Abstract

The fundamental operation in binder jet three-dimensional printing is the deposition of liquid binder into a powder layer to selectively bond particles together. Upon droplet impact, the binder spreads into the powder bed forming a bound network of wetted particles called a primitive. A computational fluid dynamics framework is proposed to directly simulate the capillary and hydrodynamic effects of the interfacial flow that is responsible for primitive formation. The computational model uses the volume-of-fluid method for capturing dynamic binder-air interfaces, and the immersed boundary method is adopted to include particle geometries on numerical Cartesian grids. Three-phase contact angles are prescribed through an interface extension algorithm. Binder droplet impact on powder beds of varying contact angle are simulated. Furthermore, the numerical model is used to simulate liquid bridges connecting binary and ternary particle systems, and the resulting capillary and hydrodynamic forces are validated by comparison with published experimental and theoretical model results.

References

1.
Ziaee
,
M.
, and
Crane
,
N. B.
,
2019
, “
Binder Jetting: A Review of Process, Materials, and Methods
,”
Addit. Manuf.
,
28
, pp.
781
801
.
2.
Mostafaei
,
A.
,
Elliott
,
A. M.
,
Barnes
,
J. E.
,
Li
,
F.
,
Tan
,
W.
,
Cramer
,
C. L.
,
Nandwana
,
P.
, and
Chmielus
,
M.
,
2020
, “
Binder Jet 3D Printing–Process Parameters, Materials, Properties, and Challenges
,”
Prog. Mater. Sci.
, p.
100707
.
3.
Gokuldoss
,
P. K.
,
Kolla
,
S.
, and
Eckert
,
J.
,
2017
, “
Additive Manufacturing Processes: Selective Laser Melting, Electron Beam Melting and Binder Jetting Election Guidelines
,”
Materials
,
10
(
6
), p.
672
.
4.
Parab
,
N. D.
,
Barnes
,
J. E.
,
Zhao
,
C.
,
Cunningham
,
R. W.
,
Fezzaa
,
K.
,
Rollett
,
A. D.
, and
Sun
,
T.
,
2019
, “
Real Time Observation of Binder Jetting Printing Process Using High-speed x-ray Imaging
,”
Sci. Rep.
,
9
(
1
), pp.
1
10
.
5.
Wagner
,
J.
,
Shu
,
H.
,
Kilambi
,
R.
, and
Higgs III
,
C. F.
,
2019
, “
Experimental Investigation of Fluid-particle Interaction in Binder Jet 3D Printing
,”
Solid Freeform Fabrication Symposium–Additive Manufacturing
,
Austin, TX
, pp.
134
147
.
6.
Sachs
,
E.
,
Cima
,
M.
,
Cornie
,
J.
,
Brancazio
,
D.
,
Bredt
,
J.
,
Curodeau
,
A.
,
Fan
,
T.
,
Khanuja
,
S.
,
Lauder
,
A.
,
Lee
,
J.
, and
Michaels
,
S.
,
1993
, “
Three-Dimensional Printing: The Physics and Implications of Additive Manufacturing
,”
CIRP. Ann.
,
42
(
1
), pp.
257
260
.
7.
Streator
,
J. L.
,
2009
, “
A Model of Liquid-Mediated Adhesion With a 2D Rough Surface
,”
Tribol. Int.
,
42
(
10
), pp.
1439
1447
.
8.
Lores
,
A.
,
Azurmendi
,
N.
,
Agote
,
I.
, and
Zuza
,
E.
,
2019
, “
A Review on Recent Developments in Binder Jetting Metal Additive Manufacturing: Materials and Process Characteristics
,”
Powder. Metall.
,
62
(
5
), pp.
267
296
.
9.
Bredt
,
J. F.
,
1997
, “
Binder Stability and Powder/Binder Interaction in Three-Dimensional Printing
,”
Ph.D. thesis
,
Cambridge MA
.
10.
Miyanaji
,
H.
,
Zhang
,
S.
, and
Yang
,
L.
,
2018
, “
A New Physics-Based Model for Equilibrium Saturation Determination in Binder Jetting Additive Manufacturing Process
,”
Int. J. Mach. Tools. Manuf.
,
124
, pp.
1
11
.
11.
Chen
,
H.
, and
Zhao
,
Y. F.
,
2016
, “
Process Parameters Optimization for Improving Surface Quality and Manufacturing Accuracy of Binder Jetting Additive Manufacturing Process
,”
Rapid Prototy. J.
,
22
(
3
), pp.
527
538
.
12.
Shrestha
,
S.
, and
Manogharan
,
G.
,
2017
, “
Optimization of Binder Jetting Using Taguchi Method
,”
Jom
,
69
(
3
), pp.
491
497
.
13.
Lu
,
K.
, and
Reynolds
,
W. T.
,
2008
, “
3dp Process for Fine Mesh Structure Printing
,”
Powder. Technol.
,
187
(
1
), pp.
11
18
.
14.
Vaezi
,
M.
, and
Chua
,
C. K.
,
2011
, “
Effects of Layer Thickness and Binder Saturation Level Parameters on 3d Printing Process
,”
Int. J. Adv. Manuf. Technol.
,
53
(
1
), pp.
275
284
.
15.
Gaytan
,
S.
,
Cadena
,
M. A.
,
Karim
,
H.
,
Delfin
,
D.
,
Lin
,
Y.
,
Espalin
,
D.
,
Macdonald
,
E.
, and
Wicker
,
R.
,
2015
, “
Fabrication of Barium Titanate by Binder Jetting Additive Manufacturing Technology
,”
Ceram. Int.
,
41
(
5
), pp.
6610
6619
.
16.
Kafara
,
M.
,
Kemnitzer
,
J.
,
Westermann
,
H.-H.
, and
Steinhilper
,
R.
,
2018
, “
Influence of Binder Quantity on Dimensional Accuracy and Resilience in 3D-Printing
,”
Procedia Manufact.
,
21
, pp.
638
646
.
17.
Haeri
,
S.
, and
Shrimpton
,
J.
,
2012
, “
On the Application of Immersed Boundary, Fictitious Domain and Body-Conformal Mesh Methods to Many Particle Multiphase Flows
,”
Int. J. Multiphase. Flow.
,
40
, pp.
38
55
.
18.
Nan
,
W.
,
Pasha
,
M.
,
Bonakdar
,
T.
,
Lopez
,
A.
,
Zafar
,
U.
,
Nadimi
,
S.
, and
Ghadiri
,
M.
,
2018
, “
Jamming During Particle Spreading in Additive Manufacturing
,”
Powder. Technol.
,
338
, pp.
253
262
.
19.
Desai
,
P. S.
, and
Higgs
,
C. F.
,
2019
, “
Spreading Process Maps for Powder-Bed Additive Manufacturing Derived From Physics Model-based Machine Learning
,”
Metals
,
9
(
11
), p.
1176
.
20.
Zhang
,
W.
,
Mehta
,
A.
,
Desai
,
P. S.
, and
Higgs
,
C.
,
2017
, “
Machine Learning Enabled Powder Spreading Process Map for Metal Additive Manufacturing (AM)
,”
Solid Freeform Fabrication Symposium–Additive Manufacturing
,
Austin, TX
, pp.
1235
1249
.
21.
Desai
,
P. S.
,
Mehta
,
A.
,
Dougherty
,
P. S.
, and
Higgs III
,
C. F.
,
2019
, “
A Rheometry Based Calibration of a First-order Dem Model to Generate Virtual Avatars of Metal Additive Manufacturing (am) Powders
,”
Powder. Technol.
,
342
, pp.
441
456
.
22.
Tan
,
H.
,
2016
, “
Three-dimensional Simulation of Micrometer-Sized Droplet Impact and Penetration Into the Powder Bed
,”
Chem. Eng. Sci.
,
153
, pp.
93
107
.
23.
Hirt
,
C. W.
, and
Nichols
,
B. D.
,
1981
, “
Volume of Fluid (vof) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
(
1
), pp.
201
225
.
24.
Khairallah
,
S. A.
,
Anderson
,
A. T.
,
Rubenchik
,
A.
, and
King
,
W. E.
,
2016
, “
Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones
,”
Acta. Mater.
,
108
, pp.
36
45
.
25.
Bidare
,
P.
,
Bitharas
,
I.
,
Ward
,
R.
,
Attallah
,
M.
, and
Moore
,
A. J.
,
2018
, “
Fluid and Particle Dynamics in Laser Powder Bed Fusion
,”
Acta. Mater.
,
142
, pp.
107
120
.
26.
Tan
,
J.
,
Tang
,
C.
, and
Wong
,
C.
,
2018
, “
Study and Modeling of Melt Pool Evolution in Selective Laser Melting Process of Ss316l
,”
MRS Commun.
,
8
(
3
), pp.
1178
1183
.
27.
Villanueva
,
W.
,
Grönhagen
,
K.
,
Amberg
,
G.
, and
Ågren
,
J.
,
2009
, “
Multicomponent and Multiphase Simulation of Liquid-Phase Sintering
,”
Comput. Mater. Sci.
,
47
(
2
), pp.
512
520
.
28.
Fujita
,
M.
,
Koike
,
O.
, and
Yamaguchi
,
Y.
,
2015
, “
Direct Simulation of Drying Colloidal Suspension on Substrate Using Immersed Free Surface Model
,”
J. Comput. Phys.
,
281
, pp.
421
448
.
29.
Schlottke
,
J.
, and
Weigand
,
B.
,
2008
, “
Direct Numerical Simulation of Evaporating Droplets
,”
J. Comput. Phys.
,
227
(
10
), pp.
5215
5237
.
30.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
,
1992
, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.
31.
Peskin
,
C. S.
,
1977
, “
Numerical Analysis of Blood Flow in the Heart
,”
J. Comput. Phys.
,
25
(
3
), pp.
220
252
.
32.
Nangia
,
N.
,
Johansen
,
H.
,
Patankar
,
N. A.
, and
Bhalla
,
A. P. S.
,
2017
, “
A Moving Control Volume Approach to Computing Hydrodynamic Forces and Torques on Immersed Bodies
,”
J. Comput. Phys.
,
347
, pp.
437
462
.
33.
MacNeice
,
P.
,
Olson
,
K. M.
,
Mobarry
,
C.
,
De Fainchtein
,
R.
, and
Packer
,
C.
,
2000
, “
Paramesh: A Parallel Adaptive Mesh Refinement Community Toolkit
,”
Comput. Phys. Commun.
,
126
(
3
), pp.
330
354
.
34.
Harlow
,
F. H.
, and
Welch
,
J. E.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface
,”
Phys. Fluids
,
8
(
12
), pp.
2182
2189
.
35.
Anderson
,
J. D.
,
2010
,
Computational Fluid Dynamics: The Basics with Applications
,
McGraw-Hill
,
New York
.
36.
Rider
,
W. J.
, and
Kothe
,
D. B.
,
1998
, “
Reconstructing Volume Tracking
,”
J. Comput. Phys.
,
141
(
2
), pp.
112
152
.
37.
Weymouth
,
G. D.
, and
Yue
,
D. K. -P.
,
2010
, “
Conservative Volume-of-Fluid Method for Free-Surface Simulations on Cartesian-Grids
,”
J. Comput. Phys.
,
229
(
8
), pp.
2853
2865
.
38.
Tryggvason
,
G.
,
Scardovelli
,
R.
, and
Zaleski
,
S.
,
2011
,
Direct Numerical Simulations of Gas–Liquid Multiphase Flows
,
Cambridge University Press
,
New York
.
39.
Xiao
,
F.
,
Honma
,
Y.
, and
Kono
,
T.
,
2005
, “
A Simple Algebraic Interface Capturing Scheme Using Hyperbolic Tangent Function
,”
Int. J. Numer. Methods Fluids
,
48
(
9
), pp.
1023
1040
.
40.
Xiao
,
F.
,
Ii
,
S.
, and
Chen
,
C.
,
2011
, “
Revisit to the Thinc Scheme: A Simple Algebraic Vof Algorithm
,”
J. Comput. Phys.
,
230
(
19
), pp.
7086
7092
.
41.
Yokoi
,
K.
,
2007
, “
Efficient Implementation of Thinc Scheme: A Simple and Practical Smoothed Vof Algorithm
,”
J. Comput. Phys.
,
226
(
2
), pp.
1985
2002
.
42.
Ii
,
S.
,
Sugiyama
,
K.
,
Takeuchi
,
S.
,
Takagi
,
S.
,
Matsumoto
,
Y.
, and
Xiao
,
F.
,
2012
, “
An Interface Capturing Method with a Continuous Function: The Thinc Method with Multi-Dimensional Reconstruction
,”
J. Comput. Phys.
,
231
(
5
), pp.
2328
2358
.
43.
Chorin
,
A. J.
,
1968
, “
Numerical Solution of the Navier-Stokes Equations
,”
Math. Comput.
,
22
(
104
), pp.
745
762
.
44.
Wesseling
,
P.
,
1992
,
Introduction To Multigrid Methods
,
John Wiley and Sons
,
New York
.
45.
Trottenberg
,
U.
,
Oosterlee
,
C. W.
, and
Schuller
,
A.
,
2000
,
Multigrid
,
Elsevier
,
San Diego, CA
.
46.
Kothe
,
D.
, and
Mjolsness
,
R.
,
1992
, “
Ripple-a New Model for Incompressible Flows With Free Surfaces
,”
AIAA. J.
,
30
(
11
), pp.
2694
2700
.
47.
Bussmann
,
M.
,
Kothe
,
D. B.
, and
Sicilian
,
J. M.
,
2002
, “
Modeling High Density Ratio Incompressible Interfacial Flows
,”
Fluids Engineering Division Summer Meeting
, Vol.
36150
,
Montreal, Quebec, Canada
, pp.
707
713
.
48.
Rudman
,
M.
,
1998
, “
A Volume-Tracking Method for Incompressible Multifluid Flows With Large Density Variations
,”
Int. J. Numer. Methods Fluids
,
28
(
2
), pp.
357
378
.
49.
Pathak
,
A.
, and
Raessi
,
M.
,
2016
, “
A 3D Fully Eulerian, VOF-Based Solver to Study the Interaction Between Two Fluids and Moving Rigid Bodies Using the Fictitious Domain Method
,”
J. Comput. Phys.
,
311
, pp.
87
113
.
50.
Fuster
,
D.
,
Arrufat
,
T.
,
Crialesi-Esposito
,
M.
,
Ling
,
Y.
,
Malan
,
L.
,
Pal
,
S.
,
Scardovelli
,
R.
,
Tryggvason
,
G.
, and
Zaleski
,
S.
,
2018
, “
A Momentum-Conserving, Consistent, Volume-of-Fluid Method for Incompressible Flow on Staggered Grids
,” arXiv preprint arXiv:1811.12327.
51.
Popinet
,
S.
,
2009
, “
An Accurate Adaptive Solver for Surface-Tension-Driven Interfacial Flows
,”
J. Comput. Phys.
,
228
(
16
), pp.
5838
5866
.
52.
Renardy
,
Y.
, and
Renardy
,
M.
,
2002
, “
Prost: a Parabolic Reconstruction of Surface Tension for the Volume-of-Fluid Method
,”
J. Comput. Phys.
,
183
(
2
), pp.
400
421
.
53.
Liovic
,
P.
,
Francois
,
M.
,
Rudman
,
M.
, and
Manasseh
,
R.
,
2010
, “
Efficient Simulation of Surface Tension-Dominated Flows Through Enhanced Interface Geometry Interrogation
,”
J. Comput. Phys.
,
229
(
19
), pp.
7520
7544
.
54.
Cummins
,
S. J.
,
Francois
,
M. M.
, and
Kothe
,
D. B.
,
2005
, “
Estimating Curvature From Volume Fractions
,”
Comput. Struct.
,
83
(
6–7
), pp.
425
434
.
55.
Francois
,
M. M.
,
Cummins
,
S. J.
,
Dendy
,
E. D.
,
Kothe
,
D. B.
,
Sicilian
,
J. M.
, and
Williams
,
M. W.
,
2006
, “
A Balanced-force Algorithm for Continuous and Sharp Interfacial Surface Tension Models Within a Volume Tracking Framework
,”
J. Comput. Phys.
,
213
(
1
), pp.
141
173
.
56.
Lopez
,
J.
,
Zanzi
,
C.
,
Gomez
,
P.
,
Zamora
,
R.
,
Faura
,
F.
, and
Hernandez
,
J.
,
2009
, “
An Improved Height Function Technique for Computing Interface Curvature From Volume Fractions
,”
Comput. Methods. Appl. Mech. Eng.
,
198
(
33–36
), pp.
2555
2564
.
57.
Fadlun
,
E.
,
Verzicco
,
R.
,
Orlandi
,
P.
, and
Mohd-Yusof
,
J.
,
2000
, “
Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations
,”
J. Comput. Phys.
,
161
(
1
), pp.
35
60
.
58.
Sun
,
X.
, and
Sakai
,
M.
,
2016
, “
Numerical Simulation of Two-Phase Flows in Complex Geometries by Using the Volume-of-Fluid/Immersed-Boundary Method
,”
Chem. Eng. Sci.
,
139
, pp.
221
240
.
59.
Sun
,
X.
, and
Sakai
,
M.
,
2016
, “
Direct Numerical Simulation of Gas-Solid-Liquid Flows With Capillary Effects: An Application to Liquid Bridge Forces Between Spherical Particles
,”
Phys. Rev. E
,
94
(
6
), p.
063301
.
60.
Washino
,
K.
,
Tan
,
H.
,
Salman
,
A.
, and
Hounslow
,
M.
,
2011
, “
Direct Numerical Simulation of Solid–Liquid–Gas Three-Phase Flow: Fluid–Solid Interaction
,”
Powder. Technol.
,
206
(
1–2
), pp.
161
169
.
61.
Sussman
,
M.
,
2001
, “
An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries
,”
Adaptive Method Lines
, pp.
207
231
.
62.
Patel
,
H.
,
Das
,
S.
,
Kuipers
,
J.
,
Padding
,
J.
, and
Peters
,
E.
,
2017
, “
A Coupled Volume of Fluid and Immersed Boundary Method for Simulating 3d Multiphase Flows With Contact Line Dynamics in Complex Geometries
,”
Chem. Eng. Sci.
,
166
, pp.
28
41
.
63.
Yokoi
,
K.
,
Vadillo
,
D.
,
Hinch
,
J.
, and
Hutchings
,
I.
,
2009
, “
Numerical Studies of the Influence of the Dynamic Contact Angle on a Droplet Impacting on a Dry Surface
,”
Phys. Fluids.
,
21
(
7
), p.
072102
.
64.
O’Brien
,
A.
, and
Bussmann
,
M.
,
2020
, “
A Moving Immersed Boundary Method for Simulating Particle Interactions At Fluid-Fluid Interfaces
,”
J. Comput. Phys.
,
402
, p.
109089
.
65.
Fujita
,
M.
,
Koike
,
O.
, and
Yamaguchi
,
Y.
,
2013
, “
Computation of Capillary Interactions Among Many Particles At Free Surface
,”
Appl. Phys. Express.
,
6
(
3
), p.
036501
.
66.
Weller
,
H. G.
,
2008
, “
A New Approach to VOF-Based Interface Capturing Methods for Incompressible and Compressible Flow
,”
OpenCFD Ltd. Report TR/HGW
,
4
, p.
35
.
67.
Lafaurie
,
B.
,
Nardone
,
C.
,
Scardovelli
,
R.
,
Zaleski
,
S.
, and
Zanetti
,
G.
,
1994
, “
Modelling Merging and Fragmentation in Multiphase Flows with Surfer
,”
J. Comput. Phys.
,
113
(
1
), pp.
134
147
.
68.
Das
,
S.
,
Patel
,
H.
,
Milacic
,
E.
,
Deen
,
N.
, and
Kuipers
,
J.
,
2018
, “
Droplet Spreading and Capillary Imbibition in a Porous Medium: A Coupled IB-VOF Method Based Numerical Study
,”
Phys. Fluids.
,
30
(
1
), p.
012112
.
69.
Bussmann
,
M.
,
Chandra
,
S.
, and
Mostaghimi
,
J.
,
2000
, “
Modeling the Splash of a Droplet Impacting a Solid Surface
,”
Phys. Fluids.
,
12
(
12
), pp.
3121
3132
.
70.
Brakke
,
K. A.
,
1992
, “
The Surface Evolver
,”
Exp. Math.
,
1
(
2
), pp.
141
165
.
71.
Pitois
,
O.
,
Moucheront
,
P.
, and
Chateau
,
X.
,
2000
, “
Liquid Bridge Between Two Moving Spheres: An Experimental Study of Viscosity Effects
,”
J. Colloid. Interface. Sci.
,
231
(
1
), pp.
26
31
.
72.
Wang
,
J.-P.
,
Gallo
,
E.
,
François
,
B.
,
Gabrieli
,
F.
, and
Lambert
,
P.
,
2017
, “
Capillary Force and Rupture of Funicular Liquid Bridges Between Three Spherical Bodies
,”
Powder. Technol.
,
305
, pp.
89
98
.
73.
Pitois
,
O.
,
Moucheront
,
P.
, and
Chateau
,
X.
,
2001
, “
Rupture Energy of a Pendular Liquid Bridge
,”
Eur. Phys. J. B-Condensed Matter Complex Syst.
,
23
(
1
), pp.
79
86
.
74.
Washino
,
K.
,
Chan
,
E. L.
,
Matsumoto
,
T.
,
Hashino
,
S.
,
Tsuji
,
T.
, and
Tanaka
,
T.
,
2017
, “
Normal Viscous Force of Pendular Liquid Bridge between Two Relatively Moving Particles
,”
J. Colloid. Interface. Sci.
,
494
, pp.
255
265
.
75.
Matthewson
,
M.
,
1988
, “
Adhesion of Spheres by Thin Liquid Films
,”
Philos. Mag. A
,
57
(
2
), pp.
207
216
.
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