Molecular velocities have been measured inside a hypersonic, normal shock wave, where the gas experiences rapid changes in its macroscopic properties. As first hypothesized by Mott-Smith, but never directly observed, the molecular velocity distribution exhibits a qualitatively bimodal character that is derived from the distribution functions on either side of the shock. Quantitatively correct forms of the molecular velocity distribution function in highly nonequilibrium flows can be calculated, by means of the Direct Simulation Monte Carlo technique.
Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier—Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater than 1.2, the Burnett predictions are more accurate than the Navier—Stokes results. Temperature—density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.
One-dimensional shock wave properties in helium and argon are predicted using Monte Carlo direct simulation. The collision model is based directly on the interatomic potential, taking angular scattering into account. The potential is assumed to be of the Maitland–Smith [n(r)−6] form. The detailed validity of the simulation is studied by comparing the predicted macroscopic and microscopic flow properties in shock waves to a wide range of available data.
Stencil printing is a critical first step in surface mount assembly. It is often cited that about 50% or more of the defects found in the assembly of PCBs are attributed to stencil printing ['I. Manufacturing techniques for the assembly of certain flip chips, chip scale packages and fine pitch ball grid arrays are testing the l i t s of current stencil printing capabilities. A thorough understanding of basic stencil printing principles would facilitate the design of printers, stencils and pastes, and would ultimately permit the extension of reliable print techniques to the very fine print arena.For small apertures, solder paste volume and consistency are critical to solder joint reliability. The work described in this paper examines the release performance of various solder pastes from a variety of aperture sizes and geometries. The focus of this study is a comparison of square versus circular apertures when the nominal volume of paste to be deposited is kept constant. This method of study is contrasted with published work wherein squares versus circles have been studied, but, in those, the dimensions (not volumes) were the same (e.g., 12 mil diameter circle as compared to a 12 mil (on a side) square aperture).
Stencil printing is a critical first step in surface mount assembly. However, its robustness can be called into question because of the fact that about 50% or more of the defects found in the assembly of printed circuit boards (PCBs) are attributed to stencil printing 1. Manufacturing techniques for the assembly of certain flip chips, chip scale packages, 0201s, and fine pitch ball grid arrays are testing the limits of current stencil printing capabilities. This paper focuses on understanding the release of solder paste from the stencil, based on experimental and modeling approaches. The primary goal of the study is to characterize the performance of various aperture sizes and geometries based on release efficiencies and to compare them to predictions. The resulting model validation helps us better understand the print process for small features and offers options for increasing print yields. The study is divided into two phases. The first phase examines the release performance of various solder pastes from a variety of aperture sizes and geometries. The focus of this study is a comparison of square versus circular apertures when the nominal volume of paste to be deposited is kept constant. The second phase consists of developing a model that predicts paste-release efficiencies from small apertures and validating the model with experimental results.
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