Thickness optimum

Fig. 5 Normalized optimum conditions as a function of normalized preform thickness. Optimum deposition uniformity is insensitive to preform thickness, but maximum deposition rates fall asSocS 7 2...

Thickness of the laminar layer is deterrnined both by the need to reproduce fine detail in the object and by the penetration depth of the actinic laser light into the monomer bath (21,76). There is thus a trade-off between precision of detail in the model and time required for stereohthography, ie, the number of layers that have to be written, and an optimum Light-absorbing initiator concentration in the monomer bath corresponding to the chosen layer thickness. Titanocene-based initiators, eg, bis-perfluorophenyltitanocene has been recommended for this apphcation (77). Mechanistic aspects of the photochemistry of titanocenes and mechanisms of photoinitiation have been reviewed (76). 

An example in support of the first point is the case of optimum insulation thickness. A tank, optimally insulated when first installed, can fall below optimal if the value of heat is quadmpled. This change can justify twice the old iasulation thickness on a new tank. However, the old tank may have to function with its old iasulation. The reason is that there are large costs associated with preparation to iasulate. This means that the cost of an added increment of iasulation is much greater than assumed ia the optimum iasulation thickness formulas (Fig. 15). 

The use of porous formers ia the dippiag process, or porous molds prepared from plaster of Paris or uaglazed porcelaia with a surface pore size smaller than the majority of mbber particles, has been widely adopted ia the latex iadustry. With the porous porcelaia formers, the mbber particles are filtered oa the surface of the formers. The mbber latex coagulates because of its high coaceatratioa to form a film of increa sing thickness as more water is absorbed iato the ceramic. Its rate of iacrease diminishes sharply beyoad an optimum period of time, however, depending on the various characteristics of the ceramic. 

In a static system, the gel-layer thickness rapidly increases and flux drops to uneconomicaHy low values. In equation 6, however, iCis a function of the system hydrodynamics. Typically, high flux is sustained by moving the solution bulk tangentially to the membrane surface. This action decreases the gel thickness and increases the overall hydrauHc permeabiUty. For any given channel dimension, there is an optimum velocity which maximizes productivity (flux per energy input). 

Calendering operations are done routinely, and warm roUs (40—90°C) are recommended for optimum sheet smoothness. A process aid, such as low molecular weight polyethylene wax, is often used. Sheet thicknesses of 0.5—1.3 mm (20—50 mils) can normally be produced. 

Optimal economic insulation thickness may be determined Iw various methods. Two of these are the minimum-total-cost method and the incremental-cost method (or marginal-cost method). The minimum-total-cost method involves the actual calculations of lost energy and insulation costs for each insulation thickness. The thickness producing the lowest total cost is the optimal economic solution. The optimum thickness is determined to be the point where the last dollar invested in insulation results in exactly 1 in energy-cost savings ( ETI— Economic Thickness for Industrial Insulation, Conservation Pap. 46, Federal Energy Administration, August 1976). The incremental-cost method provides a simplified and direcl solution for the least-cost thickness. 

Angle of slope The optimum slope of inclined vibrating screens is that which will handle the greatest volume of oversize and still remove the available undersize required by the standards of the particular operation. To separate a material into coarse and fine fractions, the bed thickness must be limited so that vibration can stratify the load and allow fines to work their way to the screen surface and pass through the opening. Increased slope naturally increases the rate of travel, and at a given rate it reduces the bed thickness. 

What is the optimum material for the pressure hull What are the mass, wall thickness and limiting failure mechanism of the optimum pressure hull ... 

The optimum material is alumina, with a mass of 2.02 tonne, a wall thickness of 41 mm and a limiting failure mechanism of external-pressure buckling. 

Ellipsometry can be sensitive to layers of matter only one atom thick. For example, oxidation of freshly cleaved single-crystal graphite can be monitored from the first monolayer and up. The best thicknesses for the ellipsometric study of thin films are between about 1 nm and 1000 nm. Although the spectra become complicated, films thicker than even 1 pm can be studied. Flat planar materials are optimum, but surface and interfacial roughness can be quantitatively determined if the roughness scale is smaller than about 100 nm. Thus ellipsometry is ideal for the investigation of interfacial surfaces in optical coatings and semiconductor struc-... 

Perhaps the most useful application of ISS stems from its ability to monitor very precisely the concentration and thickness of contaminants on metals during development of optimum processing and cleaning operations. One particularly important application involves quantitatively monitoring total carbon on cleaned steels before paint coating. This has been usefid in helping to develop optimum bond... 

The rubber particles should not be so small that they are completely embedded in a craze. It is interesting to note that in high-impact polystyrene crazes tend to be about 2 p.m thick and the optimum particle sizes observed as a result of experience are quoted in the range 1-10 p.m. For ABS the figures are about 0.5 p.m and 0.1-l.Op.m respectively. 

Example 2.9 A solid polyethylene beam is 10 mm thick and IS mm wide. If it is to be replaced with a sandwich section with solid polyethylene in the two outer skins and polyethylene foam (density = 200 kg/m ) in the centre, calculate the dimensions of the sandwich beam if it is to have optimum stiffness at the same weight as the solid beam. If the foam material costs 20% more than the solid material, calculate the increase or decrease in cost of the sandwich beam. 

It is interesting to generalise this solution for any core skin density ratio. Fig. 2.20 shows how the optimum skin thickness varies with D. This is independent of the solid material density or modulus but is based on a weight... 

Fig. 2.20 Variation of optimum skin thickness with core skin density ratio...

As a batch filtration proceeds, so the rate of filtrate collection decreases due to the increased cake thickness. While operation with thin filter cake results in a higher instantaneous filtration rate, however, it also requires more frequent dismantling of the filter and discharge of the filter cake. There is thus an optimum balance between filtration time and down time. 

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