Effect of size

Size eifect may be quantified through rather simple, but refined considerations. Metallurgical variability that results in the dependence of fatigue limit Of or Sf on specimen size is also responsible for the dependency of tensile strength r on specimen size. According to flie WeibuU theory of the weakest link (see Sect. 4.1.7) the ratio of the ultimate strength r, i of a specimens of volume Vi to that of specimen of volume V2 is inversely proportional to the power of the ratio of the respective volumes 

When a specimen is put in monotonic traction the entire volume exerts a reaction, but under cyclic loads only the surface is involved in the initiation process till a depth of about 500 pm. Below that dimension internal inclusions to be effective initiation sites must compensate the reduced concentration factor (see Fig. 3.21) with an increase in size which reduces their probability of existence. Therefore in a cylindrical specimen of diameter d and length I the proves volume to be considered from the fatigue point of view is 

Equation (3.21) will be used to evaluate the size effect on fatigue limit Sf passing from a standard cylindrical specimen of 6 mm diameter to a larger one having a diameter of 20 mm. Assume that the l/d ratio remains constant and equal to 3 (fatigue specimens have l/d 3) and m — 25 (poor quality material), Eq. (3.21) yields 

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Reaction and Transport Interactions. The importance of the various design and operating variables largely depends on relative rates of reaction and transport of reactants to the reaction sites. If transport rates to and from reaction sites are substantially greater than the specific reaction rate at meso-scale reactant concentrations, the overall reaction rate is uncoupled from the transport rates and increasing reactor size has no effect on the apparent reaction rate, the macro-scale reaction rate. When these rates are comparable, they are coupled, that is they affect each other. In these situations, increasing reactor size alters mass- and heat-transport rates and changes the apparent reaction rate. Conversions are underestimated in small reactors and selectivity is affected. Selectivity does not exhibit such consistent impacts and any effects of size on selectivity must be deterrnined experimentally. 

TABLE 15-9 Effect of Size of Opening between Compartments ... 

Minimum Fluidizing Velocity U,nj, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one of the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen audYu [A.l.Ch.E.j., 610-612 (1966)] given below can then be used to back calculate d. This gives a particle size that takes into account effects of size distribution and sphericity. The correlation can then be used to estimate U, at process conditions, if U,nj cannot be determined experimentally, use the expression below directly. 

Figure 4.3. Energy versus bond rotation in methylsuccinic acid (schematic). The diagram shows the greater stability of staggered as compared with eclipsed forms, and the effect of size and dipole moment of substituents on the barriers. The slope of the curve at any point represents the force opposing rotation there. ( = energy of activation of rotation.) (After Gordon )...

The amount of heat absorbed by a vessel exposed to an open fire is markedly affected by the size and character of the installation and by the environment. These conditions are evaluated by the following equation, in whieh the effect of size on the heat input is shown by the exponent of A, the vessel wetted area, and the effect of other conditions is included in a factor F ... 

Tables. Effect of size of particles CaC03 and treatment of the filler by stearinic acid on the value of the yield strength zy of the molten polycarbonate [162]...

Effect of size in stating material strength properties. Property tables, unless otherwise stated for plastics, metals, and so on, list strength values based on a specified size, yet larger components generally fail at a lower stress than a similar smaller component made of the same material. 

Comparison of Eq. (184) with Eq. (183) shows the effect of size distribution for the case of fast chemical reaction with simultaneous diffusion. This serves to emphasize the error that may arise when one applies uniform-drop-size assumptions to drop populations. Quantitatively the error is small, because 1 — is small in comparison with the second term in the brackets [i.e., kL (kD)112). Consequently, Eq. (184) and Eq. (183) actually give about the same result. In general, the total average mass-transfer rate in the disperser has been evaluated in this model as a function of the following parameters ... 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

Mass loss determinations refer to the total change resulting from reactant decomposition and usually include contributions from a mixture of product compounds, some of which would normally be condensed under conditions used for accumulatory pressure measurements. Such information concerned with the overall process is, however, often usefully supplemented by evolved gas analyses (EGA) using appropriate analytical methods. Sestak [130] has made a detailed investigation of the effects of size and shape of reactant container on decomposition kinetics and has recommended that the sample be spread as a thin layer on the surfaces of a multiple plate holder. The catalytic activity of platinum as a reactant support may modify [131] the apparent kinetic behaviour. 

Metal ions, effect of size, 200-205 Metalloenzymes, see also Enzyme cofactors classification of, by cofactor and coupled general base, 205-207, 206 electrostatic interactions in, 205-207 SNase, 189-197... 

Biopolymers have diverse roles to play in the advancement of green nanotechnology. Nanosized derivatives of polysaccharides like starch and cellulose can be synthesized in bulk and can be used for the development of bionanocomposites. They can be promising substitutes of environment pollutant carbon black for reinforcement of rubbers even at higher loadings (upto SOphr) via commercially viable process. The combined effect of size reduction and organic modification improves filler-matrix adhesion and in turn the performance of polysaccharides. The study opens up a new and green alternative for reinforcement of rubbers. 

Barza, M., Stuart, M., and Szoka, F. (1987). Effect of size and lipid composition on the pharmacokinetics of intravitreal liposomes, Invest. Ophthalmol. Visual Sci., 28, 893-900. 

Before investigating the effect of size, shape, and structure on catalytic behavior, that is, TOFs, a set of five requirements concerning the metal particles has to be met. Besides a monodisperse size distribution, the nanoparticles should be fully reduced, unpoisoned, unperturbed by... 

CampheU CT, Parker SC, Starr DE. 2002. The effect of size-dependent nanoparticle energetics on catalyst sintering. Science 298 811-814. 

Grigorieva LK, Lidorenko NS, Nagaev EL, Chizhik SP. 1987. [Effect of sizes of metal small particles and thin plates on the rate of the chemical reactions on their surfaces]. Poverkhnost 8 131-137 (in Russian). 

If, moreover, we consider a set of peaks with the index (h) counting the orders of reflections, then the effects of size and instrumental broadening are readily eliminated... 

In terms of shape and size, catalysts are typically presented as extrudates (cylindrical, tri-lobes or four-lobes), in sizes of diameters from 0.8 mm to about 1.7 mm and lengths from 3 mm to about 7 mm. The effect of size and shape on operation concerns the pressure drop control, the fluid flow through the bed, the interparticle and intraparticle flow, the diffusion of the fluids from the external surface to the internal surface. The three and four lobes extrudates facilitates diffusion, but they are usually more fragile than the cylindrical extrudates increasing the risk of pressure drop build up. For operation of a trickle bed reactor with heavy feedstocks, for which the diffusion limitations are important, lobed extrudates are preferred. Meanwhile, for vapor phase reactors large cylindrical extrudates are used. 

The structure of a vapor-quenched alloy may be either crystalline, in which the periodicity of the unit cell is repeated within the crystallites, or amorphous, in which there is no translational periodicity even over a distance of several lattice spacings. Mader (64) has given the following criteria for the formation of an amorphous structure the equilibrium diagram must show limited terminal solubilities of the two components, and a size difference of greater than 10% should exist between the component atoms. A ball model simulation experiment has been used to illustrate the effects of size difference and rate of deposition on the structure of quench-cooled alloy films (68). Concentrated alloys of Cu-Ag (35-65%... 

Figure 1. Effect of size on particle deposition in the respiratory tract. (Reproduced with permission from ref. 1. Copyright 1966 Pergamon.)...

Barak, N.A.E. and C.F. Mason. 1990a. Mercury, cadmium, and lead in eels and roach the effects of size, season and locality on metal concentrations in flesh and liver. Sci. Total Environ. 92 249-256. 

Amselem, S., A.J. Domb, C.R. Alving, Lipospheres as Vaccine Carrier Systems Effects of Size, Charge, and Phospholipid Composition, Vaccine Research. 1, 383, 1992. 

Fig. 1 The effect of size on metals. Whereas bulk metal and metal nanoparticles have a continuous band of energy levels, the limited number of atoms in metal clusters results in discrete energy levels, allowing interaction with light by electronic transitions between energy levels. Metal clusters bridge the gap between single atoms and nanoparticles. Even though in the figure the energy levels are denoted as singlets, we must remark that the spin state of the silver clusters is not yet firmly established...

Meyer JH, Dressman JB, Fink A, Amidon G. Effect of size and density on canine gastric emptying of nondigestible solids. Gastroenterology 1985 89 805-813. 

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