The growth kinetics of ledges during phase transformations: multistep interactions

An analysis of the growth characteristics of a train of ledges is presented, where volume diffusion in the parent phase is assumed to be the rate­- controlling factor. First a train of steps of unequal height is considered where the step heights are assumed to be consistent with a steady-state motion so that each step moves with the same speed. It is possible to analyse this situation by asymptotic methods when the steps are either far apart or close together. Explicit results are given for both two- and three-step trains and it is shown how the step heights must vary if a given train is to move steadily at a specified speed. Trains of steps of equal height are also considered and an analysis is made of the relative velocities of such steps due to their interaction.

The problem of step motion during lateral growth in solid-solid phase transformations is re-examined. Results are obtained for the steady motion of an individual ledge when volume diffusion in the parent phase is the predominant contribution to the growth rate. A comparison is made between our results and the earlier work of Jones & Trivedi (1971). There are significant differences between the two sets of results particularly in the limit of small perturbations to the Laplacian diffusion field. To confirm the accuracy of the results presented here the calculations have been made by two different methods.


2014 ◽  
Vol 14 (7) ◽  
pp. 3210-3220 ◽  
Author(s):  
Harutoshi Asakawa ◽  
Gen Sazaki ◽  
Etsuro Yokoyama ◽  
Ken Nagashima ◽  
Shunichi Nakatsubo ◽  
...  

1999 ◽  
Vol 46 (1) ◽  
pp. 72-80 ◽  
Author(s):  
Urs Lendenmann ◽  
Mario Snozzi ◽  
Thomas Egli

Kinetic models for microbial growth describe the specific growth rate (μ) as a function of the concentration of the growth-limiting nutrient (s) and a set of parameters. A typical example is the model proposed by Monod, where μ is related to s using substrate affinity (Ks) and the maximum specific growth rate (μmax). The preferred method to determine such parameters is to grow microorganisms in continuous culture and to measure the concentration of the growth-limiting substrate as a function of the dilution rate. However, owing to the lack of analytical methods to quantify sugars in the microgram per litre range, it has not been possible to investigate the growth kinetics of Escherichia coli in chemostat culture. Using an HPLC method able to determine steady-state concentrations of reducing sugars, we previously have shown that the Monod model adequately describes glucose-limited growth of E. coli ML30. This has not been confirmed for any other sugar. Therefore, we carried out a similar study with galactose and found steady-state concentrations between 18 and 840 μg·L-1 for dilution rates between 0.2 and 0.8·h-1, respectively. With these data the parameters of several models giving the specific growth rate as a function of the substrate concentration were estimated by nonlinear parameter estimation, and subsequently, the models were evaluated statistically. From all equations tested, the Monod model described the data best. The parameters for galactose utilisation were μmax = 0.75·h-1 and Ks = 67 μg·L-1. The results indicated that accurate Ks values can be estimated from a limited set of steady-state data when employing μmax measured during balanced growth in batch culture. This simplified procedure was applied for maltose, ribose, and fructose. For growth of E. coli with these sugars, μmax and Ks were for maltose 0.87·h-1, 100 μg·L-1; for ribose 0.57·h-1, 132 μg·L-1, and for fructose 0.70·h-1, 125 μg·L-1. Key words: monod model, continuous culture, galactose, glucose, fructose, maltose, ribose.


2007 ◽  
Vol 121-123 ◽  
pp. 139-144
Author(s):  
B.F. Pan ◽  
R. He ◽  
F. Gao ◽  
L.M. Ao ◽  
H.Y. Tian ◽  
...  

A safe, common, and low-cost method was proven to be effective for the synthesis of high quality CdSe nanocrystals. Cd(Ac)2 and Lauric acid were found to be the excellent cadmium precursor and solvent/ligand, respectively. The size and shape of CdSe nanocrystals synthesized by this route can be varied in a controllable manner in a broad size range, from about 2.0 nm to 4 nm. The growth kinetics of CdSe nanocrystals nucleated from TOPSe and cadmium acetate was also investigated in Lauric Acid. The rate constant for steady-state CdSe growth was found to be 4.15×10─8 m s─1 at 260°C.


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