Inspired by the thermoregulation of mammals via perspiration, cooling strategies utilizing continuously fed evaporating droplets have long been investigated in the field, yet a comprehensive modeling capturing the detailed physics of the internal liquid flow is absent. In this study, an innovative computational model is reported, which solves the governing equations with temperature-dependent thermophysical properties in an iterative manner to handle mass and heat transfer coupling at the surface of a constant shape evaporating droplet. Using the model, evaporation from a spherical sessile droplet is simulated with and without thermocapillarity. An uncommon, nonmonotonic temperature variation on the droplet surface is captured in the absence of thermocapillarity. Although similar findings were reported in previous experiments, the temperature dip was attributed to a possible Marangoni flow. This study reveals that buoyancy-driven flow is solely responsible for the nonmonotonic temperature distribution at the surface of an evaporating steadily fed spherical water droplet.
Issue Section:
Evaporation, Boiling, and Condensation
Keywords:
droplet evaporation,
steadily fed droplet,
coupling heat and mass transfer,
thermocapillarity,
buoyancy
Topics:
Drops,
Evaporation,
Temperature,
Water,
Heat,
Flow (Dynamics),
Mass transfer,
Convection,
Buoyancy,
Modeling
References
1.
Smalyukh
, I. I.
, Zribi
, O. V.
, Butler
, J. C.
, Lavrentovich
, O. D.
, and Wong
, G. C.
, 2006
, “Structure and Dynamics of Liquid Crystalline Pattern Formation in Drying Droplets of DNA
,” Phys. Rev. Lett.
, 96
(17
), p. 177801
.2.
Lim
, T.
, Jeong
, J.
, Chung
, J.
, and Chung
, J. T.
, 2009
, “Evaporation of Inkjet Printed Pico-Liter Droplet on Heated Substrates With Different Thermal Conductivity
,” J. Mech. Sci. Technol.
, 23
(7
), pp. 1788
–1794
.3.
Sefiane
, K.
, 2010
, “On the Formation of Regular Patterns From Drying Droplets and Their Potential Use for Bio-Medical Applications
,” J. Bionic Eng.
, 7
(S4
), pp. S82
–S93
.4.
Ebrahimi
, A.
, Dak
, P.
, Salm
, E.
, Dash
, S.
, Garimella
, S. V.
, Bashir
, R.
, and Alam
, M. A.
, 2013
, “Nanotextured Superhydrophobic Electrodes Enable Detection of Attomolar-Scale DNA Concentration Within a Droplet by Non-Faradaic Impedance Spectroscopy
,” Lab Chip
, 13
(21
), pp. 4248
–4256
.5.
Kokalj
, T.
, Cho
, H.
, Jenko
, M.
, and Lee
, L.
, 2010
, “Biologically Inspired Porous Cooling Membrane Using Arrayed-Droplets Evaporation
,” Appl. Phys. Lett.
, 96
(16
), p. 163703
.6.
Chakraborty
, S.
, Rosen
, M. A.
, and MacDonald
, B. D.
, 2017
, “Analysis and Feasibility of an Evaporative Cooling System With Diffusion-Based Sessile Droplet Evaporation for Cooling Microprocessors
,” Appl. Therm. Eng.
, 125
, pp. 104
–110
.7.
Duh
, J. C.
, and Yang
, W.-J.
, 1989
, “Numerical Analysis of Natural Convection in Liquid Droplets by Phase Change
,” Numer. Heat Transfer
, 16
(2
), pp. 129
–154
.8.
Lozinski
, D.
, and Matalon
, M.
, 1993
, “Thermocapillary Motion in a Spinning Vaporizing Droplet
,” Phys. Fluids A Fluid
, 5
(7
), pp. 1596
–1601
.9.
Shih
, A. T.
, and Megaridis
, C. M.
, 1996
, “Thermocapillary Flow Effects on Convective Droplet Evaporation
,” Int. J. Heat Mass Tran.
, 39
(2
), pp. 247
–257
.10.
Ruiz
, O. E.
, and Black
, W. Z.
, 2002
, “Evaporation of Water Droplets Placed on a Heated Horizontal Surface
,” ASME J. Heat Transf.
, 124
(5), pp. 854–863.11.
Bouchenna
, C.
, Saada
, M. A.
, Chikh
, S.
, and Tadrist
, L.
, 2017
, “Generalized Formulation for Evaporation Rate and Flow Pattern Prediction Inside an Evaporating Pinned Sessile Drop
,” Int. J. Heat Mass Tran.
, 109
, pp. 482
–500
.12.
Girard
, F.
, Antoni
, M.
, Faure
, S.
, and Steinchen
, A.
, 2006
, “Evaporation and Marangoni Driven Convection in Small Heated Water Droplets
,” Langmuir
, 22
(26
), pp. 11085
–11091
.13.
Hu
, H.
, and Larson
, R. G.
, 2005
, “Analysis of the Effects of Marangoni Stresses on the Microflow in an Evaporating Sessile Droplet
,” Langmuir
, 21
(9
), pp. 3972
–3980
.14.
Ristenpart
, W.
, Kim
, P.
, Domingues
, C.
, Wan
, J.
, and Stone
, H.
, 2007
, “Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops
,” Phys. Rev. Lett.
, 99
(23
), p. 234502
. 15.
Xu
, X.
, Luo
, J.
, and Guo
, D.
, 2009
, “Criterion for Reversal of Thermal Marangoni Flow in Drying Drops
,” Langmuir
, 26
(3
), pp. 1918
–1922
.16.
Zhang
, K.
, Ma
, L.
, Xu
, X.
, Luo
, J.
, and Guo
, D.
, 2014
, “Temperature Distribution Along the Surface of Evaporating Droplets
,” Phys. Rev. E
, 89
(3
), p. 032404
.17.
Barash
, L. Y.
, 2015
, “Dependence of Fluid Flows in an Evaporating Sessile Droplet on the Characteristics of the Substrate
,” Int. J. Heat Mass Tran.
, 84
, pp. 419
–426
.18.
Hu
, H.
, and Larson
, R. G.
, 2002
, “Evaporation of a Sessile Droplet on a Substrate
,” J. Phys. Chem. B
, 106
(6
), pp. 1334
–1344
.19.
Deegan
, R. D.
, Bakajin
, O.
, Dupont
, T. F.
, Huber
, G.
, Nagel
, S. R.
, and Witten
, T. A.
, 1997
, “Capillary Flow as the Cause of Ring Stains From Dried Liquid Drops
,” Nat.
, 389
(6653
), pp. 827
–829
.20.
Deegan
, R. D.
, Bakajin
, O.
, Dupont
, T. F.
, Huber
, G.
, Nagel
, S. R.
, and Witten
, T. A.
, 2000
, “Contact Line Deposits in an Evaporating Drop
,” Phys. Rev. E
, 62
(1 Pt B
), p. 756
.21.
Girard
, F.
, Antoni
, M.
, and Sefiane
, K.
, 2008
, “On the Effect of Marangoni Flow on Evaporation Rates of Heated Water Drops
,” Langmuir
, 24
(17
), pp. 9207
–9210
. 22.
Kaneda
, M.
, Hyakuta
, K.
, Takao
, Y.
, Ishizuka
, H.
, and Fukai
, J.
, 2008
, “Internal Flow in Polymer Solution Droplets Deposited on a Lyophobic Surface During a Receding Process
,” Langmuir
, 24
(16
), pp. 9102
–9109
.23.
Karapetsas
, G.
, Matar
, O. K.
, Valluri
, P.
, and Sefiane
, K.
, 2012
, “Convective Rolls and Hydrothermal Waves in Evaporating Sessile Drops
,” Langmuir
, 28
(31
), pp. 11433
–11439
.24.
Strotos
, G.
, Gavaises
, M.
, Theodorakakos
, A.
, and Bergeles
, G.
, 2008
, “Numerical Investigation on the Evaporation of Droplets Depositing on Heated Surfaces at Low Weber Numbers
,” Int. J. Heat Mass Tran.
, 51
(7–8
), pp. 1516
–1529
.25.
Ait Saada
, M.
, Chikh
, S.
, and Tadrist
, L.
, 2010
, “Numerical Investigation of Heat and Mass Transfer of an Evaporating Sessile Drop on a Horizontal Surface
,” Phys. Fluids
, 22
(11
), p. 112115
.26.
Carle
, F.
, Sobac
, B.
, and Brutin
, D.
, 2013
, “Experimental Evidence of the Atmospheric Convective Transport Contribution to Sessile Droplet Evaporation
,” Appl. Phys. Lett.
, 102
(6
), p. 061603
.27.
Yoshitake
, Y.
, Yasumatsu
, S.
, Kaneda
, M.
, Nakaso
, K.
, and Fukai
, J.
, 2009
, “Structure of Circulation Flows in Polymer Solution Droplets Receding on Flat Surfaces
,” Langmuir
, 26
(6
), pp. 3923
–3928
.28.
Churchill
, S. W.
, 2002
, “Free Convection Around Immersed Bodies
,” Heat Exchanger Design Handbook
, G. F.
Hewitt
, ed., Begell House
, New York
.29.
Akkuş
, Y.
, Çetin
, B.
, and Dursunkaya
, Z.
, 2017
, “Modeling of Evaporation From a Sessile Constant Shape Droplet
,” ASME
Paper No. ICNMM2017-5537
.30.
Mahmud
, M. A.
, and MacDonald
, B. D.
, 2017
, “Experimental Investigation of Interfacial Energy Transport in an Evaporating Sessile Droplet for Evaporative Cooling Applications
,” Phys. Rev. E
, 95
(1), p. 012609.31.
Robinson
, P. J.
, and Davies
, J. A.
, 1972
, “Laboratory Determinations of Water Surface Emissivity
,” J. Appl. Metrol.
, 11
(8
), pp. 1391
–1393
.32.
Mollaret
, R.
, Sefiane
, K.
, Christy
, J.
, and Veyret
, D.
, 2004
, “Experimental and Numerical Investigation of the Evaporation Into Air of a Drop on a Heated Surface
,” Chem. Eng. Res. Des.
, 82
(4
), pp. 471
–480
.33.
Incropera
, F. P.
, and DeWitt
, D. P.
, 1990
, Fundamentals of Heat and Mass Transfer
, Wiley
, New York
.34.
Vargaftik
, N.
, Volkov
, B.
, and Voljak
, L.
, 1983
, “International Tables of the Surface Tension of Water
,” J. Phys. Chem. Ref. Data
, 12
(3
), pp. 817
–820
.35.
Carey
, V. P.
, 1992
, Liquid-Vapor Phase Change Phenomena
, Hemisphere Publishing House
, New York
.36.
Ward
, C.
, and Duan
, F.
, 2004
, “Turbulent Transition of Thermocapillary Flow Induced by Water Evaporation
,” Phys. Rev. E
, 69
(5 Pt. 2
), p. 056308
.37.
Xu
, X.
, and Luo
, J.
, 2007
, “Marangoni Flow in an Evaporating Water Droplet
,” Appl. Phys. Lett.
, 91
(12
), p. 124102
.38.
Savino
, R.
, Paterna
, D.
, and Lappa
, M.
, 2003
, “Marangoni Flotation of Liquid Droplets
,” J. Fluid Mech.
, 479
, pp. 307
–326
.39.
Duan
, F.
, and Ward
, C.
, 2005
, “Surface Excess Properties From Energy Transport Measurements During Water Evaporation
,” Phys. Rev. E
, 72
(5
), p. 056302
.40.
Duan
, F.
, Badam
, V.
, Durst
, F.
, and Ward
, C.
, 2005
, “Thermocapillary Transport of Energy During Water Evaporation
,” Phys. Rev. E
, 72
(5
), p. 056303
.41.
Ghasemi
, H.
, and Ward
, C.
, 2010
, “Energy Transport by Thermocapillary Convection During Sessile-Water-Droplet Evaporation
,” Phys. Rev. Lett.
, 105
(13
), p. 136102
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