Power plant water usage is a coupling of the energy–water nexus; this research investigates water droplet motion, with implications for water recovery in cooling towers. Simulations of a 2.6 mm-diameter droplet motion on a hydrophobic, vertical surface were conducted in xflow using the lattice Boltzmann method (LBM). Results were compared to two experimental cases; in the first case, experimental and simulated droplets experienced 30 Hz vibrations (i.e., ±0.1 mm x-direction amplitude, ±0.2 mm y-direction amplitude) and the droplet ratcheted down the surface. In the second case, 100 Hz vibrations (i.e., ±0.8 mm x-direction amplitude, ±0.2 mm y-direction amplitude) caused droplet ejection. Simulations were then conducted for a wide range of frequencies (i.e., 10–100 Hz) and amplitudes (i.e., ±0.018–50 mm), resulting in maximum accelerations of 0.197–1970 m/s2. Under low maximum accelerations (e.g., <7 m/s2), droplets rocked upward and downward in rocking mode, but did not overcome the contact angle hysteresis and, therefore, did not move. As acceleration increased, droplets overcame the contact angle hysteresis and entered ratcheting mode. For vibrations that prompted droplet motion, droplet velocities varied between 10–1000 mm/s. At capillary numbers above approximately 0.0044 and Weber numbers above 3.6, liquid breakup was observed in ratcheting droplets (e.g., the formation of smaller child droplets from the parent droplet). It was noted that both x- and y-direction vibrations were required for droplet ejection.

References

References
1.
Hussey
,
K.
, and
Pittock
,
J.
,
2012
, “
The Energy–Water Nexus: Managing the Links Between Energy and Water for a Sustainable Future
,”
Ecology Soc.
,
17
(
1
), p. 31.
2.
DeNooyer
,
T. A.
,
Peschel
,
J. M.
,
Zhang
,
Z.
, and
Stillwell
,
A. S.
,
2016
, “
Integrating Water Resources and Power Generation: The Energy–Water Nexus in Illinois
,”
Appl. Energy
,
162
, pp.
363
371
.
3.
Lubega
,
W. N.
, and
Stillwell
,
A. S.
,
2018
, “
Maintaining Electric Grid Reliability Under Hydrologic Drought and Heat Wave Conditions
,”
Appl. Energy
,
210
, pp.
538
549
.
4.
Tidwell
,
V. C.
,
Kobos
,
P. H.
,
Malczynski
,
L. A.
,
Klise
,
G.
, and
Castillo
,
C. R.
,
2011
, “
Exploring the Water-Thermoelectric Power Nexus
,”
J. Water Resour. Plann. Manage.
,
138
(
5
), pp.
491
501
.
5.
Maupin
,
M. A.
,
Kenny
,
J. F.
,
Hutson
,
S. S.
,
Lovelace
,
J. K.
,
Barber
,
N. L.
, and
Linsey
,
K. S.
,
2014
, “
Estimated Use of Water in the United States in 2010
,” U.S. Geological Survey, I.S. Geological Survey, Reston, VA, No. 2330-5703.
6.
Benn
,
S. P.
,
Poplaski
,
L. M.
,
Faghri
,
A.
, and
Bergman
,
T. L.
,
2016
, “
Analysis of Thermosyphon/Heat Pipe Integration for Feasibility of Dry Cooling for Thermoelectric Power Generation
,”
Appl. Therm. Eng.
,
104
, pp.
358
374
.
7.
Shoele
,
K.
, and
Mittal
,
R.
,
2016
, “
Energy Harvesting by Flow-Induced Flutter in a Simple Model of an Inverted Piezoelectric Flag
,”
J. Fluid Mech.
,
790
, pp.
582
606
.
8.
Ghosh
,
R.
,
Ray
,
T. K.
, and
Ganguly
,
R.
,
2015
, “
Cooling Tower Fog Harvesting in Power Plants–A Pilot Study
,”
Energy
,
89
, pp.
1018
1028
.
9.
Damak
,
M.
, and
Varanasi
,
K. K.
,
2018
, “
Electrostatically Driven Fog Collection Using Space Charge Injection
,”
Sci. Adv.
,
4
(
6
), p.
eaao5323
.
10.
Fessehaye
,
M.
,
Abdul-Wahab
,
S. A.
,
Savage
,
M. J.
,
Kohler
,
T.
,
Gherezghiher
,
T.
, and
Hurni
,
H.
,
2014
, “
Fog-Water Collection for Community Use
,”
Renewable Sustainable Energy Rev.
,
29
, pp.
52
62
.
11.
Jaen
,
M. V. M.
,
2002
, “
Fog Water Collection in a Rural Park in the Canary Islands (Spain)
,”
Atmos. Res.
,
64
(
1
), pp.
239
250
.
12.
Olivier
,
J.
, and
De Rautenbach
,
C.
,
2002
, “
The Implementation of Fog Water Collection Systems in South Africa
,”
Atmos. Res.
,
64
(
1–4
), pp.
227
238
.
13.
Estrela
,
M. J.
,
Valiente
,
J. A.
,
Corell
,
D.
,
Fuentes
,
D.
, and
Valdecantos
,
A.
,
2009
, “
Prospective Use of Collected Fog Water in the Restoration of Degraded Burned Areas Under Dry Mediterranean Conditions
,”
Agric. Meteorol.
,
149
(
11
), pp.
1896
1906
.
14.
Quéré
,
D.
,
Azzopardi
,
M.-J.
, and
Delattre
,
L.
,
1998
, “
Drops at Rest on a Tilted Plane
,”
Langmuir
,
14
(
8
), pp.
2213
2216
.
15.
Al-Sharafi
,
A.
,
Yilbas
,
B. S.
, and
Ali
,
H.
,
2017
, “
Water Droplet Adhesion on Hydrophobic Surfaces: Influence of Droplet Size and Inclination Angle of Surface on Adhesion Force
,”
ASME J. Fluids Eng.
,
139
(
8
), p.
081302
.
16.
Daniel
,
S.
,
Sircar
,
S.
,
Gliem
,
J.
, and
Chaudhury
,
M. K.
,
2004
, “
Ratcheting Motion of Liquid Drops on Gradient Surfaces
,”
Langmuir
,
20
(
10
), pp.
4085
4092
.
17.
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
.
18.
Ghosh
,
A.
,
Ganguly
,
R.
,
Schutzius
,
T. M.
, and
Megaridis
,
C. M.
,
2014
, “
Wettability Patterning for High-Rate, Pumpless Fluid Transport on Open, Non-Planar Microfluidic Platforms
,”
Lab Chip
,
14
(
9
), pp.
1538
1550
.
19.
Schutzius
,
T. M.
,
Graeber
,
G.
,
Elsharkawy
,
M.
,
Oreluk
,
J.
, and
Megaridis
,
C. M.
,
2014
, “
Morphing and Vectoring Impacting Droplets by Means of Wettability-Engineered Surfaces
,”
Sci. Rep.
,
4
, p.
7029
.https://www.nature.com/articles/srep07029
20.
Benilov
,
E.
, and
Billingham
,
J.
,
2011
, “
Drops Climbing Uphill on an Oscillating Substrate
,”
J. Fluid Mech.
,
674
, pp.
93
119
.
21.
Brunet
,
P.
,
Eggers
,
J.
, and
Deegan
,
R.
,
2007
, “
Vibration-Induced Climbing of Drops
,”
Phys. Rev. Lett.
,
99
(
14
), p.
144501
.
22.
Chaudhury
,
M. K.
,
Chakrabarti
,
A.
, and
Daniel
,
S.
,
2015
, “
Generation of Motion of Drops With Interfacial Contact
,”
Langmuir
,
31
(
34
), pp.
9266
9281
.
23.
Daniel
,
S.
,
Chaudhury
,
M. K.
, and
De Gennes
,
P.-G.
,
2005
, “
Vibration-Actuated Drop Motion on Surfaces for Batch Microfluidic Processes
,”
Langmuir
,
21
(
9
), pp.
4240
4248
.
24.
Dong
,
L.
,
Chaudhury
,
A.
, and
Chaudhury
,
M.
,
2006
, “
Lateral Vibration of a Water Drop and Its Motion on a Vibrating Surface
,”
Eur. Phys. J. E
,
21
(
3
), pp.
231
242
.
25.
Mettu
,
S.
, and
Chaudhury
,
M. K.
,
2011
, “
Motion of Liquid Drops on Surfaces Induced by Asymmetric Vibration: Role of Contact Angle Hysteresis
,”
Langmuir
,
27
(
16
), pp.
10327
10333
.
26.
Noblin
,
X.
,
Buguin
,
A.
, and
Brochard-Wyart
,
F.
,
2009
, “
Vibrations of Sessile Drops
,”
Eur. Phys. J.: Spec. Top.
,
166
(
1
), pp.
7
10
.
27.
Noblin
,
X.
,
Kofman
,
R.
, and
Celestini
,
F.
,
2009
, “
Ratchetlike Motion of a Shaken Drop
,”
Phys. Rev. Lett.
,
102
(
19
), p.
194504
.
28.
Mettu
,
S.
, and
Chaudhury
,
M. K.
,
2008
, “
Motion of Drops on a Surface Induced by Thermal Gradient and Vibration
,”
Langmuir
,
24
(
19
), pp.
10833
10837
.
29.
Huber
,
R. A.
, and
Derby
,
M. M.
,
2017
, “
Droplet Coalescence and Departure on a Vibrating Film During Humid Air Condensation
,”
ASME
Paper No. ICNMM2017-5555.
30.
Bormashenko
,
E.
,
Pogreb
,
R.
,
Whyman
,
G.
,
Bormashenko
,
Y.
, and
Erlich
,
M.
,
2007
, “
Vibration-Induced Cassie-Wenzel Wetting Transition on Rough Surfaces
,”
Appl. Phys. Lett.
,
90
(
20
), p.
201917
.
31.
Mettu
,
S.
, and
Chaudhury
,
M. K.
,
2010
, “
Stochastic Relaxation of the Contact Line of a Water Drop on a Solid Substrate Subjected to White Noise Vibration: Roles of Hysteresis
,”
Langmuir
,
26
(
11
), pp.
8131
8140
.
32.
Shastry
,
A.
,
Case
,
M. J.
, and
Böhringer
,
K. F.
,
2006
, “
Directing Droplets Using Microstructured Surfaces
,”
Langmuir
,
22
(
14
), pp.
6161
6167
.
33.
Liu
,
H.
,
Ju
,
Y.
,
Wang
,
N.
,
Xi
,
G.
, and
Zhang
,
Y.
,
2015
, “
Lattice Boltzmann Modeling of Contact Angle and Its Hysteresis in Two-Phase Flow With Large Viscosity Difference
,”
Phys. Rev. E
,
92
(
3
), p.
033306
.
34.
Srivastava
,
S.
,
ten Thije Boonkkamp
,
J.
, and
Toschi
,
F.
,
2014
, “
Lattice Boltzmann Method for Contact Line Dynamics
,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
35.
Wu
,
T.-C.
,
2015
, “
Two-Phase Flow in Microchannels With Application to PEM Fuel Cells
,”
Ph.D thesis
, University of Victoria, Victoria, Canada.http://dspace.library.uvic.ca/handle/1828/6005
36.
Malgarinos
,
I.
,
Nikolopoulos
,
N.
,
Marengo
,
M.
,
Antonini
,
C.
, and
Gavaises
,
M.
,
2014
, “
VOF Simulations of the Contact Angle Dynamics During the Drop Spreading: Standard Models and a New Wetting Force Model
,”
Adv. Colloid Interface Sci.
,
212
, pp.
1
20
.
37.
Hao
,
L.
, and
Cheng
,
P.
,
2009
, “
Lattice Boltzmann Simulations of Liquid Droplet Dynamic Behavior on a Hydrophobic Surface of a Gas Flow Channel
,”
J. Power Sources
,
190
(
2
), pp.
435
446
.
38.
Bao
,
Y. B.
, and
Meskas
,
J.
,
2011
, “
Lattice Boltzmann Method for Fluid Simulations
,”
Department of Mathematics, Courant Institute of Mathematical Sciences, New York University
,
New York
.
39.
Kang
,
X.
,
Tang
,
W.
, and
Liu
,
S.
,
2016
, “
Lattice Boltzmann Method for Simulating Disturbed Hemodynamic Characteristics of Blood Flow in Stenosed Human Carotid Bifurcation
,”
ASME J. Fluids Eng.
,
138
(
12
), p.
121104
.
40.
Murdock
,
J. R.
,
Ibrahim
,
A.
, and
Yang
,
S.-L.
,
2018
, “
An Efficient Method of Generating and Characterizing Filter Substrates for Lattice Boltzmann Analysis
,”
ASME J. Fluids Eng.
,
140
(
4
), p.
041203
.
41.
Wafik
,
A.
,
Fethi
,
A.
,
Keirsbulck
,
L.
, and
Sassi
,
B. N.
,
2015
, “
Experimental and Numerical Investigations Using Lattice Boltzmann Method to Study Shedding Vortices in an Unsteady Confined Flow Around an Obstacle
,”
ASME J. Fluids Eng.
,
137
(
10
), p.
101203
.
42.
Yuan
,
P.
, and
Schaefer
,
L.
,
2006
, “
A Thermal Lattice Boltzmann Two-Phase Flow Model and Its Application to Heat Transfer Problems—Part 1: Theoretical Foundation
,”
ASME J. Fluids Eng.
,
128
(
1
), pp.
142
150
.
43.
Yuan
,
P.
, and
Schaefer
,
L.
,
2006
, “
A Thermal Lattice Boltzmann Two-Phase Flow Model and Its Application to Heat Transfer Problems—Part 2: Integration and Validation
,”
ASME J. Fluids Eng.
,
128
(
1
), pp.
151
156
.
44.
Bhardwaj
,
S.
,
Dalal
,
A.
,
Biswas
,
G.
, and
Mukherjee
,
P. P.
,
2018
, “
Analysis of Droplet Dynamics in a Partially Obstructed Confinement in a Three-Dimensional Channel
,”
Phys. Fluids
,
30
(
10
), p.
102102
.
45.
XFlow
,
2018
, “
XFlow 2018 Theory Guide
,” Dassaullt Systemes, Vélizy-Villacoublay, France, pp. 1–25.
46.
Shih
,
T.-H.
,
Povinelli
,
L. A.
,
Liu
,
N.-S.
,
Potapczuk
,
M. G.
, and
Lumley
,
J.
,
1999
, “
A Generalized Wall Function
,” National Aeronautics and Space Administration, Report No.
NASA/TM-1999-209398
https://ntrs.nasa.gov/search.jsp?R=19990081113.
47.
Chen
,
X.
,
Doughramaji
,
N.
,
Betz
,
A. R.
, and
Derby
,
M. M.
,
2017
, “
Droplet Ejection and Sliding on a Flapping Film
,”
AIP Adv.
,
7
(
3
), p.
035014
.
48.
Fan
,
J.
,
Wilson
,
M.
, and
Kapur
,
N.
,
2011
, “
Displacement of Liquid Droplets on a Surface by a Shearing Air Flow
,”
J. Colloid Interface Sci.
,
356
(
1
), pp.
286
292
.
49.
Seevaratnam
,
G.
,
Ding
,
H.
,
Michel
,
O.
,
Heng
,
J.
, and
Matar
,
O.
,
2010
, “
Laminar Flow Deformation of a Droplet Adhering to a Wall in a Channel
,”
Chem. Eng. Sci.
,
65
(
16
), pp.
4523
4534
.
50.
Yang
,
A.-S.
, and
Tsai
,
W.-M.
,
2006
, “
Ejection Process Simulation for a Piezoelectric Microdroplet Generator
,”
ASME J. Fluids Eng.
,
128
(
6
), pp.
1144
1152
.
51.
Castillo
,
J. E.
,
Weibel
,
J. A.
, and
Garimella
,
S. V.
,
2015
, “
The Effect of Relative Humidity on Dropwise Condensation Dynamics
,”
Int. J. Heat Mass Transfer
,
80
, pp.
759
766
.
52.
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
), p.
8864
.
53.
Perez
,
M.
,
Brechet
,
Y.
,
Salvo
,
L.
,
Papoular
,
M.
, and
Suery
,
M.
,
1999
, “
Oscillation of Liquid Drops Under Gravity: Influence of Shape on the Resonance Frequency
,”
Europhys. Lett.
,
47
(
2
), p.
189
.
54.
Duan
,
R.-Q.
,
Koshizuka
,
S.
, and
Oka
,
Y.
,
2003
, “
Two-Dimensional Simulation of Drop Deformation and Breakup at Around the Critical Weber Number
,”
Nucl. Eng. Des.
,
225
(
1
), pp.
37
48
.
55.
Strotos
,
G.
,
Malgarinos
,
I.
,
Nikolopoulos
,
N.
, and
Gavaises
,
M.
,
2016
, “
Predicting Droplet Deformation and Breakup for Moderate Weber Numbers
,”
Int. J. Multiphase Flow
,
85
, pp.
96
109
.
56.
Jain
,
M.
,
Prakash
,
R. S.
,
Tomar
,
G.
, and
Ravikrishna
,
R.
,
2015
, “
Secondary Breakup of a Drop at Moderate Weber Numbers
,”
Proc. R. Soc. A
,
471
(
2177
), p.
0930
.
57.
Kékesi
,
T.
,
Amberg
,
G.
, and
Wittberg
,
L. P.
,
2014
, “
Drop Deformation and Breakup
,”
Int. J. Multiphase Flow
,
66
, pp.
1
10
.
58.
Stone
,
H. A.
,
1994
, “
Dynamics of Drop Deformation and Breakup in Viscous Fluids
,”
Annu. Rev. Fluid Mech.
,
26
(
1
), pp.
65
102
.
You do not currently have access to this content.