Flattening ratio

Several other special cases have also been analyzed numerically, leading to simplified formulations for the flattening ratio, as detailed below in each model group. 

Fukanuma and Ohmori15101 also presented an analytical model for the flattening ratio of a molten metal droplet on a surface as a function of time and compared the model prediction to experimental data for molten tin and zinc droplets. An expression for the flattening ratio was derived based on some simplified assumptions and approximations ... 

One of the earliest analytical models for the calculation of flattening ratio of a droplet impinging on a solid surface was developed by Jones.1508] In this model, the effects of surface tension and solidification were ignored. Thus, the flattening ratio is only a function of the Reynolds number. Discrepancies between experimental results and the predictions by this model have been reported and discussed by Bennett and PoulikakosJ380]... 

For droplets of high surface tension, the droplet flattening process may be governed by the transformation of impact kinetic energy to surface energy. In case that this mechanism dominates, the flattening ratio becomes only dependent on the Weber number, as derived by Madej ski by fitting the numerical results of the full analytical model ... 

In Madejski s full model,l401 solidification of melt droplets is formulated using the solution of analogous Stefan problem. Assuming a disk shape for both liquid and solid layers, the flattening ratio is derived from the numerical results of the solidification model for large Reynolds and Weber numbers ... 

Sobolev et al)5111 conducted a series of analytical studies on droplet flattening, and solidification on a surface in thermal spray processes, and recently extended the analytical formulas for the flattening of homogeneous (single-phase) droplets to composite powder particles. Under the condition Re 1, the flattening ratios on smooth and rough surfaces are formulated as ... 

Fig. 10.51 a-c. Quantitative indexes in carpal tunnel syndrome, a Nerve cross-sectional area. This measure is calculated at the point of maximum nerve swelling by the transverse (a) and anteroposterior (b) diameters of the nerve using the ellipse formula [abjc/4]. b,c Flattening ratio. This measure is determined at the distal carpal tunnel by dividing the transverse diameter (aj of the nerve by its anteroposterior diameter (b). In c, the measurement of nerve diameters for calculating the flattening ratio is shown in a transverse 12-5 MHz US image of the distal carpal tunnel. The threshold values for these measurements are reported in Sect. 10.5.2.3... 

In the tubular process a thin tube is extruded (usually in a vertically upward direction) and by blowing air through the die head the tube is inflated into a thin bubble. This is cooled, flattened out and wound up. The ratio of bubble diameter to die diameter is known as the blow-up ratio, the ratio of the haul-off rate to the natural extrusion rate is referred to as the draw-down ratio and the distance between the die and the frost line (when the extrudate becomes solidified and which can often be seen by the appearance of haziness), the freeze-line distance. 

AuSn has the nickel arsenide structure, B8, with abnormally small axial ratio (c/a = 1.278, instead of the normal value 1.633). Each tin atom is surrounded by six gold atoms, at the corners of a trigonal prism, with Au-Sn = 2.847 A. and each gold atom is surrounded by six tin atoms, at the corners of a flattened octahedron, and two gold atoms, at 2.756 A., in the opposed directions through the centers of the two large faces of the octahedron. 

The flattening of our figure of equilibrium is defined by the ratio oj jlndk and depends only on the angular velocity and density of a fluid, but it is independent of a size. Because of this the dimensions of a planet do not affect its flattening. 

At the instant of contact between a sphere and a flat specimen there is no strain in the specimen, but the sphere then becomes flattened by the surface tractions which creates forces of reaction which produce strain in the specimen as well as the sphere. The strain consists of both hydrostatic compression and shear. The maximum shear strain is at a point along the axis of contact, lying a distance equal to about half of the radius of the area of contact (both solids having the same elastic properties with Poisson s ratio = 1/3). When this maximum shear strain reaches a critical value, plastic flow begins, or twinning occurs, or a phase transformation begins. Note that the critical value may be very small (e.g., in pure simple metals it is zero) or it may be quite large (e.g., in diamond). 

Beryllium was first demonstrated to be present in low-metallicity stars by Gilmore, Edvardsson and Nissen (1991) and soon confirmed by others, e.g. Ryan ei al. (1992) who gave the argument for a flattening in the Be/Fe ratio at [Fe/H]... 

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