The notion of permeability is very important in understanding and modeling the flow behavior of fluids in a special type of porous medium (i.e., the underfill flow in flip-chip packaging). This paper presents a new concept regarding permeability in a porous medium, namely two types of permeability: superficial permeability (with consideration of both the pore cross-sectional area and the solid matrix cross-sectional area) and pore permeability (with consideration of the pore cross-sectional area only). Subsequently, the paper proposes an analytical model (i.e., equation) for the pore permeability and superficial permeability of an underfill porous medium in a flip-chip packaging, respectively. The proposed model along with several similar models in literature is compared with a reliable numerical model developed with the computational fluid dynamics (CFD) technique, and the result of the comparison shows that the proposed model for permeability is the most accurate one among all the analytical models in literature. The main contributions of the paper are as follows: (1) the provision of a more accurate analytical model for the permeability of an underfill porous medium in flip-chip packaging, (2) the finding of two types of permeability depending on how the cross-sectional area is taken, and (3) the correction of an error in the others' model in literature.
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March 2018
Research-Article
A Further Study on the Analytical Model for the Permeability in Flip-Chip Packaging
X. J. Yao,
X. J. Yao
School of Mechanical and Power Engineering,
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Search for other works by this author on:
J. J. Fang,
J. J. Fang
School of Mechanical and Power Engineering,
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Search for other works by this author on:
Wenjun Zhang
Wenjun Zhang
School of Mechatronics and Automation,
Shanghai University,
Shanghai 200444, China;
Shanghai University,
Shanghai 200444, China;
Department of Mechanical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N 5A9, Canada
e-mail: chris.zhang@usask.ca
University of Saskatchewan,
Saskatoon, SK S7N 5A9, Canada
e-mail: chris.zhang@usask.ca
Search for other works by this author on:
X. J. Yao
School of Mechanical and Power Engineering,
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
J. J. Fang
School of Mechanical and Power Engineering,
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China
Wenjun Zhang
School of Mechatronics and Automation,
Shanghai University,
Shanghai 200444, China;
Shanghai University,
Shanghai 200444, China;
Department of Mechanical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N 5A9, Canada
e-mail: chris.zhang@usask.ca
University of Saskatchewan,
Saskatoon, SK S7N 5A9, Canada
e-mail: chris.zhang@usask.ca
1Corresponding author.
Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received February 12, 2017; final manuscript received October 27, 2017; published online March 2, 2018. Assoc. Editor: Yi-Shao Lai.
J. Electron. Packag. Mar 2018, 140(1): 011001 (6 pages)
Published Online: March 2, 2018
Article history
Received:
February 12, 2017
Revised:
October 27, 2017
Citation
Yao, X. J., Fang, J. J., and Zhang, W. (March 2, 2018). "A Further Study on the Analytical Model for the Permeability in Flip-Chip Packaging." ASME. J. Electron. Packag. March 2018; 140(1): 011001. https://doi.org/10.1115/1.4038391
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