scholarly journals Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190245 ◽  
Author(s):  
Irina V. Alexandrova ◽  
Dmitri V. Alexandrov
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Steady State ◽  
Growth Rates ◽  
Fine Particles ◽  
Protein Crystallization ◽  
Growth Time ◽  
Nonlinear Behaviour ◽  
Unsteady State ◽  
State Growth

This manuscript is devoted to the nonlinear dynamics of particulate assemblages in metastable liquids, caused by various dynamical laws of crystal growth and nucleation kinetics. First of all, we compare the quasi-steady-state and unsteady-state growth rates of spherical crystals in supercooled and supersaturated liquids. It is demonstrated that the unsteady-state rates transform to the steady-state ones in a limiting case of fine particles. We show that the real crystals evolve slowly in a more actual case of unsteady-state growth laws. Various growth rates of particles are tested against experimental data in metastable liquids. It is demonstrated that the unsteady-state rates describe the nonlinear behaviour of experimental curves with increasing the growth time or supersaturation. Taking this into account, the crystal-size distribution function and metastability degree are analytically found and compared with experimental data on crystallization in inorganic and organic solutions. It is significant that the distribution function is shifted to smaller sizes of particles if we are dealing with the unsteady-state growth rates. In addition, a complete analytical solution constructed in a parametric form is simplified in the case of small fluctuations in particle growth rates. In this case, a desupercooling/desupersaturation law is derived in an explicit form. Special attention is devoted to the biomedical applications for insulin and protein crystallization. This article is part of the theme issue ‘Patterns in soft and biological matters’.

scholarly journals On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization

2019 ◽  
Vol 377 (2143) ◽  
pp. 20180214 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Irina G. Nizovtseva
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Growth Rates ◽  
Biomedical Applications ◽  
Size Distribution Function ◽  
Porcine Insulin ◽  
Unsteady State ◽  
State Growth

A generalized theory of nucleation and growth of crystals in a metastable (supercooled or supersaturated) liquid is developed taking into account two principal effects: the diffusion mechanism of the particle-size distribution function in the space of particle radii and the unsteady-state growth rates of individual crystals induced by fluctuations in external temperature or concentration field. A system of the Fokker–Planck and balance integro-differential equations is formulated and analytically solved in a parametric form for arbitrary nucleation kinetics and arbitrary growth rates of individual crystals. The particle-size distribution function and system metastability are found in an explicit form. The Weber–Volmer–Frenkel–Zel'dovich and Meirs kinetic mechanisms, as well as the unsteady-state growth rates of nuclei (Alexandrov & Alexandrova 2019 Phil. Trans. R. Soc. A 377 , 20180209 ( doi:10.1098/rsta.2018.0209 )), are considered as special cases. Some potential biomedical applications of the present theory for crystal growth from supersaturated solutions are discussed. The theory is compared with experimental data on protein and insulin crystallization (growth dynamics of the proteins lysozyme and canavalin as well as of bovine and porcine insulin is considered). The hat-shaped particle-size distribution functions for lysozyme and canavalin crystals as well as for bovine and porcine insulin are found. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

scholarly journals Estimates of the steady state growth rates for some European countries

2012 ◽  
Vol 29 (4) ◽  
pp. 1119-1125 ◽  
Author(s):  
Paolo Casadio ◽  
Antonio Paradiso ◽  
B. Bhaskara Rao
Keyword(s):  
Steady State ◽  
Growth Rates ◽  
European Countries ◽  
Steady State Growth ◽  
State Growth

scholarly journals Gene activities for ribosomal components in Escherichia coli B/r

1975 ◽  
Vol 150 (3) ◽  
pp. 469-475 ◽  
Author(s):  
H Bremer ◽  
P P Dennis
Keyword(s):  
Escherichia Coli ◽  
Steady State ◽  
Ribosomal Rna ◽  
Growth Rates ◽  
Ribosomal Proteins ◽  
Rrna Genes ◽  
Steady State Growth ◽  
State Growth ◽  
Escherichia Coli B

The relative transcriptional activities of genes coding for ribosomal RNA (rRNA) and ribosomal proteins (r-proteins) at a steady-state growth rates ranging from 0.65 to 2.1 doublings/h can be estimated from previous measurements of the synthesis rates of stable and unstable RNA (Pato & von Meyenburg, 1970; Nierlich, 1972a,b; Bremer et al., 1973; Dennis & Bremer, 1973b, 1974b) and ribosomal proteins (Schleif, 1967; Dennis & Bremer, 1974a). Comparison of these transcriptional activities suggests that the expression of the r-protein genes and rRNA genes is controlled seperately.

Application of the Marais - Ekama Activated Sludge Model to Large Plants

1982 ◽  
Vol 14 (6-7) ◽  
pp. 581-598 ◽  
Author(s):  
H A Nicholls
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Activated Sludge ◽  
Large Scale ◽  
Unsteady State ◽  
Activated Sludge Model ◽  
Nitrate Concentrations ◽  
Utilisation Rate ◽  
Oxygen Utilisation ◽  
State Responses

The Marais-Ekama model was used to successfully predict the performance of two 50 000 m3/d five-stage nutrient removing activated sludge plants. The experimental data used to test the model was obtained by monitoring the feed, effluent and contents of each reactor in the process, every two hours for 4 days. In addition, a respirometer was developed to measure the oxygen utilisation rate automatically every 30 minutes. All data collected was found to be valid, as acceptable COD and nitrogen balances across the plants were possible. The data was then compared with the steady state and unsteady state responses of the model. It was found that the model could successfully predict the COD, TKN, Ammonia and nitrate concentrations in the effluent and illustrate some shortcomings in the process layouts. This indicated that the model could be used by designers and operators of large-scale plants to predict performance and highlight problem areas.

Measurement of Unsteady State Growth Rates of Micro-Organisms

Nature ◽  
1965 ◽  
Vol 208 (5007) ◽  
pp. 263-265 ◽  
Author(s):  
R. I. MATELES ◽  
D. Y. RYU ◽  
T. YASUDA
Keyword(s):  
Growth Rates ◽  
Unsteady State ◽  
State Growth ◽  
Micro Organisms

Validation of Transonic Axial Compressor Stage Unsteady-State Rotor-Stator Simulations

2017 ◽  
Author(s):  
Paul Galpin ◽  
Thorsten Hansen ◽  
Georg Scheuerer ◽  
Ryan Kelly ◽  
Adam Hickman ◽  
...  
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Total Pressure ◽  
Axial Compressor ◽  
Compressor Stage ◽  
Unsteady State ◽  
Mean Flow ◽  
Steady State Method ◽  
Rotor Stator Interaction ◽  
Transonic Axial Compressor

The paper describes the validation of steady-state and unsteady CFD simulations against experimental data from a single-stage, transonic axial compressor stage. The experimental data include overall compressor performance, high-resolution traverses of total pressure and total temperature, and unsteady-state total pressure measurements downstream of the rotor. Various numerical rotor-stator interaction methods were applied across the operational speedline. These included a steady-state method mixing plane, and a transient time inclination method that accounts for the unsteady rotor to stator pitch change. Best practice procedures were employed to assess and quantify the sensitivity of the simulations to numerical error like mesh and timestep size, turbulence model error and systematic errors related to tip gap, and steady-state or unsteady-state flow assumptions. The effect of turbulence on the mean flow is modelled by a URANS approach based on the SST model and its extensions for laminar-turbulent transition and reattachment prediction. The complex unsteady flow interactions between the rotor and stator were validated against steady-state and unsteady experimental data. The compressor flow is explained in detail including transonic flow features like shock boundary layer interactions. Comparisons are made between the various rotor-stator interaction simulation methods and the experimental data.

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