-Qin; Sun Xiang-Yu; Ai Hong-Ru

doi:10.7498/aps.63.086801

Abstract

Partially wetted (PW) droplets specially exist on textured surfaces with proper nano-structural parameters. Such tiny drops can depart from surfaces by coalescence-induced jumping, and become the main medium for dropwise condensation heat transfer. Therefore, it is of great importance to study the relationship between nano-structural parameters and PW drop post-merging jumping. In this study, the principle of minimum energy increasing during condensed droplets growth was used to judge if a condensed drop is in PW state. The initial shape of a coalesced droplet was determined based on the conservation of PW drop interface free energy and viscous dissipation energy before and after two or more PW condensed droplets merge. The dynamic equation describing the shape conversion of the post-coalescence droplet was then solved. Whether jumping or not of a merged drop was determined by whether the base radius of the droplet can reduce to 0 and if existing a up moving speed of drop gravity center at this moment. The calculation results show that PW droplets can form only on the textured-surfaces with certain nano-pillar height and relatively larger ratio between pillar diameter and pitch, dn/s, while completely wetted droplets easily form on the surfaces with low pillar height and dn/s less than 0.1. Meanwhile, post-coalescence jumping of PW droplets closely relates to nano-structural parameters. Not all PW drops can jump after merging. Instead, self-propelled jumping of PW drops takes place only on the surfaces with relatively higher nano-pillar height and suitable dn/s. Moreover, PW drop size and the scale ratio between two PW droplets to merge also have significant effect on the coalescence-induced jumping. It is difficult for a merged drop to jump spontaneously if the size of PW drops is too large or too small, or the scale ratio of two PW drops is too small. Finally, post-coalescence jumping of multi-droplets is easier than that of two drops since more surplus interface free energy exists in the former case. The calculation results of this model are well consistent with the experimental observations in literatures for whether the post-coalescence condensed drops jump on nano-textured surfaces, with accuracy of 95%. In conclusion, coalescence-induced jumping takes place only when PW droplets with suitable size on the textured surfaces with proper nano-structural parameters.

Keywords:

Authors and contacts

1.
School of Chemical Engineering, Dalian University of Technology, Dalian 116024, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 50876015).

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Cited By

[1]	Miljkovic N, Wang E N 2013 MRS Bull. 38 397
[2]
[3]	Miljkovic N, Enright R, Nam Y, Lopez K, Dou N, Sack J, Wang E N 2013 Nano Lett. 13 179
[4]
[5]	Rykaczewski K, Paxson A T, Anand S, Chen X M, Wang Z K, Varanasi K K 2013 Langmuir 29 881
[6]	Wisdom K M, Watson J A, Qu X P, Liu F J, Watson G S, Chen C H 2013 Proc. Natl. Acad. Sci. USA 110 7992
[7]
[8]	Enright R, Miljkovic N, Al-Obeidi A, Thompson C V, Wang E N 2012 Langmuir 28 14424
[9]
[10]
[11]	Miljkovic N, Enright R, Wang E N 2012 ACS Nano 6 1776
[12]	Chen X M, Wu J, Ma R Y, Hua M, Koratkar N, Yao S H, Wang Z K 2011 Adv. Funct. Mater. 21 4617
[13]
[14]
[15]	Boreyko J B, Chen C H 2009 Phys. Rev. Lett. 103 184501
[16]	Boreyko J B, Chen C H 2010 Phys. Fluids 22 091110
[17]
[18]
[19]	Feng J, Pang Y C, Qin Z Q, Ma R Y, Yao S H 2012 ACS Appl. Mater. Interfaces 4 6618
[20]
[21]	Boreyko J B, Collier C P 2013 ACS Nano 7 1618
[22]
[23]	Zhang Q L, He M, Chen J, Wang J J, Song Y L, Jiang L 2013 Chem. Commun. 49 4516
[24]	He M, Zhou X, Zeng X P, Cui D P, Zhang Q L, Chen J, Li H L, Wang J J, Cao Z X, Song Y L, Jiang L 2012 Soft Matter 8 6680
[25]
[26]
[27]	Boreyko J B, Chen C H 2013 Int. J. Heat. Mass. Trans. 61 409
[28]
[29]	Boreyko J B, Zhao Y J, Chen C H 2011 Appl. Phys. Lett. 99 234105
[30]
[31]	Feng J, Qin Z Q, Yao S H 2012 Langmuir 28 6067
[32]	Yang Z, Wu Y Z, Ye Y F 2012 Chin. Phys. B 21 126801
[33]
[34]	Gong M G, Xu X L, Yang Z Liu Y S, Liu L 2010 Chin. Phys. B 19 56701
[35]
[36]
[37]	Yu J, Wang H J, Shao W J, Xu X L 2014 Chin. Phys. B 23 16803
[38]
[39]	Gu C Y, Di Q F, Shi L Y, Wu F, Wang W C, Yu Z B 2008 Acta Phys. Sin. 57 3071 (in Chinese) [顾春元, 狄勤丰, 施利毅, 吴非, 王文昌, 余祖斌 2008 物理学报 57 3071]
[40]	Liang L X, Deng Y, Wang Y 2013 Chin. Phys. Lett. 30 108104
[41]
[42]	Wang B, Nian J Y, Tie L, Zhang Y B, Guo Z G 2013 Acta Phys. Sin. 62 146801 (in Chinese) [王奔, 念敬妍, 铁璐, 张亚斌, 郭志光 2013 物理学报 62 146801]
[43]
[44]	Rykaczewski K, Osborn W A, Chinn J, Walker M L, Scott J H J, Jones W, Hao C L, Yao S H, Wang Z K 2012 Soft Matter 8 8786
[45]
[46]
[47]	Rykaczewski K 2012 Langmuir 28 7720
[48]
[49]	Rykaczewski K, Scott J H J 2011 ACS Nano 5 5962
[50]	Liu T Q, Sun W, Li X Q, Sun X Y, Ai H R 2013 Acta Phys. Chim. Sin. 29 1762 (in Chinese) [刘天庆, 孙玮, 李香琴, 孙相彧, 艾宏儒 2013 物理化学学报 29 1762]
[51]
[52]
[53]	Narhe R D, Beysens D A 2006 Europhys. Lett. 75 98
[54]
[55]	Narhe R D, Beysens D A 2007 Langmuir 23 6486
[56]
[57]	Narhe R D, Beysens D A 2004 Phys. Rev. Lett. 93 76103
[58]
[59]	Wier K A, Mccarthy T J 2006 Langmuir 22 2433
[60]	Jung Y C, Bhushan B 2008 J. Microsc. Oxford 229 127
[61]
[62]
[63]	Lafuma A, Quere D 2003 Nature Mater. 2 457
[64]	Narhe R D, Gonzalez-Vinas W, Beysens D A 2010 Appl. Surf. Sci. 256 4930
[65]
[66]
[67]	Chen X L, Lu T 2009 Sci. China Series G: Phys. Mech. Astron. 52 233
[68]	Xiao X C, Cheng Y T, Sheldon B W, Rankin J 2008 J. Mater. Res. 23 2174
[69]
[70]
[71]	Furuta T, Sakai M, Isobe T, Nakajima A 2010 Langmuir 26 13305
[72]	Dietz C, Rykaczewski K, Fedorov A, Joshi Y 2010 J. Heat Transfer 132 080904
[73]
[74]	Kulinich S A, Farhadi S, Nose K, Du X W 2011 Langmuir 27 25
[75]
[76]
[77]	Liu T Q, Sun W, Sun X Y, Ai H R 2012 Colloid Surface A 414 366
[78]
[79]	Liu T Q, Sun W, Sun X Y, Ai H R 2012 Acta Phys. Chim. Sin. 28 1206 (in Chinese) [刘天庆, 孙玮, 孙相彧, 艾宏儒 2012 物理化学学报 28 1206]
[80]
[81]	Wang F C, Yang F Q, Zhao Y P 2011 Appl. Phys. Lett. 98 053112
[82]	Peng B L, Wang S F, Lan Z, Xu W, Wen R F, Ma X H 2013 Appl. Phys. Lett. 102 151601
[83]
[84]
[85]	Harris J W, Stocker H 1998 Handbook of Mathematics and Computational Science (New York: Springer-Verlag) p107
[86]
[87]	Dorrer C, Ruehe J 2008 Adv. Mater. 20 159
[88]
[89]	Cheng J T, Vandadi A, Chen C L 2012 Appl. Phys. Lett. 101 131909
[90]
[91]	Torresin D, Tiwari M K, Del Col D, Poulikakos D 2013 Langmuir 29 840

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Vol. 63, Issue 8 - 2014-04-20

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