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This paper presents numerical modeling and experimental results for the problem of underfill flow in a large die with a non-uniform bump pattern in a flip-chip packaging configuration. Two different 2-D flow models coupled with the volume-of-fluid (VOF) method are applied to track the underfill flow front during the simulation of flip-chip encapsulation. The first model employs the modified Washburn model and uses a time-dependent inlet velocity to account for the flow resistance across the gap direction in the presence of bump interconnects. The second model introduces a momentum source term in the Stokes equation to represent the gapwise resistance. Rheological properties, surface tension, and dynamic contact angles for an underfill material are experimentally determined. Simulation results based on the two models are compared with in-situ flow visualization conducted using bumped quartz dies. The comparison demonstrates the applicability of each model for simulating the underfill encapsulation process.

In this paper, numerical modeling and experimental results are presented for underfill flow in a large die with a nonuniform bump pattern in a flip-chip packaging configuration. Two different 2-D flow models coupled with the volume-of-fluid method are applied to track the underfill flow front during the simulation of the flip-chip encapsulation process. The first model employs the modified Washburn model and uses a timedependent inlet velocity to account for the flow resistance across the gap direction in the presence of bump interconnects. The second model introduces a momentum source term in the Stokes equation to represent the gapwise flow resistance. Rheological properties, surface tension, and dynamic contact angles for commercial underfill material and the effect of flux residue on underfill wetting properties are experimentally determined. Simulation results based on the two models are compared with in-situ flow visualization conducted using bumped quartz dies. The modified Stokes model yields better predictions of the underfill penetration length as a function of time and the total flow-out time. This model is then used to investigate the effects of dynamic contact angles and temperature-dependent underfill viscosity on underfill flow in a large die with a nonuniform bump pattern.Index Terms-Flip-chip, nonuniform bump pattern, quartz die, simulation, underfill flow.

The presence of bacterial biofilms is detrimental in a wide range of healthcare situations especially wound healing. Physical debridement of biofilms is a method widely used to remove them. This study evaluates the use of microfluidic jet impingement to debride biofilms. In this case, a biofilm is treated as a saturated porous medium also having linear elastic properties. A numerical modeling approach is used to calculate the von Mises stress distribution within a porous medium under fluid-structure interaction (FSI) loading to determine the initial rupture of the biofilm structure. The segregated model first simulates the flow field to obtain the FSI interface loading along the fluid-solid interface and body force loading within the porous medium. A stress-strain model is consequently used to calculate the von Mises stress distribution to obtain the biofilm deformation. Under a vertical jet, 60% of the deformation of the porous medium can be accounted for by treating the medium as if it was an impermeable solid. However, the maximum deformation in the porous medium corresponds to the point of maximum shear stress which is a different position in the porous medium than that of the maximum normal stress in an impermeable solid. The study shows that a jet nozzle of 500 μm internal diameter (ID) with flow of Reynolds number (Re) of 200 can remove the majority of biofilm species.