Spectral analysis and experimental study of lateral capillary dynamics for flip-chip applications

This article presents a study on the dynamics of lateral motion of a liquid meniscus confined by a pad and a chip moving parallel to the pad. This problem is a typical flip-chip case study, whose use is widespread in industrial assembly. The proposed model describing this dynamics is built upon two coupled physics: the Navier-Stokes equation governing the liquid flow between the pad and the chip, and the Newton's law describing the motion of the chip. This coupled problem is solved with a spectral method based on Chebyshev polynomials, by assuming a linear analytical expression of the lateral stiffness of the meniscus in the cases of circular and square pads. The theoretical results are benchmarked with literature results and thoroughly experimentally validated. From these results, we propose a map giving the characteristic time of the chip dynamics according to only two non-dimensional parameters, constructed with the physical (density, surface tension, and viscosity), geometrical (pad area and gap), or dynamical (chip mass) parameters of the problem

Two-Fluid Boundary Layer Stability

The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode found in the classical hydrodynamical stability theory an additional Yih-mode exists due to the two-fluid interface. The effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-newtonian character of the lower fluid on the stability characteristics are determined, Also the mechanisms leading to instability for the two modes are reported. The results are compared with analytical, numerical and experimental results reported in the literatur

Two-fluid boundary layer stability

The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode (hard mode) found in the classical hydrodynamical stability theory an additional Yih-mode (interfacial mode) exists due to the two-fluid interface. Effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-Newtonian character of the lower fluid on the stability characteristics are determined. The interfacial mode is found to be very sensitive against viscosity stratification. However, with a highly viscous liquid layer, the system approaches a single-layer behavior. The shear-thinning non-Newtonian liquid layer is observed to have a stabilizing effect for both of the modes. Surface tension is stabilizing for shea waves for the interfacial mode but a more complex effect was observed for the hard mode. Gravity is stabilizing with a favorable density stratification. Density stratification alone is destabilizing for low and moderate values of this parameter but becomes stabilizing for higher values. When the external boundary layer profile is turbulent, the interfacial mode is more likely to be observed in an experiment. Agreement of the obtained results with experimental, theoretical and numerical results reported in the literature is good. This is encouraging as the study is intended for solving the stability characteristics of de/anti-icing fluid-air systems and comparing the results with the experimental data when they become available. (C) 1998 American Institute of Physics. [S1070-6631(98)01811-X]

Nonequilibrium High Temperature Boundary Layers around Bodies of Revolution

In this paper, efficient and accurate hermitian type multi-point finite difference methods are used to develop a general boundary layer code for analyzing reacting flows around bodies of revolution.The main motivation is the investigation of the influence of different physico-chemical models for transport properties,chemical kinetics and finite rate wall catalysis, on relevant quantities such as wall heat transfer and skin friction. The effect of wall catalysis is especially important in the study of properties of thermal protection materials, for which a boundary layer code is a very useful tool, because it allows the computation of the heat flux at a cost that is a fraction of a Navier-Stokes computation. Computations performed on different test cases show the ability of the code to cope with a wide range of nonequilibrium conditions, making it a useful tool for physico-chemical studies

Implementation and Validation of the Spalart-Allmaras Turbulence Model for Application in Hypersonic Flows

The Spalart and Almaras turbulence model has been implemented in a finite volume code using a implicit finite difference technique. A wide range of turbulent flows have been computed in validation phase and numerical results are shown. A special attention is paid to the hypersonic applications. A hypersonic wind tunnel flow and a Mach 5 flow over a hollow-cylinder-flare have been considered and a critical comparison between the numerical results and experimental data is reported