Abstract

Droplet heat transfer in between parallelly located superhydrophobic plates is examined. The thermal field inside the droplet is predicted by adopting the experimental conditions. The influence of plates spacing (heights) on the thermal response of the droplet fluid is investigated. Particle injection velocimetry (PIV) is used to validate the velocity predictions. We demonstrated that predictions of flow velocity are in agreement with those of the PIV results. The heating of the droplet in the absence of the top plate gives four circulation cells in the droplet. Once the top superhydrophobic plate is introduced, the flow structure alters, and the number of the circulating structures reduces to two. Lowering the height of the plates increases the droplet Laplace pressure while modifying the fluid flow and thermal behavior. The Bond number is lower than one for all the cases considered; hence, demonstrating that the Marangoni force affects the formation of the circulation cells. The cells redistribute the heated fluid in the droplet interior, which is clearly apparent for the plates with small heights. Temperature enhancement in the droplet bottom section is attributed to the flow current formed due to heat diffusion. The Nusselt number corresponding to the bottom plate increases as the plate heights reduces; however, the opposite is true for that corresponding to the top plate.

References

References
1.
Bon
,
B.
,
Klausner
,
J. F.
, and
Mckenna
,
E.
,
2013
, “
The Hoodoo: A new Surface Structure for Enhanced Boiling Heat Transfer
,”
ASME J. Therm. Sci. Eng. Appl.
,
5
(
1
), p.
011003
. 10.1115/1.4007439
2.
Han
,
J. T.
,
Xu
,
X.
, and
Cho
,
K.
,
2005
, “
Diverse Access to Artificial Superhydrophobic Surfaces Using Block Copolymers
,”
Langmuir
,
21
(
15
), pp.
6662
6665
. doi:10.1021/la051042+
3.
Li
,
M.
,
Zhai
,
J.
,
Liu
,
H.
,
Song
,
Y.
,
Jiang
,
L.
, and
Zhu
,
D.
,
2003
, “
Electrochemical Deposition of Conductive Superhydrophobic Zinc Oxide Thin Films
,”
J. Phys. Chem. B
,
107
(
37
), pp.
9954
9957
. 10.1021/jp035562u
4.
Woodward
,
I.
,
Schofield
,
W. C. E.
,
Roucoules
,
V.
, and
Badyal
,
J. P. S.
,
2003
, “
Super-Hydrophobic Surfaces Produced by Plasma Fluorination of Polybutadiene Films
,”
Langmuir
,
19
(
8
), pp.
3432
3438
. 10.1021/la020427e
5.
Cai
,
S.
,
Zhang
,
Y.
,
Zhang
,
H.
,
Yan
,
H.
,
Lv
,
H.
, and
Jiang
,
B.
,
2014
, “
Sol–Gel Preparation of Hydrophobic Silica Antireflective Coatings With low Refractive Index by Base/Acid two-Step Catalysis
,”
ACS Appl. Mater. Interfaces
,
6
(
14
), pp.
11470
11475
. 10.1021/am501972y
6.
Nuraje
,
N.
,
Khan
,
W. S.
,
Lei
,
Y.
,
Ceylan
,
M.
, and
Asmatulu
,
R.
,
2013
, “
Superhydrophobic Electrospun Nanofibers
,”
J. Mater. Chem. A
,
1
(
6
), pp.
1929
1946
. 10.1039/C2TA00189F
7.
Yilbas
,
B. S.
,
Matthews
,
A.
,
Karatas
,
C.
,
Leyland
,
A.
,
Khaled
,
M.
,
Abu-Dheir
,
N.
,
Al-Aqeeli
,
N.
, and
Nie
,
X.
,
2014
, “
Laser Texturing of Plasma Electrolytically Oxidized Aluminum 6061 Surfaces for Improved Hydrophobicity
,”
ASME J. Manuf. Sci. Eng.
,
136
(
5
), p.
054501
. 10.1115/1.4027977
8.
Gong
,
Z.
,
Wang
,
J.
,
Wu
,
L.
,
Wang
,
X.
,
,
G
, and
Liao
,
L.
,
2013
, “
Fabrication of Super Hydrophobic Surfaces on Copper by Solution-Immersion
,”
Chin. J. Chem. Eng.
,
21
(
8
), pp.
920
926
. 10.1016/S1004-9541(13)60569-8
9.
Tam
,
D.
,
von ARNIM
,
V.
,
McKinley
,
G. H.
, and
Hosoi
,
A.
,
2009
, “
Marangoni Convection in Droplets on Superhydrophobic Surfaces
,”
J. Fluid Mech.
,
624
, pp.
101
123
. 10.1017/S0022112008005053
10.
Lu
,
G.
,
Duan
,
Y.-Y.
,
Wang
,
X.-D.
, and
Lee
,
D.-J.
,
2011
, “
Internal Flow in Evaporating Droplet on Heated Solid Surface
,”
Int. J. Heat Mass Transfer
,
54
(
19–20
), pp.
4437
4447
. 10.1016/j.ijheatmasstransfer.2011.04.039
11.
Al-Sharafi
,
A.
, and
Yilbas
,
B. S.
,
2019
, “
Heat Transfer and Flow Characteristics Inside Droplet Formed on Water Surface
,”
Heat Transfer Eng.
, pp.
1
21
. 10.1080/01457632.2019.1589991
12.
Misyura
,
S. Y.
,
2017
, “
Evaporation of a Sessile Water Drop and a Drop of Aqueous Salt Solution
,”
Sci. Rep.
,
7
(
1
), p.
14759
. 10.1038/s41598-017-15175-1
13.
Che
,
Z.
,
Wong
,
T. N.
,
Nguyen
,
N.-T.
, and
Yang
,
C.
,
2015
, “
Three Dimensional Features of Convective Heat Transfer in Droplet-Based Microchannel Heat Sinks
,”
Int. J. Heat Mass Transfer
,
86
, pp.
455
464
. 10.1016/j.ijheatmasstransfer.2015.03.030
14.
Gibbons
,
M. J.
,
Di Marco
,
P.
, and
Robinson
,
A. J.
,
2018
, “
Local Heat Transfer to an Evaporating Superhydrophobic Droplet
,”
Int. J. Heat Mass Transfer
,
121
, pp.
641
652
. 10.1016/j.ijheatmasstransfer.2018.01.007
15.
Cheng
,
Y.
,
Wang
,
F.
,
Xu
,
J.
,
Liu
,
D.
, and
Sui
,
Y.
,
2018
, “
Numerical Investigation of Droplet Spreading and Heat Transfer on hot Substrates
,”
Int. J. Heat Mass Transfer
,
121
, pp.
402
411
. 10.1016/j.ijheatmasstransfer.2018.01.026
16.
Al-Sharafi
,
A.
,
Yilbas
,
B. S.
,
Ali
,
H.
, and
AlAqeeli
,
N.
,
2018
, “
A Water Droplet Pinning and Heat Transfer Characteristics on an Inclined Hydrophobic Surface
,”
Sci. Rep.
,
8
(
1
), p.
3061
. 10.1038/s41598-018-21511-w
17.
Li
,
D.
,
Duan
,
X.
,
Zheng
,
Z.
, and
Liu
,
Y.
,
2018
, “
Dynamics and Heat Transfer of a Hollow Droplet Impact on a Wetted Solid Surface
,”
Int. J. Heat Mass Transfer
,
122
, pp.
1014
1023
. 10.1016/j.ijheatmasstransfer.2018.02.017
18.
Al-Sharafi
,
A.
,
Yilbas
,
B. S.
, and
Ali
,
H.
,
2018
, “
Heat and Flow Analysis of a Water Droplet on Hydrophobic and Hydrophilic Phase Change Material
,”
Int. J. Heat Mass Transfer
,
122
, pp.
749
764
. 10.1016/j.ijheatmasstransfer.2018.02.032
19.
Fujimoto
,
H.
,
Obana
,
W.
,
Ashida
,
M.
,
Hama
,
T.
, and
Takuda
,
H.
,
2017
, “
Hydrodynamics and Heat Transfer Characteristics of oil-in-Water Emulsion Droplets Impinging on hot Stainless Steel Foil
,”
Exp. Therm. Fluid. Sci.
,
85
, pp.
201
212
. 10.1016/j.expthermflusci.2017.02.024
20.
Yilbas
,
B. S.
,
Al-Sharafi
,
A.
,
Ali
,
H.
, and
Al-Aqeeli
,
N.
,
2017
, “
Dynamics of a Water Droplet on a Hydrophobic Inclined Surface: Influence of Droplet Size and Surface Inclination Angle on Droplet Rolling
,”
RSC Adv.
,
7
(
77
), pp.
48806
48818
. 10.1039/C7RA09345D
21.
Zheng
,
Z.
,
Zhou
,
L.
,
Du
,
X.
, and
Yang
,
Y.
,
2016
, “
Numerical Investigation on Conjugate Heat Transfer of Evaporating Thin Film in a Sessile Droplet
,”
Int. J. Heat Mass Transfer
,
101
, pp.
10
19
. 10.1016/j.ijheatmasstransfer.2016.05.005
22.
Phadnis
,
A.
, and
Rykaczewski
,
K.
,
2017
, “
The Effect of Marangoni Convection on Heat Transfer During Dropwise Condensation on Hydrophobic and Omniphobic Surfaces
,”
Int. J. Heat Mass Transfer
,
115
, pp.
148
158
. 10.1016/j.ijheatmasstransfer.2017.08.026
23.
Wen
,
R.
,
Lan
,
Z.
,
Peng
,
B.
,
Xu
,
W.
,
Ma
,
X.
, and
Cheng
,
Y.
,
2016
, “
Droplet Departure Characteristics and Dropwise Condensation Heat Transfer at low Steam Pressure
,”
ASME J. Heat Transfer
,
138
(
7
), p.
071501
. 10.1115/1.4032956
24.
COMSOL
,
2018
,
The Platform for Physics-Based Modeling and Simulation
,
COMSOL, Inc.
,
Burlington, MA
, http://www.comsol.com/comsol-multiphysics.
25.
Mackenzie
,
J. A.
, and
Mekwi
,
W. R.
,
2011
, “
An Unconditionally Stable Second-Order Accurate ALE–FEM Scheme for two-Dimensional Convection–Diffusion Problems
,”
IMA J. Numerical Anal.
,
32
(
3
), pp.
888
905
. 10.1093/imanum/drr021
26.
Yong
,
W. Y. D.
,
Zhang
,
Z.
,
Cristobal
,
G.
, and
Chin
,
W. S.
,
2014
, “
One-pot Synthesis of Surface Functionalized Spherical Silica Particles
,”
Colloids Surf., A
,
460
, pp.
151
157
. 10.1016/j.colsurfa.2014.03.039
27.
Heib
,
F.
, and
Schmitt
,
M.
,
2016
, “
Statistical Contact Angle Analyses With the High-Precision Drop Shape Analysis (HPDSA) Approach: Basic Principles and Applications
,”
Coatings
,
6
(
4
), p.
57
. 10.3390/coatings6040057
28.
Al-Sharafi
,
A.
,
Yilbas
,
B. S.
, and
Hassan
,
G.
,
2019
, “
Droplet on oil Impregnated Surface: Temperature and Velocity Fields
,”
Int. J. Therm. Sci.
,
146
, p.
106054
. 10.1016/j.ijthermalsci.2019.106054
29.
Novakova
,
L.
,
2016
, “
Deformation Correction Algorithm for PIV Data
,”
AIP Conf. Proc.
,
1768
(
1
), p.
020008
. 10.1063/1.4963030
30.
De Santo
,
M.
,
Liguori
,
C.
, and
Pietrosanto
,
A.
,
2000
, “
Uncertainty Characterization in Image-Based Measurements: a Preliminary Discussion
,”
IEEE Trans. Instrum. Meas.
,
49
(
5
), pp.
1101
1107
. 10.1109/19.872937
31.
Bhattacharya
,
S.
,
Charonko
,
J. J.
, and
Vlachos
,
P. P.
,
2018
, “
Particle Image Velocimetry (PIV) Uncertainty Quantification Using Moment of Correlation (MC) Plane
,”
Meas. Sci. Technol.
,
29
(
11
), p.
115301
. 10.1088/1361-6501/aadfb4
32.
Lin
,
J.
,
Chen
,
H.
,
Ji
,
Y.
, and
Zhang
,
Y.
,
2012
, “
Functionally Modified Monodisperse Core–Shell Silica Nanoparticles: Silane Coupling Agent as Capping and Size Tuning Agent
,”
Colloids Surf., A
,
411
, pp.
111
121
. 10.1016/j.colsurfa.2012.06.047
33.
Aussillous
,
P.
, and
Quéré
,
D.
,
2004
, “
Shapes of Rolling Liquid Drops
,”
J. Fluid Mech.
,
512
, pp.
133
151
. 10.1017/S0022112004009747
34.
Larson
,
R. G.
,
2014
, “
Transport and Deposition Patterns in Drying Sessile Droplets
,”
AIChE J.
,
60
(
5
), pp.
1538
1571
. 10.1002/aic.14338
35.
Kang
,
K. H.
,
Lim
,
H. C.
,
Lee
,
H. W.
, and
Lee
,
S. J.
,
2013
, “
Evaporation-Induced Saline Rayleigh Convection Inside a Colloidal Droplet
,”
Phys. Fluids
,
25
(
4
), p.
042001
. 10.1063/1.4797497
36.
Dash
,
S.
,
Chandramohan
,
A.
,
Weibel
,
J. A.
, and
Garimella
,
S. V.
,
2014
, “
Buoyancy-Induced on-the-Spot Mixing in Droplets Evaporating on Nonwetting Surfaces
,”
Phys. Rev. E
,
90
(
6
), p.
062407
. 10.1103/PhysRevE.90.062407
37.
Halliday
,
D.
,
Resnick
,
R.
, and
Walker
,
J.
,
2010
,
Fundamentals of Physics Extended
,
John Wiley and Sons
,
NJ
.
You do not currently have access to this content.