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Theoretical Equations (theoretical + equation)
Selected AbstractsKinetic Model for Crystallization in White Ceramic GlazesJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 1 2001Agustin Escardino Theoretical equations have been developed for crystal growth rate in layers of small frit (glass) particles during firing. Throughout the process, the crystalline and the glassy phases have different compositions; therefore, the system can be considered a pseudo-two-component system consisting of a crystallizable component (structural unit) and a noncrystallizable mixture of several components. The concentration of the crystallizable component decreases in the residual glassy phase during the crystal growth process, on integrating at the surfaces of crystals having the same composition. Throughout the crystal growth process, a concentration gradient of the crystallizable component is therefore produced in the glassy phase, which results in mass transport by diffusion of this component from the bulk residual glassy phase to the surfaces of the crystals. Equations have been derived assuming that the diffusion step of the crystallizable component through the residual glassy phase is the overall crystal growth process rate-controlling step. [source] Correlation of peel and burst tests for pouchesPACKAGING TECHNOLOGY AND SCIENCE, Issue 2 2001Rosamari Feliú-Báez Abstract Theoretical equations based on force diagrams were developed in order to explain pouch behaviour during a restrained burst test. According to the resulting equation, P,=,2 S/D, the burst pressure (P) increases directly with seal strength (S) and inversely with the distance between the restraining plates (D). After performing a restrained burst test and a peel test on Tyvek/plastic pouches, it was found that the theoretical development did not exactly explain burst test results in terms of peel test values. The test results demonstrate that even though the peeling times for the peel and burst tests were controlled to be the same, the theoretical formula (P,=,2 S/D) tends to overestimate the burst pressure. The overestimation increases at smaller gaps. These results are an indication that the formula is not universal and they suggest that it is an oversimplification. It might work for some materials at a particular set of testing conditions but not for others. Copyright © 2001 John Wiley & Sons, Ltd. [source] Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat-flux vibration (effects of aspect ratio on the fields)HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2007Shota Matsumura Abstract In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat-flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of ,=1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number ,m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ,r, estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is ,=5 and the Prandtl number is Pr=0.71 for a range of the Rayleigh number Ra. However, ,m has two local maxima for a larger Ra, which is peculiar to the case of larger ,. The time variation of sub-components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of ,m agrees well with that of the sub-component of velocity for the first resonance angular velocity ,r. For the other angular velocity ,r2, the phase of ,m agrees with that of the sub-component of temperature. Moreover, we found that the boundary angular velocity ,0 between the first two of the five , regions, which classify the thermal convection fields against ,, can be expressed by a function of ,, Ra, and Pr and that ,m is independent of , and Ra for a relatively wide range of ,/,0. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 158, 171, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20149 [source] Uncertainty analysis of heat release rate measurement from oxygen consumption calorimetryFIRE AND MATERIALS, Issue 6 2005Sylvain BrohezArticle first published online: 1 JUL 200 Abstract Oxygen consumption calorimetry remains the most widespread method for the measurement of the heat release rate from experimental fire tests. In a first step, this paper examines by theoretical analysis the uncertainty associated with this measurement, especially when CO and soot corrections are applied. Application of theoretical equations is presented for chlorobenzene which leads to high values of CO and soot yields. It appears that the uncertainty of CO and soot corrections are high when the fuel composition is unknown. In a second step, a theoretical analysis is provided when the simplest measurement procedure is used for oxygen consumption calorimetry. The overall uncertainty can be dominated either by the uncertainty associated with the oxygen concentration, the assumed heat of combustion, the fumes mass flow rate or the assumed combustion expansion factor depending on the oxygen depletion. Copyright © 2005 John Wiley & Sons, Ltd. [source] Interpretation of the optical rotatory dispersion in telluriumJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2002Ivo Vy An interpretation of the most recent experimental data on the optical rotatory dispersion of tellurium is presented. The experimental data are approximated by theoretical equations which were derived using the model of three coupled oscillators. The applied mathematical method is based on the sum of least squares. The derived equations are also helpful when modelling the circular dichroism of tellurium and discussing the sense of the rotation of the linear polarized light with regard to the crystal structure. [source] Electrosprayed polymer particles: Effect of the solvent propertiesJOURNAL OF APPLIED POLYMER SCIENCE, Issue 1 2009Chul Ho Park Abstract Electrospraying technology has been studied in many fields to produce particles of various substances from nanoscale to microscale sizes. Unlike pure liquids, droplets formed by electrospraying that are comprised of polymer solutions undergo additional solidification processes involving solvent evaporation, which primarily determine the particle size and morphology. Herein, the effects of the solvent properties on the morphology and dimensions of solidified particles were systematically studied. In general, the size of the solidified spherical particles with smooth surfaces reflected that of the initially formed liquid droplets, which could partially be estimated by theoretical equations developed for pure liquids. Particle sizes increased with an increase in polymer content and a decrease in the boiling point of the volatile solvent. Inhomogeneous drying processes related to phase separation or skin formation resulted in hollow, cuplike, and porous particle structures, with particle sizes and morphologies that were outside of the scope of the theoretical treatments. The selection of a proper solvent or solvent mixture seemed to be a convenient way to control the particle morphologies, such as hollow, cuplike, or porous structures. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009 [source] Zirconocene-catalyzed copolymerization of methyl methacrylate with other methacrylate monomersJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 15 2004Giorgos Karanikolopoulos Abstract Statistical copolymers of methyl methacrylate (MMA) with n -butyl-, s -butyl, t -butyl-, n -hexyl-, decyl-, stearyl-, allyl-, trimethylsilyl- and trimethylsilyloxyethyl methacrylate were prepared by zirconocene-catalyzed copolymerization. The reactivity ratios of MMA copolymers with butyl-, hexyl-, and stearyl methacrylate were estimated using the Finemann,Ross, the inverted Finemann,Ross, and the Kelen,Tüdos graphical methods. Structural parameters of the copolymers were obtained from the calculated dyad sequences, derived by using the reactivity ratios. The effect of the nature of the methacrylate ester group and the catalytic system used on the copolymer structure is discussed. The glass-transition temperature (Tg) values of MMA copolymers with butyl- and hexyl methacrylate were measured and examined in the frame of several theoretical equations, allowing the prediction of these Tg values. The best fit was obtained using Barton and Johnston equations, taking the monomer sequence distribution of the copolymers into account. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3761,3774, 2004 [source] The determination of membrane transport parameters with the cell pressure probe: theory suggests that unstirred layers have significant impactPLANT CELL & ENVIRONMENT, Issue 12 2005MELVIN T. TYREE ABSTRACT A simulation model was written to compute the time-kinetics of turgor pressure, P, change in Chara corallina during cell pressure probe experiments. The model allowed for the contribution of a membrane plus zero, one, or two unstirred layers of any desired thickness. The hypothesis that a cell with an unstirred layer is a composite membrane that will follow the same kind of kinetics with or without unstirred layers was tested. Typical ,osmotic pulse' experiments yield biphasic curves with minimum or maximum pressures, Pmin(max), at time tmin(max) and a solute exponential decay with halftime . These observed data were then used to compute composite membrane properties, namely the parameters Lp = the hydraulic conductance, , = reflection coefficient and Ps = solute permeability using theoretical equations. Using the simulation model, it was possible to fit an experimental data set to the same values of Pmin(max), tmin(max) and incorporating different, likely values of unstirred layer thickness, where each thickness requires a unique set of plasmalemma membrane values of Lp, , and Ps. We conclude that it is not possible to compute plasmalemma membrane properties from cell pressure probe experiments without independent knowledge of the unstirred layer thickness. [source] Computational Oral Absorption Simulation for Low-Solubility CompoundsCHEMISTRY & BIODIVERSITY, Issue 11 2009Kiyohiko Sugano Abstract Bile micelles play an important role in oral absorption of low-solubility compounds. Bile micelles can affect solubility, dissolution rate, and permeability. For the pH,solubility profile in bile micelles, the Henderson,Hasselbalch equation should be modified to take bile-micelle partition into account. For the dissolution rate, in the Nernst,Brunner equation, the effective diffusion coefficient in bile-micelle media should be used instead of the monomer diffusion coefficient. The diffusion coefficient of bile micelles is 8- to 18-fold smaller than that of monomer molecules. For permeability, the effective diffusion coefficient in the unstirred water layer adjacent to the epithelial membrane, and the free fraction at the epithelial membrane surface should be taken into account. The importance of these aspects is demonstrated here using several in vivo and clinical oral-absorption data of low-solubility model compounds. Using the theoretical equations, the food effect on oral absorption is further discussed. [source] | ||||||||||||||||