Mechanisms for the formation of bead defects, such as humping, gouging, rippling, and other unexpected surface patterns, encountered in welding or drilling are interpreted and reviewed from thermal-fluid science viewpoint. These defects usually accompanying with porosity, undercut, segregation, stress concentration, etc., seriously reduce the properties and strength of the joint or solidification. Even though different mechanisms for formation of the defects have been extensively proposed in the past, more systematical understanding of pattern formations from thermal, fluid, physics, electromagnetic, pattern selections, and metallurgy sciences is still limited. The effects of working parameters and properties on humping and rippling, for example, can be systematically and quantitatively interpreted from scale analysis presented in this work. Good comparison with experimental results reveals mechanisms of different surface patterns. The mechanistic findings for bead defects are also useful for other manufacturing and materials processing.

1.
Arata
,
Y.
, 1986,
Plasma, Electron and Laser Beam Technology
,
American Society for Metals
,
Materials Park, OH
.
2.
1991, “
Welding Handbook, Welding Processes
,” Vol.
2
, 8th ed.,
R. L.
O’Brien
, ed.,
American Welding Society
,
Miami, FL
.
3.
Campbell
,
H. C.
, 1991, “
Visual Inspection of Welds
,”
Weld. J.
,
70
, pp.
79
80
.
4.
Wei
,
P. S.
,
Chuang
,
K. C.
,
Ku
,
J. S.
,
DebRoy
,
T.
, and
Chen
,
K. H.
, 2011, “
Mechanisms of Spiking and Humping in Keyhole Welding
,” (to be published in IEEE Transactions on Components and Packaging Technologies).
5.
Katayama
,
S.
,
Matsunawa
,
A.
, and
Kojima
,
K.
, 1998, “
CO2 Laser Weldability of Aluminum Alloys (2nd Report): Defect Formation Conditions and Causes
,”
Weld. Int.
0950-7116,
12
, pp.
774
789
.
6.
Hall
,
A. C.
, and
Robino
,
C. V.
, 2004, “
Association of Microstructural Features and Rippling Phenomenon in 304 Stainless Steel Gas Tungsten Arc Welds
,”
Sci. Technol. Weld. Joining
1362-1718,
9
, pp.
103
108
.
7.
Bennett
,
W. S.
, and
Mills
,
G. S.
, 1974, “
GTA Weldability Studies on High Manganese Stainless Steels
,“
Weld. J.
,
53
, pp.
548
-s–553-
s
.
8.
Matsuda
,
F.
,
Ushio
,
M.
,
Nakagawa
,
H.
, and
Nakata
,
K.
, 1980, “
Effects of Electromagnetic Stirring on the Weld Solidification Structure of Aluminum Alloys
,”
An International Conference on Arc Physics and Weld Pool Behaviour
, Vol.
1
, London, May 8–10,
The Welding Institute
,
Cambridge, UK
, Paper 10, pp.
337
347
.
9.
Okada
,
T.
,
Yokoya
,
S.
, and
Ishizaki
,
K.
, 1988, “
Effect of Surface-Active Elements on TIG Arc Welding Phenomena
,” IIW Doc.212-708-88.
10.
Sundell
,
R. E.
,
Solomon
,
H. D.
,
Harris
,
L. P.
, and
Wojcik
,
L. A.
,
Savage
,
W. F.
, and
Walsh
,
D. W.
, 1983, “
Minor Element Effects on Gas-Tungsten-Arc Weld Penetration
,” General Electric Co. Corp. Report No. SRD-83-066.
11.
Mills
,
K. C.
, and
Keene
,
B. J.
, 1990, “
Factors Affecting Variable Weld Penetration
,”
Int. Mater. Rev.
0950-6608,
35
, pp.
185
216
.
12.
Garland
,
J. G.
, and
Davies
,
G. J.
, 1970, “
Surface Rippling and Growth Perturbations During Weld Pool Solidification
,”
Met. Constr. Br. Weld. J.
0026-0541,
2
, pp.
171
175
.
13.
Arata
,
Y.
, and
Miyamoto
,
I.
, 1972, “
Some Fundamental Properties of High Power Laser Beam as a Heat Source (Report 3)-Metal Heating by Laser Beam
,”
Trans. Jpn. Weld. Soc.
0385-9282,
3
, pp.
163
180
.
14.
Ishida
,
T.
, 1988, “
Surface Bead Formation of a Mild Steel by Pulsed Current TIG Arc
,”
J. Mater. Sci.
0022-2461,
23
, pp.
3232
3242
.
15.
Wei
,
P. S.
,
Chang
,
C. Y.
, and
Chen
,
C. T.
, 1996, “
Surface Ripple in Electron-Beam Welding Solidification
,”
ASME J. Heat Transfer
0022-1481,
118
, pp.
960
969
.
16.
Lee
,
S.
,
Yang
,
D.
, and
Nikumb
,
S.
, 2008, “
Femtosecond Laser Micromilling of Si Wafers
,”
Appl. Surf. Sci.
0169-4332,
254
, pp.
2996
3005
.
17.
Wei
,
P. S.
,
Chen
,
Y. H.
,
Ku
,
J. S.
, and
Ho
,
C. Y.
, 2003, “
Active Solute Effects on Surface Ripples in Electron-Beam Welding Solidification
,”
Metall. Mater. Trans. B
1073-5615,
34
, pp.
421
432
.
18.
Bradstreet
,
B. J.
, 1968, “
Effect of Surface Tension and Metal Flow on Weld Bead Formation
,”
Weld. J.
,
47
, pp.
314
-s–322-
s
.
19.
Cho
,
M. H.
, and
Farson
,
D. F.
, 2007, “
Understanding Bead Hump Formation in Gas Metal Arc Welding Using a Numerical Simulation
,”
Metall. Mater. Trans. B
1073-5615,
38
, pp.
305
319
.
20.
Nguyen
,
T. C.
,
Weckman
,
D. C.
, and
Johnson
,
D. A.
, 2007, “
The Discontinuous Weld Bead Defect in High-Speed Gas Metal Arc Welds
,”
Weld. J.
,
86
, pp.
360
-s–372-
s
.
21.
Wu
,
C. S.
,
Hu
,
Z. K.
, and
Zhang
,
Y. M.
, 2009, “
Suppression of Weld-Bead Defects and Increase in the Critical Welding Speed During High-Speed Arc Welding
,“
Proc. Inst. Mech. Eng., Part B
0954-4054,
223
, pp.
751
757
.
22.
Akahide
,
K.
,
Ukebe
,
T.
, and
Tsuboi
,
J.
, 1982, “
Correlation Between Bead Dimensions and Welding Parameters in Submerged-Arc Welding
,”
Trans. Jpn. Weld. Soc.
0385-9282,
13
, pp.
76
.
23.
Nomura
,
H.
,
Sugitani
,
Y.
, and
Tsuji
,
M.
, 1982, “
Behaviour of Molten Pool in Submereged Arc Welding: Observation by X-Ray Fluoroscopy
,”
Q. J. Jpn. Weld. Soc.
0288-4771,
51
, pp.
767
775
.
24.
Kumagai
,
M.
, and
Okuda
,
N.
, 1986, “
Research on Bead Formation in Submerged Arc Welding. III. Effect of Flux Height on the Bead Appearance in Submerged Arc Welding
,”
Q. J. Jpn. Weld. Soc.
0288-4771,
4
, pp.
283
289
.
25.
Paton
,
B. E.
,
Mandel’berg
,
S. L.
, and
Sidorenko
,
B. G.
, 1971, “
Certain Special Features of the Formation of Welds Made at High Speeds
,”
Avt. Svarka
,
8
, pp.
1
6
.
26.
Yamamoto
,
T.
, and
Shimada
,
W.
, 1975, “
A Study on Bead Formation in High Speed TIG Arc Welding at Low Gas Pressure
,”
Proceedings of the Advanced Welding Technology, The Second International Symposium of the Japan Welding Society on Advanced Welding Technology
, Osaka, Japan, Japan Welding Society, Paper No. 2-2-(7), pp.
321
326
.
27.
Savage
,
W. F.
,
Nippes
,
E. F.
, and
Agusa
,
K.
, 1979,”
Effect of Arc Force on Defect Formation in GTA Welding
,”
Weld. J.
,
58
, pp.
212
-s–224-
s
.
28.
Hiramoto
,
S.
,
Ohmine
,
M.
,
Okuda
,
T.
, and
Shinmi
,
A.
, 1987, “
Deep Penetration Welding With High Power CO2 Laser
,”
Proceedings of the International Conference on Laser Advanced Material Processing-Science and Application
, May 21–23, Osaka, Japan, High Temperature Society of Japan and Japan Laser Processing Society, pp.
157
162
.
29.
Albright
,
C. E.
, and
Chiang
,
S.
, 1988, “
High-Speed Laser Welding Discontinuities
,”
J. Laser Appl.
1042-346X,
1
, pp.
18
24
.
30.
Tsukamoto
,
S.
,
Irie
,
H.
,
Inagaki
,
M.
, and
Hashimoto
,
T.
, 1983, “
Effect of Focal Position on Humping Bead Formation in Electron Beam Welding
,”
Trans. National Research Institute for Metals
,
25
, pp.
62
67
.
31.
Tsukamoto
,
S.
,
Irie
,
H.
,
Inagaki
,
M.
, and
Hashimoto
,
T.
, 1984, “
Effect of Beam Current on Humping Bead Formation in Electron Beam Welding
,”
Trans National Research Institute for Metals
,
26
, pp.
133
140
.
32.
Tomie
,
M.
,
Abe
,
N.
, and
Arata
,
Y.
, 1989, “
Tandem Electron Beam Welding (Report IX)-High Speed Tandem Electron Beam Welding
,”
Trans. JWRI
0387-4508,
18
, pp.
175
180
.
33.
Shiu
,
T. R.
,
Grigoropoulos
,
C. P.
,
Cahill
,
D. G.
, and
Greif
,
R.
, 1999, “
Mechanism of Bump Formation on Glass Substrates During Laser Texturing
,”
J. Appl. Phys.
0021-8979,
86
, pp.
1311
1316
.
34.
Schiaffino
,
S.
, and
Sonin
,
A. A.
, 1997, “
Formation and Stability of Liquid and Molten Beads on a Solid Surface
,”
J. Fluid Mech.
0022-1120,
343
, pp.
95
110
.
35.
Ho
,
C. M.
, and
Tai
,
Y. C.
, 1998, “
Micro-Electro-Mechanical-Systems (MEMS) and Fluid Flows
,”
Annu. Rev. Fluid Mech.
0066-4189,
30
, pp.
579
612
.
36.
Lau
,
J. H.
,
Shangguan
,
D.
,
Lau
,
D. C. Y.
,
Kung
,
T. T. W.
, and
Lee
,
S. W. R.
, 2004, “
Thermal-Fatigue Life Prediction Equation for Wafer-Level Chip Scale Package (WLCSP) Lead-Free Solder Joints on Lead-Free Printed Circuit Board (PCB)
,”
Proceedings of the 54th 2004 Electronic Components and Technology Conference
, Vol.
2
, pp.
1563
1569
.
37.
Soderstrom
,
E.
, and
Mendez
,
P.
, 2006, “
Humping Mechanisms Present in High Speed Welding
,”
Sci. Technol. Weld. Joining
1362-1718,
11
, pp.
572
579
.
38.
Mendez
,
P. F.
, and
Eagar
,
T. W.
, 2003, “
Penetration and Defect Formation in High-Current Arc Welding
,”
Weld. J.
,
82
, pp.
296
-s–306-
s
.
39.
Shimada
,
W.
, and
Hoshinouchi
,
S.
, 1982, “
A Study on Bead Formation by Low Pressure TIG Arc and Prevention of Under-Cut Bead
,”
Trans. Jpn. Weld. Soc.
0385-9282,
51
, pp.
280
286
.
40.
Mendez
,
P. F.
,
Niece
,
K. L.
, and
Eagar
,
T. W.
, 2000, “
Humping Formation in High Current GTA Welding
,”
Proceedings of the International Conference on Joining of Advanced and Specialty Materials II
, Cincinnati, OH, ASM International, Nov., pp.
151
158
.
41.
Tsukamoto
,
S.
,
Irie
,
H.
,
Hashimoto
,
T.
, and
Inagaki
,
M.
, 1982, “
Humping Bead Formation in Electron Beam Welding (Report 1)-Effect of Focal Position on Humping Bead Formation
,”
Q. J. Jpn. Weld. Soc.
0288-4771,
51
, pp.
286
291
.
42.
Marya
,
M.
, and
Edwards
,
G. R.
, 2001, “
Factors Controlling the Magnesium Weld Morphology in Deep Penetration Welding by a CO2 Laser
,”
J. Mater. Eng. Perform.
1059-9495,
10
, pp.
435
443
.
43.
Nishiguchi
,
K.
,
Matsuyama
,
K.
,
Terai
,
K.
, and
Ikeda
,
K.
, 1975, “
Bead Formation in High Speed Gas-Shielded Metal-Arc Welding
,”
Proceedings of the Second International Symposium on JWS Advanced Welding Technology
, Osaka, Japan, Japan Welding Society, Paper 2-2-(10).
44.
Kawahito
,
Y.
,
Mizutani
,
M.
, and
Katayama
,
S.
, 2007, “
Elucidation of High-Power Fibre Laser Welding Phenomena of Stainless Steel and Effect of Factors on Weld Geometry
,”
J. Phys. D: Appl. Phys.
0022-3727,
40
, pp.
5854
5859
.
45.
Tong
,
H.
, and
Giedt
,
W. H.
, 1969, “
Radiographs of the Electron Beam Welding Cavity
,”
Rev. Sci. Instrum.
0034-6748,
40
, pp.
1283
1285
.
46.
Batteh
,
J. J.
,
Chen
,
M. M.
, and
Mazumder
,
J.
, 2000, “
A Stagnation Flow-Analysis of the Heat Transfer and Fluid-Flow Phenomena in Laser Drilling
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
801
807
.
47.
Wei
,
P. S.
, and
Giedt
,
W. H.
, 1985, “
Surface Tension Gradient-Driven Flow Around an Electron Beam Welding Cavity
,”
Weld. J.
,
64
, pp.
251
-s–259-
s
.
48.
Wei
,
P. S.
, and
Chiou
,
L. R.
, 1988, “
Molten Metal Flow Around the Base of a Cavity During a High-Energy Beam Penetrating Process
,”
ASME J. Heat Transfer
0022-1481,
110
, pp.
918
923
.
49.
Nguyen
,
T. C.
,
Weckman
,
D. C.
,
Johnson
,
D. A.
, and
Kerr
,
H. W.
, 2006, “
Review—High Speed Fusion Weld Bead Defects
,”
Sci. Technol. Weld. Joining
1362-1718,
11
, pp.
618
633
.
50.
Yamauchi
,
N.
, and
Taka
,
T.
, 1978, “
Bead Formation in TIG Welding
,” International Institute of Welding, Document No. 212-437-78.
51.
Yamauchi
,
N.
, and
Taka
,
T.
, 1979, “
TIG Arc Welding With a Hollow Tungsten Electrode
,” International Institute of Welding, Document No. 212-452-79.
52.
Troyer
,
W.
,
Tomsic
,
M.
, and
Barhorst
,
R.
, 1977, “
Investigation of Pulsed Wave Shapes
,”
Weld. J.
,
56
, pp.
26
32
.
53.
Shimokusu
,
Y.
,
Fukumoto
,
S.
,
Nayama
,
M.
,
Ishide
,
T.
,
Tsubota
,
S.
,
Matunawa
,
A.
, and
Katayama
,
S.
, 2002, “
Application of Pulse Modulated High Power YAG Laser to Thick Plate Welding
,”
Q. J. Jpn. Weld. Soc.
0288-4771,
20
, pp.
477
483
.
54.
Ishizaki
,
K.
,
Yokoya
,
S.
, and
Okada
,
T.
, 1988, “
Weldability of Stainless Steel
,” Report, Nippon Institute of Technology, Saitama, Japan to VAMAS Meeting on Technical Working Area, Weld Characteristics, NPL, Teddington.
55.
Hirata
,
H.
,
Ogawa
,
K.
, and
Taka
,
T.
, 1999, “
Effect of Chemical Compositions on Bead Formation in TIG Arc Welding-Effect of Chemical Compositions on Weldability in Fabrication in High Alloyed Steel (Report II)
,”
Q. J. Jpn. Weld. Soc.
0288-4771,
17
, pp.
397
402
.
56.
Takeuchi
,
Y.
,
Takagi
,
R.
, and
Shinoda
,
T.
, 1992, “
Effect of Bismuth on Weld Joint Penetration in Austenitic Stainless Steel
,”
Weld. J.
,
71
, pp.
283
-s–289-
s
.
57.
Honma
,
S.
, and
Yasuda
,
K.
, 2004, “
Study of Semi-Automatic TIG Welding
,”
Weld. Int.
0950-7116,
18
, pp.
450
455
.
58.
Nguyen
,
T. C.
,
Weckman
,
D. C.
,
Johnson
,
D. A.
, and
Kerr
,
H. W.
, 2005, “
The Humping Phenomenon During High Speed Gas Metal Arc Welding
,”
Sci. Technol. Weld. Joining
1362-1718,
10
, pp.
447
459
.
59.
Kern
,
M.
,
Berger
,
P.
, and
Hügel
,
H.
, 2000, “
Magneto-Fluid Dynamic Control of Seam Quality in CO2 Laser Beam Welding
,”
Weld. J.
,
79
, pp.
72
-s–78-
s
.
60.
Hirata
,
Y.
, 2003, “
Pulsed Arc Welding
,”
Weld. Int.
0950-7116,
17
, pp.
98
115
.
61.
Michie
,
K.
,
Blackman
,
S.
, and
Ogunbiyi
,
T. E. B.
, 1999, “
Twin-Wire GMAW: Process Characteristics and Applications
,”
Weld. J.
,
78
, pp.
31
34
.
62.
Ueyama
,
T.
,
Ohnawa
,
T.
,
Tanaka
,
M.
, and
Nakata
,
K.
, 2005, “
Effects of Torch Configuration and Welding Current on Weld Bead Formation in High Speed Tandem Pulsed Gas Metal Arc Welding of Steel Sheets
,”
Sci. Technol. Weld. Joining
1362-1718,
10
, pp.
750
759
.
63.
Kannatey-Asibu
,
E.
, Jr.
, 1991, “
Thermal Aspects of the Split-Beam Laser Welding Concept
,”
Trans. the ASME
,
113
, pp.
215
221
.
64.
Xie
,
J.
, 2002, “
Dual Beam Laser Welding
,”
Weld. J.
,
81
, pp.
223
-s–230-
s
.
65.
Arata
,
Y.
, and
Nabegata
,
E.
, 1978, “
Tandem Electron Beam Welding (Report-I)
,”
Trans. JWRI
0387-4508,
7
, pp.
101
109
.
66.
Dilthey
,
U.
, and
Wieschemann
,
A.
, 2000, “
Prospects by Combining and Coupling Laser Beam and Arc Welding Processes
,”
Rivista Italiana della Saldatura (Italy)
,
52
, pp.
749
759
.
67.
El Rayes
,
M.
,
Walz
,
C.
, and
Sepold
,
G.
, 2004, “
The Influence of Various Hybrid Welding Parameters on Bead Geometry
,”
Weld. J.
,
83
, pp.
147
-s–153-
s
.
68.
Choi
,
H. W.
,
Farson
,
D. F.
, and
Cho
,
M. H.
, 2006, “
Using a Hybrid Laser Plus GMAW Process for Controlling the Bead Humping Defect
,”
Weld. J.
,
85
, pp.
174s
179s
.
69.
Hartman
,
D. A.
,
DeLapp
,
D. R.
,
Cook
,
G. E.
, and
Barnett
,
R. J.
, 1999, “
Intelligent Fusion Control Throughout Varying Thermal Regions
,”
Industry Applications Conference, 34th IAS Annual Meeting
, Oct. 3–7, IEEE, Phoenix, AZ, pp.
635
644
.
70.
Kovacevic
,
R.
, and
Zhang
,
Y. M.
, 1996, “
Sensing Free Surface of Arc Weld Pool Using Specular Reflection: Principle and Analysis
,”
Proc. Inst. Mech. Eng.
0020-3483,
210
, pp.
553
564
.
71.
Mirapeix
,
J.
,
Cobo
,
A.
,
Fernandez
,
S.
,
Cardoso
,
R.
, and
Lopez-Higuera
,
J. M.
, 2008, “
Spectroscopic Analysis of the Plasma Continuum Radiation for On-Line Arc-Welding Defect Detection
,”
J. Phys. D: Appl. Phys.
0022-3727,
41
, p.
135202
.
72.
Cheever
,
D. L.
, and
Howden
,
D. G.
, 1969, “
Technical Note: Nature of Weld Surface Ripples
,”
Weld. J.
,
48
, pp.
179
-s–180-
s
.
73.
D’annessa
,
A. T.
, 1970, “
Sources and Effects of Growth Rate Fluctuations During Weld Metal Solidification
,”
Weld. J.
,
49
, pp.
41
-s–45-
s
.
74.
Kotecki
,
D. J.
,
Cheever
,
D. L.
, and
Howden
,
D. G.
, 1972, “
Mechanism of Ripple Formation During Weld Solidification
,”
Weld. J.
,
51
, pp.
386
-s–391-
s
.
75.
Ecer
,
G. M.
,
Tzavaras
,
A.
,
Gokhale
,
A.
, and
Brody
,
H. D.
, 1982, “
Weld Pool Fluid Motion and Ripple Formation in Pulsed-Current GTAW
,”
Trends in Welding Research in the United States
, Nov. 16–18,
S. A.
David
, ed.,
Joining Division of American Society for Metals
,
New Orleans, LA
, pp.
419
442
.
76.
Altshulin
,
S.
,
Zahavi
,
J.
,
Rosen
,
A.
, and
Nadiv
,
S.
, 1990, “
The Interaction between a Pulsed Laser Beam and a Steel Surface
,”
J. Mater. Sci.
0022-2461,
25
, pp.
2259
2263
.
77.
Xu
,
J. -J.
, and
Davis
,
S. H.
, 1984,”
Convective Thermocapillary Instabilities in Liquid Bridges
,”
Phys. Fluids
1070-6631,
27
, pp.
1102
1107
.
78.
Kamotani
,
Y.
, and
Ostrach
,
S.
, 1998, “
Theoretical Analysis of Thermocapillary Flow in Cylindrical Columns of High Prandtl Number Fluids
,”
ASME J. Heat Transfer
0022-1481,
120
, pp.
758
764
.
79.
Keller
,
J. R.
, and
Bergman
,
T. L.
, 1990, “
Thermosolutal Inducement of No-Slip Free Surfaces in Combined Marangoni-Buoyancy Driven Cavity Flows
,”
ASME J. Heat Transfer
0022-1481,
112
, pp.
363
369
.
80.
Miller
,
C. A.
, and
Neogi
,
P.
, 1985,
Interfacial Phenomena, Equilibrium and Dynamic Effects
,
Dekker
,
New York
.
81.
Pearson
,
J. R. A.
, 1958, “
On Convection Cells Induced by Surface Tension
,”
J. Fluid Mech.
0022-1120,
4
, pp.
489
500
.
82.
Fujimura
,
K.
,
Ogawa
,
M.
, and
Seki
,
M.
, 1992, “
Possible Mechanism of the Roughness Formation on a Liquid Layer Caused by a High Heat Flux
,”
Fusion Eng. Des.
0920-3796,
19
, pp.
183
191
.
83.
Ogawa
,
M.
,
Araki
,
M.
,
Seki
,
M.
,
Kunugi
,
T.
,
Fukaya
,
K.
, and
Ise
,
H.
, 1992, “
Experimental Study on Melting and Evaporation of Metal Exposed to Intense Hydrogen Ion Beam
,”
Fusion Eng. Des.
0920-3796,
19
, pp.
193
202
.
84.
Ang
,
L. K.
,
Lau
,
Y. Y.
,
Gilgenbach
,
R. M.
,
Spindler
,
H. L.
,
Lash
,
J. S.
, and
Kovaleski
,
S. D.
, 1998, “
Surface Instability of Multipulse Laser Ablation on a Metallic Target
,”
J. Appl. Phys.
0021-8979,
83
, pp.
4466
4471
.
85.
Chandrasekhar
,
S.
, 1961,
Hydrodynamic and Hydromagnetic Stability
,
Oxford University Press
,
London
.
86.
Bennett
,
T. D.
,
Grigoropoulos
,
C. P.
, and
Krajnovich
,
D. J.
, 1995, “
Near-Threshold Laser Sputtering of Gold
,”
J. Appl. Phys.
0021-8979,
77
, pp.
849
864
.
87.
Seifert
,
N.
,
Betz
,
G.
, and
Husinsky
,
W.
, 1996, “
Hydrodynamic Phenomena During Laser Irradiation: a Finite Difference Approach
,”
Appl. Surf. Sci.
0169-4332,
96–98
, pp.
33
38
.
88.
Lugomer
,
S.
, 2007, “
Micro-fluid Dynamics via Laser-Matter Interaction: Vortex Filament Structures, Helical Instability, Reconnection, Merging, and Undulation
,”
Phys. Lett. A
0375-9601,
361
, pp.
87
97
.
89.
Keilmann
,
F.
, 1983, “
Laser-Driven Corrugation Instability of Liquid Metal Surfaces
,”
Phys. Rev. Lett.
0031-9007,
51
, pp.
2097
2100
.
90.
Emel’yanov
,
V. I.
,
Konov
,
V. I.
,
Tokarev
,
V. N.
, and
Seminogov
,
V. N.
, 1989, “
Formation of Periodic Surface Ripples Under the Action of Pulsed Carbon Dioxide Laser Radiation on Fused Silica
,”
J. Opt. Soc. Am. B
0740-3224,
6
, pp.
104
114
.
91.
Kolasinski
,
K. W.
, 2007, “
Solid Structure Formation During the Liquid/Solid Phase Transition
,”
Curr. Opin. Solid State Mater. Sci.
1359-0286,
11
, pp.
76
85
.
92.
Mullins
,
W. W.
, and
Sekerka
,
R. F.
, 1964, “
Stability of a Planar Interface During Solidification of a Dilute Binary Alloy
,”
J. Appl. Phys.
0021-8979,
35
, pp.
444
451
.
93.
Rutter
,
J. W.
, and
Chalmers
,
B.
, 1953, “
A Prismatic Substructure Formed During Solidification of Metals
,”
Can. J. Phys.
0008-4204,
31
, pp.
15
39
.
94.
Bösch
,
M. A.
, and
Lemons
,
R. A.
, 1981, “
Laser-Induced Melt Dynamics of Si and Silica
,”
Phys. Rev. Lett.
0031-9007,
47
, pp.
1151
1155
.
95.
Weizman
,
M.
,
Nickel
,
N. H.
,
Sieber
,
I.
, and
Yan
,
B.
, 2008, “
Laser-Induced Self-Organization in Silicon-Germanium Thin Films
,”
J. Appl. Phys.
0021-8979,
103
, p.
093536
.
96.
Style
,
R. W.
, and
Wettlaufer
,
J. S.
, 2007, “
Evaporatively Driven Morphological Instability
,”
Phys. Rev. E
1063-651X,
76
, p.
011602
.
97.
Gräf
,
S.
,
Staupendahl
,
G.
,
Seiser
,
C.
,
Meyer
,
B. –J.
, and
Müller
,
F. A.
, 2010, “
Enhanced Melt Pool Stirring in Welding With Dynamic Polarized Laser Beam
,”
Sci. Technol. Weld. Joining
1362-1718,
15
, pp.
208
212
.
98.
Itoh
,
K.
,
Watanabe
,
W.
, and
Ozeki
,
Y.
, 2009, “
Nonlinear Ultrafast Focal-Point Optics for Microscopic Imaging, Manipulation, and Machining
,”
Proc. IEEE
0018-9219,
97
, pp.
1011
1030
.
99.
Emel’yanov
,
V. I.
,
Zemskov
,
E. M.
, and
Seminogov
,
V. N.
, 1984, “
Theory of the Formation of “Normal” and “Anomalous” Gratings on the Surfaces of Absorbing Condensed Media Exposed to Laser Radiation
,”
Sov. J. Quantum Electron.
0049-1748,
14
, pp.
1515
1521
.
100.
Birnbaum
,
M.
, 1965, “
Semiconductor Surface Damage Produced by Ruby Lasers
,”
J. Appl. Phys.
0021-8979,
36
, pp.
3688
3689
.
101.
Lenzner
,
M.
, 1999, “
Femtosecond Laser-Induced Damage of Dielectrics
,”
Int. J. Mod. Phys. B
0217-9792,
13
, pp.
1559
1578
.
102.
Young
,
J. F.
,
Preston
,
J. S.
,
van Driel
,
H. M.
, and
Sipe
,
J. E.
, 1983, “
Laser-Induced Periodic Surface Structure. II. Experiments on Ge, Si, Al, and Brass
,”
Phys. Rev. B
0556-2805,
27
, pp.
1155
1172
.
103.
Siegman
,
A. E.
, and
Fauchet
,
P. M.
, 1986, “
Stimulated Wood’s Anomalies on Laser-Illuminated Surfaces
,”
IEEE J. Quantum Electron.
0018-9197,
22
, pp.
1384
1403
.
104.
Pedraza
,
A. J.
,
Guan
,
Y. F.
,
Fowlkes
,
J. D.
, and
Smith
,
D. A.
, 2004, “
Nanostructures Produced by Ultraviolet Laser Irradiation of Silicon. I. Rippled Structures
,”
J. Vac. Sci. Technol. B
1071-1023,
22
, pp.
2823
2835
.
105.
Anthony
,
T. R.
, and
Cline
,
H. E.
, 1977, “
Surface Rippling Induced by Surface-Tension Gradients During Laser Surface Melting and Alloying
,”
J. Appl. Phys.
0021-8979,
48
, pp.
3888
3894
.
106.
Glicksman
,
M. E.
, and
Schaefer
,
R. J.
, 1968, “
In Situ Observations of Dendritic Growth and Remelting Processes During Metallic Solidification
,”
The Solidification of Metals
,
Iron and Steel Institute
,
London
, pp.
43
48
and
124
125
.
107.
Ryzhkov
,
F. N.
, and
Bashkatov
,
A. V.
, and
Uglov
,
A. A.
, 1972, “
Mechanism of Formation of Electron-Beam Welds
,”
Svar. Proiz.
,
5
, pp.
10
12
.
108.
Ostrach
,
S.
, 1982, “
Low-Gravity Fluid Flows
,”
Annu. Rev. Fluid Mech.
0066-4189,
14
, pp.
313
345
.
109.
Chen
,
M. M.
, 1987, “
Thermocapillary Convection in Materials Processing
,”
Interdisciplinary Issues in Materials Processing and Manufacturing
,
S. K.
Samanta
,
R.
Komanduri
,
R.
McMeeking
,
M. M.
Chen
, and
A.
Tseng
, eds.,
ASME
,
New York
, pp.
541
558
.
110.
Arata
,
Y.
,
Tomie
,
M.
,
Abe
,
N.
, and
Yao
,
X. -Y.
, 1987, “
Observation of Molten Metal Flow During EB Welding
,”
Trans. JWRI
0387-4508,
16
, pp.
13
16
.
111.
Low
,
D. K. Y.
, and
Li
,
L.
, 2000,
Laser Drilling of Transparent Media for the Study of Material Removal, Taper and Spatter Formation Mechanisms
,
ICALEO
, pp.
105
114
.
112.
Fabbro
,
R.
, 2002, “
Basic Processes in Deep Penetration Laser Welding
,”
ICALEO’2002
, Oct., Scottsdale, AZ.
113.
Slavin
,
G. A.
, and
Trokhinskaya
,
N. M.
, 1983, “
Relationship Between Thermal and Hydrodynamic Processes in the Pool in Welding Thin Sheet Materials With a Continuous Arc
,”
Svar. Proiz. (Weld. Production)
,
4
, pp.
4
6
.
114.
Hu
,
J.
,
Guo
,
H.
, and
Tsai
,
H. L.
, 2008, “
Weld Pool Dynamics and the Formation of Ripples in 3D Gas Metal Arc Welding
,”
Int. J. Heat Mass Transfer
0017-9310,
51
, pp.
2537
2552
.
115.
Kou
,
S.
, and
Wang
,
Y. H.
, 1986, “
Weld Pool Convection and Its Effect
,”
Weld. J.
,
65
, pp.
63
-s–70-
s
.
116.
Zacharia
,
T.
,
David
,
S. A.
,
Vitek
,
J. M.
, and
DebRoy
,
T.
, 1989, “
Weld Pool Development During GTA and Laser Beam Welding of Type 304 Stainless Steel, Part I—Theoretical Analysis
,”
Weld. J.
,
68
, pp.
499
-s–509-
s
.
117.
Chakraborty
,
N.
,
Chakraborty
,
S.
, and
Dutta
,
P.
, 2004, “
Three-Dimensional Modeling of Turbulent Weld Pool Convection in GTAW Processes
,”
Numer. Heat Transf., Part A
,
45
, pp.
391
413
.
118.
Iwamoto
,
M.
,
Ye
,
M.
,
Grigoropoulos
,
C. P.
, and
Greif
,
R.
, 1998, “
Numerical Analysis of Pulsed Laser Heating for the Deformation of Metals
,”
Numer. Heat Transf., Part A
,
34
, pp.
791
804
.
119.
Ki
,
H.
,
Mohanty
,
P. S.
, and
Mazumder
,
J.
, 2002, “
Modeling of Laser Keyhole Welding: Part II. Simulation of Keyhole Evolution, Velocity, Temperature Profile, and Experimental Verification
,”
Metall. Mater. Trans. A
1073-5623,
33
, pp.
1831
1842
.
120.
Lee
,
J. Y.
,
Ko
,
S. H.
,
Farson
,
D. F.
, and
Yoo
,
C. D.
, 2002, “
Mechanism of Keyhole Formation and Stability in Stationary Laser Welding
,”
J. Phys. D: Appl. Phys.
0022-3727,
35
, pp.
1570
1576
.
121.
He
,
X.
,
Fuerschbach
,
P. W.
, and
DebRoy
,
T.
, 2003, “
Heat Transfer and Fluid Flow During Laser Spot Welding of 304 Stainless Steel
,”
J. Phys. D: Appl. Phys.
0022-3727,
36
, pp.
1388
1398
.
122.
Zhou
,
J.
,
Tsai
,
H. L.
, and
Wang
,
P. C.
, 2006, “
Transport Phenomena and Keyhole Dynamics During Pulsed Laser Welding
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
680
690
.
123.
Schwarz-Selinger
,
T.
,
Cahill
,
D. G.
,
Chen
,
S. -C.
,
Moon
,
S. -J.
, and
Grigoropoulos
,
C. P.
, 2001, “
Micron-Scale Modifications of Si Surface Morphology by Pulsed-Laser Texturing
,”
Phys. Rev. B
0556-2805,
64
, p.
155323
.
124.
Balandin
,
V. Yu.
,
Gernert
,
U.
,
Nink
,
T.
, and
Bostanjoglo
,
O.
, 1997, “
Segregation and Surface Transport of Impurities: New Mechanisms Affecting the Surface Morphology of Laser Treated Metals
,”
J. Appl. Phys.
0021-8979,
81
, pp.
2835
2838
.
125.
Röntzsch
,
L.
,
Heinig
,
K. -H.
,
Schuller
,
J. A.
, and
Brongersma
,
M. L.
, 2007, “
Thin Film Patterning by Surface-Plasmon-Induced Thermocapillarity
,”
Appl. Phys. Lett.
0003-6951,
90
, p.
044105
.
126.
Arata
,
Y.
,
Matsuda
,
F.
, and
Murakami
,
T.
, 1973, “
Some Dynamic Aspects of Weld Molten Metal in Electron Beam Welding
,”
Trans. Jpn. Weld. Research Institute
,
2
, pp.
23
32
.
127.
Irie
,
H.
,
Tsukamoto
,
S.
, and
Inagaki
,
M.
, 1984, “
Relation between Beam Properties and Shape of Fusion Zone in Electron Beam Welding-Abnormally Expanded Fusion Zone
,”
Trans. National Research Institute for Metals
,
26
, pp.
287
296
.
128.
Gratzke
,
U.
,
Kapadia
,
P. D.
,
Dowden
,
J.
,
Kroos
,
J.
, and
Simon
,
G.
, 1992, “
Theoretical Approach to the Humping Phenomenon in Welding Processes
,”
J. Phys. D: Appl. Phys.
0022-3727,
25
, pp.
1640
1647
.
129.
Viskanta
,
R.
, 1988, “
Heat Transfer During Melting and Solidification of Metals,” 50th Anniversary Issue
,
ASME J. Heat Transfer
0022-1481,
110
, pp.
1205
1219
.
130.
Tytkin
,
Yu. M.
,
Ryazantsev
,
O. V.
, and
Chuvilo
,
V. N.
, 1981, “
The Mechanism of Formation of a Coarse Flaky Surface of Weld Metal in Welding Under High-Power Conditions
,”
Svar. Proiz.
,
2
, pp.
4
5
.
131.
Kumar
,
A.
, and
DebRoy
,
T.
2006, “
Toward a Unified Model to Prevent Humping Defects in Gas Tungsten Arc Welding
,”
Weld. J.
,
85
, pp.
292
-s–304-
s
.
132.
Bush
,
J. W. M.
,
Aristoff
,
J. M.
, and
Hosoi
,
A. E.
, 2006, “
An Experimental Investigation of the Stability of the Circular Hydraulic Jump
,”
J. Fluid Mech.
0022-1120,
558
, pp.
33
52
.
133.
Mogyorósi
,
P.
,
Piglmayer
,
K.
, and
Bäuerle
,
D.
, 1989, “
Ar+ Laser-Induced Chemical Etching of Molybdenum in Chlorine Atmosphere
,”
Surf. Sci.
0039-6028,
208
, pp.
232
244
.
134.
Bäuerle
,
D.
, 1996,
Laser Processing and Chemistry
,
Springer-Verlag
,
New York
.
135.
Mathur
,
M.
,
DasGupta
,
R.
,
Selvi
,
N. R.
,
John
,
N. S.
,
Kulkarni
,
G. U.
, and
Govindarajan
,
R.
, 2007, “
Gravity-Free Hydraulic Jumps and Metal Femtoliter Cups
,”
Phys. Rev. Lett.
0031-9007,
98
, p.
164502
.
136.
Lin
,
M. L.
, and
Eagar
,
T. W.
, 1985, “
Influence of Arc Pressure on Weld Pool Geometry
,”
Weld. J.
,
64
, pp.
163
-s–169-
s
.
137.
Bejan
,
A.
, 1995,
Convection Heat Transfer
,
Wiley
,
New York
.
138.
Jeffreys
,
H.
, 1925, “
On the Formation of Water Waves by Wind
,”
Proc. R. Soc. London, Ser. A
0950-1207,
107
, pp.
189
206
.
139.
Miles
,
J. W.
, 1957, “
On the Generation of Surface Waves by Shear Flows
,”
J. Fluid Mech.
0022-1120,
3
, pp.
185
204
.
140.
Lighthill
,
M. J.
, 1962, “
Physical Interpretation of the Mathematical Theory of Wave Generation by Wind
,”
J. Fluid Mech.
0022-1120,
14
, pp.
385
398
.
141.
Hogan
,
J. M.
, and
Ayyaswamy
,
P. S.
, 1985, “
Linear Stability of a Viscous-Inviscid Interface
,”
Phys. Fluids
1070-6631,
28
, pp.
2709
2715
.
142.
Shtemler
,
Y. M.
,
Mond
,
M.
,
Cherniavskii
,
V.
,
Golbraikh
,
E.
, and
Nissim
,
Y.
, 2008, “
An Asymptotic Model for the Kelvin–Helmholtz and Miles Mechanisms of Water Wave Generation by Wind
,”
Phys. Fluids
1070-6631,
20
, p.
094106
.
143.
Yih
,
C. S.
, 1965,
Dynamics of Nonhomogeneous Fluids
,
Macmillan
,
New York
.
144.
Hsieh
,
D. Y.
, 1978, “
Interfacial Stability With Mass and Heat Transfer
,”
Phys. Fluids
1070-6631,
21
, pp.
745
748
.
145.
Funada
,
T.
, and
Joseph
,
D. D.
, 2001, “
Viscous Potential Flow Analysis of Kelvin-Helmholtz Instability in a Channel
,”
J. Fluid Mech.
0022-1120,
445
, pp.
263
283
.
146.
Chang
,
I. -D.
, and
Russell
,
P. E.
, 1965, “
Stability of a Liquid Layer Adjacent to a High-Speed Gas Stream
,”
Phys. Fluids
1070-6631,
8
, pp.
1018
1026
.
147.
Asthana
,
R.
, and
Agrawal
,
G. S.
, 2007, “
Viscous Potential Flow Analysis of Kelvin-Helmholtz Instability With Mass Transfer and Vaporization
,”
Physica A
0378-4371,
382
, pp.
389
404
.
148.
Sharp
,
D. H.
, 1984, “
An Overview of Rayleigh-Taylor Instability
,”
Physica D
0167-2789,
12
, pp.
3
18
.
149.
Richtmyer
,
R. D.
, 1960, “
Taylor Instability in Shock Acceleration of Compressible Fluids
,”
Commun. Pure Appl. Math.
0010-3640,
13
, pp.
297
319
.
150.
Meshkov
,
E. E.
, 1969, “
Instability of the Interface of Two Gases Accelerated by a Shock Wave
,”
Fluid Dyn.
0015-4628,
4
, pp.
101
104
.
151.
Velikovich
,
A. L.
, and
Dimonte
,
G.
, 1996, “
Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability
,”
Phys. Rev. Lett.
0031-9007,
76
, pp.
3112
3115
.
152.
Mikaelian
,
K. O.
, 1994, “
Oblique Shocks and the Combined Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov Instabilities
,”
Phys. Fluids
1070-6631,
6
, pp.
1943
1945
.
153.
Alexeev
,
A.
, and
Oron
,
A.
, 2007, “
Suppression of the Rayleigh-Taylor Instability of Thin Liquid Films by the Marangoni Effect
,”
Phys. Fluids
1070-6631,
19
, p.
082101
.
154.
Ozen
,
O.
, and
Narayanan
,
R.
, 2006, “
A Note on the Rayleigh-Taylor Instability With Phase Change
,”
Phys. Fluids
1070-6631,
18
, p.
042110
.
155.
Piriz
,
A. R.
,
Corta’zar
,
O. D.
,
Lo’pezCela
,
J. J.
, and
Tahir
,
N. A.
, 2006, “
The Rayleigh-Taylor Instability
,”
Am. J. Phys.
0002-9505,
74
, pp.
1095
1098
.
156.
Davis
,
S. H.
, 1980, “
Moving Contact Lines and Rivulet Instabilities. Part 1. The Static Rivulet
,”
J. Fluid Mech.
0022-1120,
98
, pp.
225
242
.
157.
Gau
,
H.
,
Herminghaus
,
S.
,
Lenz
,
P.
, and
Lipowsky
,
R.
, 1999, “
Liquid Morphologies on Structured Surfaces: From Microchannels to Microchips
,”
Science
0036-8075,
283
, pp.
46
49
.
158.
Speth
,
R. L.
, and
Lauga
,
E.
, 2009, “
Capillary Instability on a Hydrophilic Stripe
,”
New J. Phys.
1367-2630,
11
, p.
075024
.
159.
Frenkel
,
A. L.
,
Babchin
,
A. J.
,
Levich
,
B. G.
,
Shlang
,
T.
, and
Sivashinsky
,
G. I.
, 1987, “
Annular Flows Can Keep Unstable Films From Breakup: Nonlinear Saturation of Capillary Instability
,”
J. Colloid Interface Sci.
0021-9797,
115
, pp.
225
233
.
160.
Gauglitz
,
P. A.
, and
Radke
,
C. J.
, 1988, “
An Extended Evolution Equation for Liquid Film Breakup in Cylindrical Capillaries
,”
Chem. Eng. Sci.
0009-2509,
43
, pp.
1457
1465
.
161.
Kurz
,
W.
, and
Fisher
,
D. J.
, 1989,
Fundamentals of Solidification
,
Trans. Tech.
,
Aedermannsdorf, Switzerland
.
162.
Prosperetti
,
A.
, and
Plesset
,
M. S.
, 1984, “
The Stability of an Evaporating Liquid Surface
,”
Phys. Fluids
1070-6631,
27
, pp.
1590
1602
.
163.
Zhang
,
N.
, and
Chao
,
D. F.
, 1999, “
Mechanisms of Convection Instability in Thin Liquid Layers Induced by Evaporation
,”
Int. Commun. Heat Mass Transfer
0735-1933,
26
, pp.
1069
1080
.
164.
Takashima
,
M.
, 1981, “
Surface Tension Driven Instability in a Horizontal Liquid Layer With a Deformable Free Surface. II Overstability
,”
J. Phys. Soc. Jpn.
0031-9015,
50
, pp.
2751
2756
.
165.
Nemchinsky
,
V. A.
, 1997, “
The Role of Thermocapillary Instability in Heat Transfer in a Liquid Metal Pool
,”
Int. J. Heat Mass Transfer
0017-9310,
40
, pp.
881
891
.
166.
Smorodin
,
B. L.
,
Mikishev
,
A. B.
,
Nepomnyashchy
,
A. A.
, and
Myznikova
,
B. I.
, 2009, “
Thermocapillary Instability of a Liquid Layer Under Heat Flux Modulation
,”
Phys. Fluids
1070-6631,
21
, p.
062102
.
167.
Wei
,
P. S.
,
Ting
,
C. N.
,
Yeh
,
J. S.
,
DebRoy
,
T.
,
Chung
,
F. K.
, and
Yan
,
G. H.
, 2009, “
Origin of Wavy Weld Boundary
,”
J. Appl. Phys.
0021-8979,
105
, p.
053508
.
168.
Wei
,
P. S.
,
Yeh
,
J. S.
,
Ting
,
C. N.
,
DebRoy
,
T.
,
Chung
,
F. K.
, and
Lin
,
C. L.
, 2009, “
The Effects of Prandtl Number on Wavy Weld Boundary
,“
Int. J. Heat Mass Transfer
0017-9310,
52
, pp.
3790
3798
.
169.
Sahoo
,
P.
,
DebRoy
,
T.
, and
McNallan
,
M. J.
, 1988,”
Surface Tension of Binary Metal-Surface Active Solute Systems under Conditions Relevant to Welding Metallurgy
,”
Metall. Trans. B
0360-2141,
19
, pp.
483
491
.
170.
Heiple
,
C. R.
, and
Roper
,
J. R.
, 1982,”
Mechanism for Minor Element Effect on GTA Fusion Zone Geometry
,”
Weld. J.
,
61
, pp.
97
-s–102-
s
.
171.
Lei
,
Y.
,
Shi
,
Y.
,
Murakawa
,
H.
, and
Ueda
,
Y.
, 1997, “
Numerical Analysis of the Effect of Sulfur Content Upon Fluid Flow and Weld Pool Geometry for Type 304 Stainless Steel
,”
Trans. JWRI
0387-4508,
26
, pp.
8
15
.
172.
Wang
,
Y.
,
Shi
,
Q.
, and
Tsai
,
H. L.
, 2001, “
Modeling of the Effects of Surface-Active Elements on Flow Patterns and Weld Penetration
,”
Metall. Mater. Trans. B
1073-5615,
32
, pp.
145
161
.
173.
Wei
,
P. S.
, and
Chow
,
Y. T.
, 1992, “
Beam Focusing Characteristics and Alloying Element Effects on High-Intensity Electron Beam Welding
,”
Metall. Trans. B
0360-2141,
23
, pp.
81
90
.
174.
Guosheng
,
Z.
,
Fauchet
,
P. M.
, and
Siegman
,
A. E.
, 1982, “
Growth of Spontaneous Periodic Surface Structures on Solids During Laser Illumination
,”
Phys. Rev. B
0556-2805,
26
, pp.
5366
5381
.
175.
Sipe
,
J. E.
,
Young
,
J. F.
,
Preston
,
J. S.
, and
van Driel
,
H. M.
, 1983, “
Laser-Induced Periodic Surface Structure. I. Theory
,”
Phys. Rev. B
0556-2805,
27
, pp.
1141
1154
.
176.
Brueck
,
S. R. J.
, and
Ehrlich
,
D. J.
, 1982, “
Simulated Surface-Plasma-Wave Scattering and Growth of a Periodic Structure in Laser-Photodeposited Metal Films
,”
Phys. Rev. Lett.
0031-9007,
48
, pp.
1678
1681
.
177.
Akhmanov
,
S. A.
,
Emel’yanov
,
V. I.
,
Koroteev
,
N. I.
, and
Seminogov
,
V. N.
, 1985, “
Interaction of Powerful Laser Radiation With the Surfaces of Semiconductors and Metals: Nonlinear Optical Effects and Nonlinear Optical Diagnostics
,”
Sov. Phys. Usp.
0038-5670,
28
, pp.
1084
1124
.
178.
Turner
,
J. S.
, 1973,
Buoyancy Effects in Fluids
,
Cambridge University Press
,
Cambridge
.
179.
Ellegaard
,
C.
,
Hansen
,
A. E.
,
Haaning
,
A.
,
Hansen
,
K.
,
Marcussen
,
A.
,
Bohr
,
T.
,
Hansen
,
J. L.
, and
Watanabe
,
S.
, 1998, “
Creating Corners in Kitchen Sinks
,”
Nature (London)
0028-0836,
392
, pp.
767
768
.
180.
Thoroddsen
,
S. T.
, and
Sakakibara
,
J.
, 1998, “
Evolution of the Fingering Pattern of an Impacting Drop
,”
Phys. Fluids
1070-6631,
10
, pp.
1359
1374
.
181.
Allen
,
R. F.
, 1975, “
The Role of Surface Tension in Splashing
,”
J. Colloid Interface Sci.
0021-9797,
51
, pp.
350
351
.
182.
Mundo
,
Chr
.,
Sommerfeld
,
M.
, and
Tropea
,
C.
, 1995, “
Droplet-Wall Collisions: Experimental Studies of the Deformation and Breakup Process
,”
Int. J. Multiphase Flow
0301-9322,
21
, pp.
151
173
.
183.
Bhola
,
R.
, and
Chandra
,
S.
, 1999, “
Parameters Controlling Solidification of Molten Wax Droplets Falling on a Solid Surface
,”
J. Mater. Sci.
0022-2461,
34
, pp.
4883
4894
.
184.
Pasandideh-Fard
,
M.
,
Qiao
,
Y. M.
,
Chandra
,
S.
, and
Mostaghimi
,
J.
, 1996, “
Capillary Effects During Droplet Impact on a Solid Surface
,”
Phys. Fluids
1070-6631,
8
, pp.
650
659
.
185.
Bejan
,
A.
, and
Gobin
,
D.
, 2006, “
Constructal Theory of Droplet Impact Geometry
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
2412
2419
.
186.
Oron
,
A.
,
Davis
,
S. H.
, and
Bankoff
,
S. G.
, 1997, “
Long-Scale Evolution of Thin Liquid Films
,”
Rev. Mod. Phys.
0034-6861,
69
, pp.
931
980
.
187.
Craster
,
R. V.
, and
Matar
,
O. K.
, 2009, “
Dynamics and Stability of Thin Liquid Films
,”
Rev. Mod. Phys.
0034-6861,
81
, pp.
1131
1198
.
188.
Bussmann
,
M.
,
Chandra
,
S.
, and
Mostaghimi
,
J.
, 2000, “
Modeling the Splash of a Droplet Impacting a Solid Surface
,”
Phys. Fluids
1070-6631,
12
, pp.
3121
3132
.
189.
Eres
,
M. H.
,
Schwartz
,
L. W.
, and
Roy
,
R. V.
, 2000, “
Fingering Phenomena for Driven Coating Films
,”
Phys. Fluids
1070-6631,
12
, pp.
1278
1295
.
190.
Dunn
,
G. J.
,
Duffy
,
B. R.
,
Wilson
,
S. K.
, and
Holland
,
D.
, 2009, “
Quasi-Steady Spreading of a Thin Ridge of Fluid With Temperature-Dependent Surface Tension on a Heated or Cooled Substrate
,”
Q. J. Mech. Appl. Math.
0033-5614,
62
, pp.
365
402
.
191.
Haskett
,
R. P.
,
Witelski
,
T. P.
, and
Sur
,
J.
, 2005, “
Localized Marangoni Forcing in Driven Thin Films
,”
Physica D
0167-2789,
209
, pp.
117
134
.
192.
Beerman
,
M.
, and
Brush
,
L. N.
, 2007, “
Oscillatory Instability and Rupture in a Thin Melt Film on its Crystal Subject to Freezing and Melting
,”
J. Fluid Mech.
0022-1120,
586
, pp.
423
448
.
You do not currently have access to this content.