Time Evolution Of Size Distribution Research Articles

Different approximate models of the sectional method for nanoparticle Brownian coagulation

Purpose– The original v2-based sectional method assumes that the selected property quantity of particles is uniformly distributed in each section, which makes particle size distribution (PSD) fluctuate dramatically in the entire size range. The number concentration in each section as well as the zeroth moment of PSD also cannot be correctly predicted in case there are not enough sections used in calculation. In order to provide a more appropriate representation of PSD, different approximate models are used to close the conservation equations. The paper aims to discuss these issues.Design/methodology/approach– The uniform distribution of the selected property quantity of particles in each section is not necessarily satisfied. Instead, the distribution is approximated using an expression with an approximation factor. Different models are investigated on recovering the initial size distribution and predicting the time evolution of size distribution as well as the first three moments so that the advantages and disadvantages of each model can be compared.Findings– The approximate model with an approximation factor of 0.8 is capable of predicting the time evolution of the zeroth moment accurately no matter how many sections are used in simulations. The original v2-based model is recommended to calculate the first and second moments as long as the section number is larger than 50, otherwise, the model with an approximation factor of 0.15 would be a preferred choice.Originality/value– Different approximate models can be used to improve the accuracy of the results supposing we know which moment is of great importance in calculation.

Effects of mixing on electrical properties of carbon nanofiber and polymer composites

AbstractWe examined electrical properties of composites of carbon nanofibers (CNFs)/linear low‐density polyethylene (LLDPE) in the range of mixing time. An addition of CNFs into LLDPE led to a decrease of electrical resistivity, and the large amounts of CNFs were required to reach the electrical percolation threshold for the longer mixing time. For the research of these phenomena, we examined the effects of mixing time on the size (length) and spatial distributions of CNFs in the composites. SEM micrographs revealed the size reduction of CNFs in a series of mixing times, although the spatial dispersion of CNFs became more uniform at longer mixing time. To describe the reduction of CNFs theoretically, we hypothesize the size distribution of CNFs obeys a governing population balance kinetics based on an irreversible dissolution process. For the process, we proposed a size dependent breakage rate coefficient proportional to the size of CNFs. The model prediction for the time evolution of size distribution of CNFs has been validated with the experimental measurement showing good agreement. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

A Dynamic Model of Size Distribution of Firms Applied to U.S. Biotechnology and Trucking Industries

The present paper attempts to contribute to the existing literature on industry dynamics by proposing a tractable structure for the analysis of the dynamic process governing the size distribution of firms. An analytical model is proposed which describes the density of the cross-sectional distribution of firm size within an industry. The model is based on the theory of diffusion processes, and the method illustrates how information on the time-evolution of size distribution of firms over an extended period of time can be used to make inferences about an underlying process. An empirical application to the evolution of size distribution of population of firms in (i) the U.S. biotechnology industry, and (ii) the U.S. interstate for-hire trucking industry illustrates the applicability of the proposed model in industry studies.

Kinetics of formation of fibrin oligomers. III. Ligation kinetics concurrent with and subsequent to oligomer assembly.

AbstractHuman fibrinogen was treated with thrombin in the presence of fibrinoligase (Factor XIIIa) and calcium ion at pH 8.5, ionic strength 0.45, and the ensuing polymerization was interrupted at various time intervals (t) both before and after the clotting time (tc) by solubilization with a solution of sodium dodecyl sulfate and urea. Aliquots of the solubilized protein were subjected to gel electrophoresis on polyacrylamide gels after disulfide reduction by dithiothreitol and on agarose gels without reduction. The degree of γ‐γ ligation was determined from the former. The latter provided the size distribution of ligated end‐to‐end sequences produced by splitting the ligated staggered overlapped oligomers down the middle, for degrees of polymerization, x, from 1 to 10. Addition of fibrinoligase (in which the activating thrombin had been inhibited by p‐nitrophenyl‐p′‐guanidinobenzoate, NPGB) to Kabi fibrinogen showed the presence of small amounts of ligatable oligomers. Addition of fibrinoligase to a polymerizing mixture in which the action of thrombin had been stopped before clotting by NPGB produced the same distribution of ligated end‐to‐end sequences that was obtained when fibrinoligase was originally present, at least for reaction times up to 0.7 of the clotting time. The kinetics of γ‐γ ligation by fibrinoligase acting on a polymerized mixture stabilized by NPGB were followed. The reaction was first order in the concentration of ligatable γ‐γ junctions and the initial velocity was proportional to the enzyme concentration. The time evolution of size distribution of ligated end‐to‐end sequences agreed with a theory based on random ligation of ligatable junctions.