Internal fluidity of a sessile droplet on a hydrophobic surface and dynamics of fine size dust particles in the droplet interior are examined for various droplet contact angles. The geometric features of the droplet incorporated in the simulations resemble the actual droplet geometry of the experiments, and simulation conditions are set in line with the experimental conditions. The dust particles are analyzed, and the surface tension of the fluid, which composes of the dust particles and water, is measured and incorporated in the analysis. Particle tracking method is adopted experimentally to validate the numerical predictions of the flow field. It is found that heat transfer from the hydrophobic surface to the droplet gives rise to the formation of two counter rotating cells inside the droplet. The Nusselt and the Bond numbers increase with increasing droplet contact angle. The number of dust particles crossing over the horizontal rake, which corresponds to the top surface of the dust particles settled in the droplet bottom, toward the droplet interior increases as the particle density reduces, which is more pronounced in the early period. Experimental findings of flow velocity well agree with its counterparts obtained from the simulations.

References

1.
Chandrasekhar
,
S.
,
1961
, Hydrodynamic and Hydrodynamic Stability, Oxford University Press, Oxford, UK.
2.
Nakajima
,
A.
,
2011
, “
Design of Hydrophobic Surfaces for Liquid Droplet Control
,”
NPG Asia Mater.
,
3
(
5
), pp.
49
56
.
3.
Gennes
,
P. D.
,
Brochard-Wyard
,
F.
,
Quéré
,
D.
, and
Reisinger
,
A.
,
2004
,
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
, Springer, Heidelberg, Germany.
4.
Smith
,
J. D.
,
Dhiman
,
R.
,
Anand
,
S.
,
Reza-Garduno
,
E.
,
Cohen
,
R. E.
,
McKinley
,
G. H.
, and
Varanasi
,
K. K.
,
2013
, “
Droplet Mobility on Lubricant-Impregnated Surfaces
,”
Soft Matter
,
9
(
6
), pp.
1772
1780
.
5.
Tam
,
D.
,
von Arnim
,
V.
,
McKinley
,
G.
, and
Hosoi
,
A.
,
2009
, “
Marangoni Convection in Droplets on Superhydrophobic Surfaces
,”
J. Fluid Mech.
,
624
, pp.
101
123
.
6.
Dombrovsky
,
L. A.
, and
Sazhin
,
S. S.
, “
A Parabolic Temperature Profile Model for Heating of Droplets
,”
ASME J. Heat Transfer
,
125
(
3
), pp.
535
537
.
7.
Dombrovsky
,
L.
, “
A Simplified non-Isothermal Model for Droplet Heating and Evaporation
,”
Int. Commun. Heat Mass Transfer
,
30
(
6
), pp.
787
796
.
8.
Petsi
,
A.
,
Kalarakis
,
A.
, and
Burganos
,
V.
,
2010
, “
Deposition of Brownian Particles During Evaporation of Two-Dimensional Sessile Droplets
,”
Chem. Eng. Sci.
,
65
(
10
), pp.
2978
2989
.
9.
Metya
,
A. K.
,
Khan
,
S.
, and
Singh
,
J. K.
,
2014
, “
Wetting Transition of the Ethanol–Water Droplet on Smooth and Textured Surfaces
,”
J. Phys. Chem. C
,
118
(
8
), pp.
4113
4121
.
10.
Xu
,
W.
, and
Choi
,
C.-H.
,
2012
, “
Effects of Surface Topography and Colloid Particles on the Evaporation Kinetics of Sessile Droplets on Superhydrophobic Surfaces
,”
ASME J. Heat Transfer
,
134
(
5
), p.
051022
.
11.
Singh
,
D. P.
, and
Singh
,
J. P.
,
2011
, “
Enhanced Evaporation of Sessile Water Droplet on Vertically Standing Ag Nanorods Film
,”
J. Phys. Chem. C
,
115
(
24
), pp.
11914
11919
.
12.
Weiß
,
D.
,
Lienemann
,
J.
,
Greiner
,
A.
,
Kauzlarić
,
D.
, and
Korvink
,
J. G.
,
2011
, “
Smoothed Particle Hydrodynamics-Based Numerical Investigation on Sessile, Oscillating Droplets
,”
Philos. Trans. R. Soc. London A
,
369
(
1945
), pp.
2565
2573
.
13.
Kang
,
K.
,
Hong
,
J.
, and
Dhont
,
J.
,
2014
, “
Local Interfacial Migration of Clay Particles Within an Oil Droplet in an Aqueous Environment
,”
J. Phys. Chem. C
,
118
(
42
), pp.
24803
24810
.
14.
Guzowski
,
J.
,
Tasinkevych
,
M.
, and
Dietrich
,
S.
,
2011
, “
Effective Interactions and Equilibrium Configurations of Colloidal Particles on a Sessile Droplet
,”
Soft Matter
,
7
(
9
), pp.
4189
4197
.
15.
Crivoi
,
A.
, and
Duan
,
F.
,
2013
, “
Amplifying and Attenuating the Coffee-Ring Effect in Drying Sessile Nanofluid Droplets
,”
Phys. Rev. E
,
87
(
4
), p.
042303
.
16.
Schnall-Levin
,
M.
,
Lauga
,
E.
, and
Brenner
,
M. P.
,
2006
, “
Self-Assembly of Spherical Particles on an Evaporating Sessile Droplet
,”
Langmuir
,
22
(
10
), pp.
4547
4551
.
17.
Straube
,
A. V.
,
2011
, “
Small-Scale Particle Advection, Manipulation and Mixing: Beyond the Hydrodynamic Scale
,”
J. Phys.: Condens. Matter
,
23
(
18
), p.
184122
.
18.
Dudášová
,
D.
,
SjoüBlom
,
J.
, and
Øye
,
G.
,
2014
, “
Characterization and Suspension Stability of Particles Recovered From Offshore Produced Water
,”
Ind. Eng. Chem. Res.
,
53
(
4
), pp.
1431
1436
.
19.
Cai
,
J.
,
Ye
,
J.
,
Chen
,
S.
,
Zhao
,
X.
,
Zhang
,
D.
,
Chen
,
S.
,
Ma
,
Y.
,
Jin
,
S.
, and
Qi
,
L.
,
2012
, “
Self-Cleaning, Broadband and Quasi-Omnidirectional Antireflective Structures Based on Mesocrystalline Rutile TiO2 Nanorod Arrays
,”
Energy Environ. Sci.
,
5
(
6
), pp.
7575
7581
.
20.
Zhang
,
L.
,
Dillert
,
R.
,
Bahnemann
,
D.
, and
Vormoor
,
M.
,
2012
, “
Photo-Induced Hydrophilicity and Self-Cleaning: Models and Reality
,”
Energy Environ. Sci.
,
5
(
6
), pp.
7491
7507
.
21.
Jacobson
,
M. Z.
,
Delucchi
,
M. A.
,
Bazouin
,
G.
,
Bauer
,
Z. A.
,
Heavey
,
C. C.
,
Fisher
,
E.
,
Morris
,
S. B.
,
Piekutowski
,
D. J.
,
Vencill
,
T. A.
, and
Yeskoo
,
T. W.
,
2015
, “
100% Clean and Renewable Wind, Water, and Sunlight (WWS) All-Sector Energy Roadmaps for the 50 United States
,”
Energy Environ. Sci.
,
8
(
7
), pp.
2093
2117
.
22.
Yilbas
,
B. S.
,
Ali
,
H.
,
Khaled
,
M. M.
,
Al-Aqeeli
,
N.
,
Abu-Dheir
,
N.
, and
Varanasi
,
K. K.
,
2015
, “
Influence of Dust and Mud on the Optical, Chemical, and Mechanical Properties of a PV Protective Glass
,”
Scientific Reports
, 5, p. 15833.
23.
Blum
,
J.
,
2006
, “
Dust Agglomeration
,”
Adv. Phys.
,
55
(
7–8
), pp.
881
947
.
24.
Khatib
,
T.
,
Kazem
,
H.
,
Sopian
,
K.
,
Buttinger
,
F.
,
Elmenreich
,
W.
, and
Albusaidi
,
A. S.
,
2013
, “
Effect of Dust Deposition on the Performance of Multi-Crystalline Photovoltaic Modules Based on Experimental Measurements
,” http://www.ijrer.com/index.php/ijrer/article/view/876/pdf,
3
(
4
), pp.
850
853
.
25.
Siddiqui
,
R.
, and
Bajpai
,
U.
,
2012
, “
Correlation Between Thicknesses of Dust Collected on Photovoltaic Module and Difference in Efficiencies in Composite Climate
,”
Int. J. Energy Environ. Eng.
,
3
(
1
), pp.
1
7
.
26.
Mampallil
,
D.
,
Tiwari
,
D.
,
van den Ende
,
D.
, and
Mugele
,
F.
,
2013
, “
Sample Preconcentration Inside Sessile Droplets Using Electrowetting
,”
Biomicrofluidics
,
7
(
4
), p.
044102
.
27.
Xu
,
X.
, and
Ma
,
L.
,
2015
, “
Analysis of the Effects of Evaporative Cooling on the Evaporation of Liquid Droplets Using a Combined Field Approach
,”
Scientific Reports
, 5, p. 8614.
28.
Al-Sharafi
,
A.
,
Sahin
,
A. Z.
,
Yilbas
,
B. S.
, and
Shuja
,
S.
,
2015
, “
Marangoni Convection Flow and Heat Transfer Characteristics of Water–CNT Nanofluid Droplets
,”
Numer. Heat Transfer, Part A
,
69
(7), pp.
763
780
.
29.
Al-Sharafi
,
A.
,
Ali
,
H.
,
Yilbas
,
B. S.
,
Sahin
,
A. Z.
,
Khaled
,
M.
,
Al-Aqeeli
,
N.
, and
Al-Sulaiman
,
F.
,
2016
, “
Influence of Thermalcapillary and Buoyant Forces on Flow Characteristics in a Droplet on Hydrophobic Surface
,”
Int. J. Therm. Sci.
,
102
, pp.
239
253
.
30.
COMSOL
,
2016
, “The Platform for Physics-Based Modeling and Simulation,” COMSOL, Inc., Burlington, MA, http://www.comsol.com/comsol-multiphysics
31.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
32.
Krause
,
M.
,
Blum
,
J.
,
Skorov
,
Y. V.
, and
Trieloff
,
M.
,
2011
, “
Thermal Conductivity Measurements of Porous Dust Aggregates—I: Technique, Model and First Results
,”
Icarus
,
214
(
1
), pp.
286
296
.
33.
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
), pp.
4437
4447
.
34.
Morsi
,
S.
, and
Alexander
,
A.
,
1972
, “
An Investigation of Particle Trajectories in Two-Phase Flow Systems
,”
J. Fluid Mech.
,
55
(
2
), pp.
193
208
.
35.
Vand
,
V.
,
1945
, “
Theory of Viscosity of Concentrated Suspensions
,”
Nature
,
155
(
3934
), pp.
364
365
.
36.
Fang
,
Y.
,
Kuang
,
S.
,
Gao
,
X.
, and
Zhang
,
Z.
,
2008
, “
Preparation of Nanoencapsulated Phase Change Material as Latent Functionally Thermal Fluid
,”
J. Phys. D
,
42
(
3
), p.
035407
.http://dx.doi.org/10.1088/0022-3727/42/3/035407
37.
Holmes
,
M.
,
Parker
,
N.
, and
Povey
,
M.
, 2011, “
Temperature Dependence of Bulk Viscosity in Water Using Acoustic Spectroscopy
,”
J. Phys.:Conf. Ser.
,
269
(
1
), p.
012011
.
38.
Reynolds
,
O.
,
1886
, “
On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,”
Proc. R. Soc. London
,
40
(
242–245
), pp.
191
203
.
39.
Yali
,
G.
,
Lan
,
W.
,
Shengqiang
,
S.
, and
Guiying
,
C.
,
2014
, “
Simulation of Dynamic Characteristics of Droplet Impact on Liquid Film
,”
Int. J. Low-Carbon Technol.
,
9
(
2
), pp.
150
156
.
40.
Thokchom
,
A. K.
,
Gupta
,
A.
,
Jaijus
,
P. J.
, and
Singh
,
A.
,
2014
, “
Analysis of Fluid Flow and Particle Transport in Evaporating Droplets Exposed to Infrared Heating
,”
Int. J. Heat Mass Transfer
,
68
, pp.
67
77
.
41.
Maroto
,
J.
,
Pérez-Munuzuri
,
V.
, and
Romero-Cano
,
M.
,
2007
, “
Introductory Analysis of Bénard–Marangoni Convection
,”
Eur. J. Phys.
,
28
(
2
), p.
311
.http://dx.doi.org/10.1088/0143-0807/28/2/016
42.
The Engineering Toolbox
,
2016
, “
Solids - Specific Heats
,” The Engineering Toolbox, http://www.engineeringtoolbox.com/specific-heat-solids-d_154.html
43.
He
,
Q.
, and
Jiao
,
D.
,
2014
, “
Explicit and Unconditionally Stable Time-Domain Finite-Element Method With a More Than “Optimal” Speedup
,”
Electromagnetics
,
34
(
3–4
), pp.
199
209
.
44.
Cui
,
Y.
,
Paxson
,
A. T.
,
Smyth
,
K. M.
, and
Varanasi
,
K. K.
,
2012
, “
Hierarchical Polymeric Textures Via Solvent-Induced Phase Transformation: A Single-Step Production of Large-Area Superhydrophobic Surfaces
,”
Colloids Surf. A
,
394
, pp.
8
13
.
45.
Alghamdi
,
M. A.
,
Almazroui
,
M.
,
Shamy
,
M.
,
Redal
,
M. A.
,
Alkhalaf
,
A. K.
,
Hussein
,
M. A.
, and
Khoder
,
M. I.
,
2015
, “
Characterization and Elemental Composition of Atmospheric Aerosol Loads During Springtime Dust Storm in Western Saudi Arabia
,”
Aerosol Air Qual. Res.
,
15
(2), pp.
440
453
.
46.
Gelderblom
,
H.
,
Bloemen
,
O.
, and
Snoeijer
,
J. H.
,
2012
, “
Stokes Flow Near the Contact Line of an Evaporating Drop
,”
J. Fluid Mech.
,
709
, pp.
69
84
.
47.
Wenzel
,
R. N.
,
1936
, “
Resistance of Solid Surfaces to Wetting by Water
,”
Ind. Eng. Chem.
,
28
(
8
), pp.
988
994
.
48.
Bico
,
J.
,
Thiele
,
U.
, and
Quéré
,
D.
,
2002
, “
Wetting of Textured Surfaces
,”
Colloids Surf. A
,
206
(
1–3
), pp.
41
46
.
49.
Bormashenko
,
E.
,
2009
, “
A Variational Approach to Wetting of Composite Surfaces: is Wetting of Composite Surfaces a One-Dimensional or Two-Dimensional Phenomenon?
,”
Langmuir
,
25
(
18
), pp.
10451
10454
.
50.
Cassie
,
A. B. D.
, and
Baxter
,
S.
,
1944
, “
Wettability of Porous Surfaces
,”
Trans. Faraday Soc.
,
40
, pp.
546
551
.
51.
Halliday
,
D.
,
Resnick
,
R.
, and
Walker
,
J.
,
2010
,
Fundamentals of Physics Extended
,
Wiley
, Hoboken, NJ.
You do not currently have access to this content.