We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.
Issue Section:
Evaporation, Boiling, and Condensation
References
1.
Schmidt
, E.
, Schurig
, W.
, and Sellschopp
, W.
, 1930
, “Versuche Über Die Kondensation Von Wasserdampf in Film-Und Tropfenform
,” Tech. Mech. Thermodyn.
, 1
(2
), pp. 53
–63
.2.
Le Fevre
, E.
, and Rose
, J.
, 1965
, “An Experimental Study of Heat Transfer by Dropwise Condensation
,” Int. J. Heat Mass Transfer
, 8
(8
), pp. 1117
–1133
.3.
Graham
, C.
, and Griffith
, P.
, 1973
, “Drop Size Distributions and Heat Transfer in Dropwise Condensation
,” Int. J. Heat Mass Transfer
, 16
(2
), pp. 337
–346
.4.
Rose
, J.
, 2002
, “Dropwise Condensation Theory and Experiment: A Review
,” Proc. Inst. Mech. Eng., Part A: J. Power Energy
, 216
(2
), pp. 115
–128
.5.
Tanasawa
, I.
, and Utaka
, Y.
, 1983
, “Measurement of Condensation Curves for Dropwise Condensation of Steam at Atmospheric Pressure
,” ASME J. Heat Transfer
, 105
(3
), pp. 633
–638
.6.
Stylianou
, S.
, and Rose
, J.
, 1983
, “Drop-to-Filmwise Condensation Transition: Heat Transfer Measurements for Ethanediol
,” Int. J. Heat Mass Transfer
, 26
(5
), pp. 747
–760
.7.
Patankar
, N. A.
, 2010
, “Supernucleating Surfaces for Nucleate Boiling and Dropwise Condensation Heat Transfer
,” Soft Matter
, 6
(8
), pp. 1613
–1620
.8.
Kim
, S.
, and Kim
, K. J.
, 2011
, “Dropwise Condensation Modeling Suitable for Superhydrophobic Surfaces
,” ASME J. Heat Transfer
, 133
(8
), p. 081502
.9.
Greenspan
, H. P.
, 1978
, “On the Motion of a Small Viscous Droplet That Wets a Surface
,” J. Fluid Mech.
, 84
(1
), pp. 125
–143
.10.
Daniel
, S.
, Chaudhury
, M. K.
, and Chen
, J. C.
, 2001
, “Fast Drop Movements Resulting From the Phase Change on a Gradient Surface
,” Science
, 291
(5504
), pp. 633
–636
.11.
Macner
, A. M.
, Daniel
, S.
, and Steen
, P. H.
, 2014
, “Condensation on Surface Energy Gradient Shifts Drop Size Distribution Toward Small Drops
,” Langmuir
, 30
(7
), pp. 1788
–1798
.12.
Ashley
, K. M.
, Meredith
, J. C.
, Amis
, E.
, Raghavan
, D.
, and Karim
, A.
, 2003
, “Combinatorial Investigation of Dewetting: Polystyrene Thin Films on Gradient Hydrophilic Surfaces
,” Polymer
, 44
(3
), pp. 769
–772
.13.
Choi
, S.-H.
, and Zhang Newby
, B.-M.
, 2003
, “Micrometer-Scaled Gradient Surfaces Generated Using Contact Printing of Octadecyltrichlorosilane
,” Langmuir
, 19
(18
), pp. 7427
–7435
.14.
Huang
, Z.
, Zhang
, J.
, Cheng
, J.
, Xu
, S.
, Pi
, P.
, Cai
, Z.
, Wen
, X.
, and Yang
, Z.
, 2012
, “Preparation and Characterization of Gradient Wettability Surface Depending on Controlling Cu (Oh) 2 Nanoribbon Arrays Growth on Copper Substrate
,” Appl. Surf. Sci.
, 259
, pp. 142
–146
.15.
Sommers
, A.
, Brest
, T.
, and Eid
, K.
, 2013
, “Topography-Based Surface Tension Gradients to Facilitate Water Droplet Movement on Laser-Etched Copper Substrates
,” Langmuir
, 29
(38
), pp. 12043
–12050
.16.
Tanaka
, H.
, 1975
, “A Theoretical Study of Dropwise Condensation
,” ASME J. Heat Transfer
, 97
(1
), pp. 72
–78
.17.
Leach
, R.
, Stevens
, F.
, Langford
, S.
, and Dickinson
, J.
, 2006
, “Dropwise Condensation: Experiments and Simulations of Nucleation and Growth of Water Drops in a Cooling System
,” Langmuir
, 22
(21
), pp. 8864
–8872
.18.
Abu-Orabi
, M.
, 1998
, “Modeling of Heat Transfer in Dropwise Condensation
,” Int. J. Heat Mass Transfer
, 41
(1
), pp. 81
–87
.19.
Ranodolph
, A.
, 2012
, Theory of Particulate Processes 2e: Analysis and Techniques of Continuous Crystallization
, Elsevier
, London.20.
Zhao
, H.
, and Beysens
, D.
, 1995
, “From Droplet Growth to Film Growth on a Heterogeneous Surface: Condensation Associated With a Wettability Gradient
,” Langmuir
, 11
(2
), pp. 627
–634
.21.
Chaudhury
, M. K.
, Chakrabarti
, A.
, and Daniel
, S.
, 2015
, “Generation of Motion of Drops With Interfacial Contact
,” Langmuir
, 31
(34
), pp. 9266
–9281
.22.
Tanaka
, H.
, 1975
, “Measurements of Drop-Size Distributions During Transient Dropwise Condensation
,” ASME J. Heat Transfer
, 97
(3
), pp. 341
–346
.23.
Maa
, J. R.
, 1978
, “Drop Size Distribution and Heat Flux of Dropwise Condensation
,” Chem. Eng. J.
, 16
(3
), pp. 171
–176
.24.
Sikarwar
, B. S.
, Battoo
, N. K.
, Khandekar
, S.
, and Muralidhar
, K.
, 2011
, “Dropwise Condensation underneath Chemically Textured Surfaces: Simulation and Experiments
,” ASME J. Heat Transfer
, 133
(2
), p. 021501
.25.
LeFevre
, E.
, and Rose
, J.
, 1966
, “A Theory of Heat Transfer by Dropwise Condensation
,” Third International Heat Transfer Conference
, Chicago, IL, Aug. 7–12, pp. 362
–375
.26.
Daniel
, S.
, and Chaudhury
, M. K.
, 2002
, “Rectified Motion of Liquid Drops on Gradient Surfaces Induced by Vibration
,” Langmuir
, 18
(9
), pp. 3404
–3407
.27.
Brochard
, F.
, 1989
, “Motions of Droplets on Solid Surfaces Induced by Chemical or Thermal Gradients
,” Langmuir
, 5
(2
), pp. 432
–438
.28.
Ito
, Y.
, Heydari
, M.
, Hashimoto
, A.
, Konno
, T.
, Hirasawa
, A.
, Hori
, S.
, Kurita
, K.
, and Nakajima
, A.
, 2007
, “The Movement of a Water Droplet on a Gradient Surface Prepared by Photodegradation
,” Langmuir
, 23
(4
), pp. 1845
–1850
.29.
Lv
, C.
, Chen
, C.
, Chuang
, Y.-C.
, Tseng
, F.-G.
, Yin
, Y.
, Grey
, F.
, and Zheng
, Q.
, 2014
, “Substrate Curvature Gradient Drives Rapid Droplet Motion
,” Phys. Rev. Lett.
, 113
(2
), p. 026101
.30.
Wang
, Q.
, Yao
, X.
, Liu
, H.
, Quéré
, D.
, and Jiang
, L.
, 2015
, “Self-Removal of Condensed Water on the Legs of Water Striders
,” Proc. Natl. Acad. Sci. U.S.A.
, 112
(30
), pp. 9247
–9252
.31.
Zheng
, Y.
, Bai
, H.
, Huang
, Z.
, Tian
, X.
, Nie
, F.-Q.
, Zhao
, Y.
, Zhai
, J.
, and Jiang
, L.
, 2010
, “Directional Water Collection on Wetted Spider Silk
,” Nature
, 463
(7281
), pp. 640
–643
.32.
Anand
, S.
, and Son
, S. Y.
, 2010
, “Sub-Micrometer Dropwise Condensation Under Superheated and Rarefied Vapor Condition
,” Langmuir
, 26
(22
), pp. 17100
–17110
.33.
Nam
, Y.
, Kim
, H.
, and Shin
, S.
, 2013
, “Energy and Hydrodynamic Analyses of Coalescence-Induced Jumping Droplets
,” Appl. Phys. Lett.
, 103
(16
), p. 161601
.34.
Liu
, F.
, Ghigliotti
, G.
, Feng
, J. J.
, and Chen
, C.-H.
, 2014
, “Numerical Simulations of Self-Propelled Jumping upon Drop Coalescence on Non-Wetting Surfaces
,” J. Fluid Mech.
, 752
, pp. 39
–65
.35.
Boreyko
, J. B.
, and Chen
, C.-H.
, 2009
, “Self-Propelled Dropwise Condensate on Superhydrophobic Surfaces
,” Phys. Rev. Lett.
, 103
(18
), p. 184501
.36.
Lai
, Y.-H.
, Hsu
, M.-H.
, and Yang
, J.-T.
, 2010
, “Enhanced Mixing of Droplets During Coalescence on a Surface With a Wettability Gradient
,” Lab Chip
, 10
(22
), pp. 3149
–3156
.37.
Brunet
, P.
, Eggers
, J.
, and Deegan
, R.
, 2007
, “Vibration-Induced Climbing of Drops
,” Phys. Rev. Lett.
, 99
(14
), p. 144501
.38.
Noblin
, X.
, Kofman
, R.
, and Celestini
, F.
, 2009
, “Ratchetlike Motion of a Shaken Drop
,” Phys. Rev. Lett.
, 102
(19
), p. 194504
.39.
De Gennes
, P.-G.
, Brochard-Wyart
, F.
, and Quéré
, D.
, 2013
, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
, Springer Science & Business Media
, New York.40.
Chandra
, S.
, and Avedisian
, C.
, 1991
, “On the Collision of a Droplet With a Solid Surface
,” Proc. R. Soc. A
, 432
(1884), pp. 13
–41
.41.
Wang
, F.-C.
, Yang
, F.
, and Zhao
, Y.-P.
, 2011
, “Size Effect on the Coalescence-Induced Self-Propelled Droplet
,” Appl. Phys. Lett.
, 98
(5
), p. 053112
.42.
Lv
, C.
, Hao
, P.
, Yao
, Z.
, Song
, Y.
, Zhang
, X.
, and He
, F.
, 2013
, “Condensation and Jumping Relay of Droplets on Lotus Leaf
,” Appl. Phys. Lett.
, 103
(2
), p. 021601
.43.
Aarts
, D. G.
, Lekkerkerker
, H. N.
, Guo
, H.
, Wegdam
, G. H.
, and Bonn
, D.
, 2005
, “Hydrodynamics of Droplet Coalescence
,” Phys. Rev. Lett.
, 95
(16
), p. 164503
.44.
Thoroddsen
, S.
, and Takehara
, K.
, 2000
, “The Coalescence Cascade of a Drop
,” Phys. Fluids
, 12
(6
), pp. 1265
–1267
.45.
Yaws
, C. L.
, 1995
, Handbook of Thermal Conductivity, Volume 3: Organic Compounds C8 to C28
, Vol. 3
, Gulf Professional Publishing
, Houston, TX.46.
Lemmon
, E.
, McLinden
, M.
, and Friend
, D.
, 2005
, “Thermophysical Properties of Fluid Systems,” NIST Chemistry WebBook, SRD 69
, National Institute of Standards and Technology, Gaithersburg, MD.47.
Vosough
, A.
, Falahat
, A.
, and Vosough
, S.
, 2011
, “Improvement Power Plant Efficiency With Condenser Pressure
,” Int. J. Multidiscip. Sci. Eng.
, 2
(3
), pp. 38–43.48.
Sikarwar
, A. S.
, Dandotiya
, D.
, and Agrawal
, S. K.
, 2013
, “Performance Analysis of Surface Condenser Under Various Operating Parameters
,” Int. J. Eng. Res. Appl.
, 3
(4
), pp. 416
–421
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