Modeling of a non-Newtonian flow between parallel plates in a flip chip encapsulation

2010 ◽  
Vol 50 (7) ◽  
pp. 995-999 ◽  
Author(s):  
Wen-Bin Young
Keyword(s):  
Flip Chip ◽  
Parallel Plates ◽  
Newtonian Flow

Influence of Gap Height in Flip Chip Underfill Process With Non-Newtonian Flow Between Two Parallel Plates

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
C. Y. Khor ◽  
M. Z. Abdullah ◽  
M. Abdul Mujeebu
Keyword(s):  
Pressure Drop ◽  
Flip Chip ◽  
3D Model ◽  
Fluid Dynamic ◽  
Power Law Model ◽  
Parallel Plates ◽  
Newtonian Flow ◽  
Filling Time ◽  
Gap Height ◽  
Volume Method

In this paper, the finite volume method (FVM) is used for the simulation of flip chip underfill process by considering non-Newtonian flow between two parallel plates that emulate the silicon die and the substrate. 3D model of two parallel plates of size 12.75 mm × 9.5 mm with gap heights of 5 μm, 15 μm, 25 μm, 35 μm, 45 μm, and 85 μm are developed and simulated by computational fluid dynamic (CFD) code, fluent 6.3.26. The flow is modeled by using power law model and volume of fluid (VOF) technique is applied for flow front tracking. The effect of change in height of the gap between the plates on the underfill process is mainly studied in the present work. It is observed that the gap height has significant influence on the melt filling time and pressure drop, as the gap height decreases filling time and pressure drop increase. The simulation results are compared with previous experimental results and found in good conformity.

A Model for Underfill Viscous Flow Considering the Resistance Induced by Solder Bumps

2004 ◽  
Vol 126 (2) ◽  
pp. 186-194 ◽  
Author(s):  
Chyi-Lang Lai ◽  
Wen-Bin Young
Keyword(s):  
Flip Chip ◽  
External Pressure ◽  
Good Prediction ◽  
Parallel Plates ◽  
Rectangular Array ◽  
Chip Technology ◽  
Solder Bumps ◽  
Proposed Model ◽  
Filling Time ◽  
Underfill Flow

During the underfill process, polymers driven by either capillary force or external pressure are filled at a low speed between the chip and substrate. Current methods treated the flow in the chip cavity as a laminar flow between parallel plates, which ignored the resistance induced by the solder bumps or other obstructions. In this study, the filling flow between solder bumps was simulated by a flow through a porous media. By using the superposition of flows through parallel plates and series of rectangular ducts, permeability of the underfill flow was fully characterized by the geometric arrangement of solder bumps and flat chips. The flow resistances caused by adjacent bumps were represented in its permeability. The model proposed in this study could provide a numerical approach to approximate and simulate the undefill process for flip-chip technology. Although the proposed model is applicable for any geometric arrangement of solder bumps, rectangular-array of solder bumps layout was used first for comparison with experimental results of other article. Comparisons of the flow-front shapes and filling time with the experimental data indicated that the flow simulation obtained from the proposed model gave a good prediction for the underfill flow.

Observations of Shear Localization in Liquid Lubricants Under Pressure

1993 ◽  
Vol 115 (3) ◽  
pp. 507-513 ◽  
Author(s):  
S. Bair ◽  
F. Qureshi ◽  
W. O. Winer
Keyword(s):  
Shear Stress ◽  
Deformation Behavior ◽  
Shear Bands ◽  
Solid Surfaces ◽  
Parallel Plates ◽  
Newtonian Flow ◽  
Contact Conditions ◽  
Fundamental Investigation ◽  
Spatial Periodicity ◽  
Nonlinear Shear

A High Pressure Flow Visualization Cell has been designed and constructed to perform a fundamental investigation of the deformation behavior of liquid lubricants under lubricated concentrated contact conditions. A pressure of 0.3 GPa and a shear stress between parallel plates of about 25 MPa has been demonstrated. Time averaged velocity profiles show no continuous slip either in the bulk or at walls. Localized slip at shear bands inclined to the walls was demonstrated to occur during nonlinear shear response. The number of shear bands increases with shear rate (and shear stress) from as few as one at the onset of non-Newtonian flow until the shear region is essentially filled with bands with a spatial periodicity of 7 μm. Bands are typically inclined 19 deg off the solid surfaces in a direction which reduces the compressive normal stress due to shear on the plane of the band.

An Asymptotic Study of the Nusselt-Graetz Problem—Part I: Large x Behavior

1974 ◽  
Vol 96 (3) ◽  
pp. 354-358 ◽  
Author(s):  
H. J. Hickman
Keyword(s):  
Nusselt Number ◽  
Laminar Flow ◽  
Laplace Transform ◽  
The Other ◽  
Circular Pipe ◽  
Parallel Plates ◽  
Newtonian Flow ◽  
Percent Error ◽  
The Laplace Transform ◽  
Analytic Expressions

A method is given for determining the large x behavior of the Nusselt number for a variety of Nusselt-Graetz problems. Exploitation of properties of the Laplace transform of the temperature yields analytic expressions for Nu as explicit functions of the other parameters of the problem. Accurate results (<1 percent error) are deduced for problems involving the laminar flow of a Newtonian flow between parallel plates and in a circular pipe (valid for all values of the wall Nusselt number).

Heat Transfer to Power-Law Non-Newtonian Flow between Parallel Plates

1980 ◽  
Vol 102 (2) ◽  
pp. 382-384 ◽  
Author(s):  
S. H. Lin ◽  
W. K. Hsu
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Parallel Plates ◽  
Newtonian Flow
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