This paper presents a study of the fluid dynamics and heat transfer phenomena occurring during the impingement of a picoliter size liquid solder droplet upon a multilayer, composite substrate. The theoretical model, based on the Lagrangian formulation, is solved numerically with the finite element method. A deforming mesh is utilized to accurately simulate the large deformations, as well as the domain nonuniformities characteristic of the spreading process. The occurrences of droplet recoiling and mass accumulation around the deposit periphery are features of the numerical simulations and yield a nonmonotonic dependence of the maximum radius on time. The results also document the transient temperature fields developing in both the solder droplet and the substrate during the impingement process. Convection effects on the temperature field development in a deforming droplet are found to be important for the entire history of spreading. The work is directly applicable to the miniature solder droplet dispension technology for the mounting of microscopic electronic components on various substrates under development at MicroFab Inc. The results of the numerical simulations are used to explain the shape of solidified microscopic solder bumps.

Issue Section:
Phase-Change Heat Transfer
Keywords:
Conjugate Heat Transfer, Liquid Metals, Materials Processing and Manufacturing Processes
Topics:
Drops, Heat transfer, Solders, Transport phenomena, Computer simulation, Temperature, Composite materials, Convection, Deformation, Electronic components, Finite element methods, Fluid dynamics, Liquid metals, Manufacturing, Materials processing, Shapes, Transients (Dynamics)
1.
Bach
P.
, and
Hassager
O.
,
1985
, “
An Algorithm for the Use of the Lagrangian Specification in Newtonian Fluid Mechanics and Application to Free-Surface Flow
,”
J. Fluid Mech.
, Vol.
152
, pp.
173
–
190
.
2.
Collins
R. J.
,
1973
, “
Bandwidth Reduction by Automatic Renumbering
,”
Int. J. Num. Meth. Engng.
, Vol.
6
, pp.
345
–
356
.
3.
Dussan
E. B., V.
,
1979
, “
On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines
,”
Annu. Rev. Fluid Mech.
, Vol.
11
, pp.
371
–
400
.
4.
Field
D. A.
,
1988
, “
Laplacian Smoothing and Delaunay Triangulations
,”
Comm. Appl. Num. Meth.
, Vol.
4
, pp.
709
–
712
.
5.
Frederiksen
C. S.
, and
Watts
A. M.
,
1981
, “
Finite Element Method for Time-Dependent Incompressible Free Surface Flow
,”
J. Comp. Phys.
, Vol.
39
, pp.
282
–
304
.
6.
Fukai
J.
,
Zhao
Z.
,
Poulikakos
D.
,
Megaridis
C.
, and
Miyatake
O.
,
1993
, “
Modeling of the Deformation of a Liquid Droplet Impinging Upon a Flat Surface
,”
Phys. Fluids A
, Vol.
5
, pp.
2588
–
2599
.
7.
Fukai
J.
,
Shiiba
Y.
,
Miyatake
O.
,
Poulikakos
D.
,
Megaridis
C.
, and
Zhao
Z.
,
1995
, “
Wetting Effects on the Spreading of a Liquid Droplet Colliding With a Flat Surface: Experiment and Modeling
,”
Phys. Fluids A
, Vol.
7
, pp.
236
–
237
.
8.
Haley
P. J.
, and
Miksis
M. J.
,
1991
, “
The Effect of the Contact Line on Droplet Spreading
,”
J. Fluid Mech.
, Vol.
223
, pp.
57
–
81
.
9.
Harlow
F. H.
, and
Welch
J. E. W.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface
,”
Phys. Fluids
, Vol.
8
, pp.
2182
–
2189
.
10.
Harlow
F. H.
, and
Shannon
J. P.
,
1967
, “
The Splash of a Liquid Droplet
,”
J. Appl. Phys.
, Vol.
38
, pp.
3855
–
3866
.
11.
Hayes, D. J., Wallace, D. B., and Boldman, M. T., 1992, “Picoliter Solder Droplet Dispension,” ISHM ’92 Proceedings, pp. 316–321.
12.
Hirt
C. W.
, and
Nichols
B. D.
,
1980
, “
Adding Limited Compressibility to Incompressible Hydrocodes
,”
J. Comp. Phys.
, Vol.
34
, pp.
390
–
400
.
13.
Huh
E.
, and
Scriven
L. E.
,
1971
, “
Hydrodynamic Model of Steady Movement of a Solid/Liquid/Fluid Contact Line
,”
J. Colloid Interface Sci.
, Vol.
35
, pp.
85
–
101
.
14.
Jones
H.
,
1971
, “
Cooling, Freezing, and Substrate Impact of Droplets Formed by Rotary Atomization
,”
J. Phys. D: Applied Physics
, Vol.
4
, pp.
1657
–
1660
.
15.
Kawahara
M.
, and
Hirano
H.
,
1983
, “
A Finite Element Method for High Reynolds Number Viscous Fluid Flow Using a Two Step Explicit Scheme
,”
Int. J. Num. Meth. Fluids
, Vol.
3
, pp.
137
–
163
.
16.
Madejski
J.
,
1976
, “
Solidification of Droplets on a Cold Surface
,”
Int. J. Heat Mass Transfer
, Vol.
19
, pp.
1009
–
1013
.
17.
Madejski
J.
,
1983
, “
Droplets on Impact With a Solid Surface
,”
Int. J. Heat Mass Transfer
, Vol.
26
, pp.
1095
–
1098
.
18.
Peraire
J.
,
Vahdati
K.
,
Morgan
K.
, and
Zienkiewicz
O. C.
,
1987
, “
Adaptive Remeshing for Compressible Flow Configurations
,”
J. Comp. Phys.
, Vol.
72
, pp.
449
–
466
.
19.
Silliman
W. J.
, and
Scriven
L. E.
,
1980
, “
Separating Flow Near a Static Contact: Slip at a Wall and Shape of a Free Surface
,”
J. Comp. Phys.
, Vol.
34
, pp.
287
–
313
.
20.
Trapaga
G.
, and
Szekely
J.
,
1991
, “
Mathematical Modeling of the Isothermal Impingement of Liquid Droplets in Spray Processes
,”
Metall. Trans. B
, Vol.
22
, pp.
901
–
914
.
21.
Wang
G. X.
, and
Matthys
E. F.
,
1991
, “
Modelling of Heat Transfer and Solidification During Splat Cooling: Effect of Splat Thickness and Splat/Substrate Thermal Contact
,”
Int. J. Rapid Solidification
, Vol.
6
, pp.
141
–
174
.
22.
Zhao, Z., 1994, “Transport Phenomena During the Impingement of Liquid Metal Droplets on a Substrate,” Ph.D Thesis, University of Illinois at Chicago, Chicago, IL.
23.
Zhao, Z., Poulikakos, D., and Fukai, J., 1996, “Heat Transfer and Fluid Dynamics During the Collision of a Liquid Droplet on a Substrate: Part II—Experiments,” Int. J. Heat Mass Transfer, in press.
This content is only available via PDF.
Copyright © 1996
 by The American Society of Mechanical Engineers
You do not currently have access to this content.