Mixing times

1998 ◽  
pp. 85-133 ◽  
Author(s):  
Laszlo Lovász ◽  
Peter Winkler
Keyword(s):  
Mixing Times

Process characteristics of screw impellers with a draught tube for Newtonian liquids. Time of homogenization

1981 ◽  
Vol 46 (9) ◽  
pp. 2032-2042 ◽  
Author(s):  
Pavel Seichter
Keyword(s):  
Flow Regime ◽  
Creeping Flow ◽  
Energy Requirements ◽  
Dimensionless Time ◽  
Mixing Times ◽  
Conductivity Method ◽  
Draught Tube ◽  
Process Characteristics ◽  
Newtonian Liquids

A conductivity method has been used to assess the homogenization efficiency of screw impellers with draught tubes. The value of the criterion of homochronousness, i.e. the dimensionless time of homogenization, in the creeping flow regime of Newtonian liquids is dependent on the geometrical simplexes of the mixing system. In particular, on the ratio of diameters of the vessel and the impeller and on the ratio of the screw lead to the impeller diameter. Expression have been proposed to calculate the mixing times. Efficiency has been examined of individual configurations of screw impellers. The lowest energy requirements for homogenization have been found for the system with the ratio D/d = 2.

scholarly journals RELAXATION OF SPHERICAL SYSTEMS WITH LONG-RANGE INTERACTIONS: A NUMERICAL INVESTIGATION

2011 ◽  
Vol 21 (08) ◽  
pp. 2279-2283 ◽  
Author(s):  
PIERFRANCESCO DI CINTIO ◽  
LUCA CIOTTI
Keyword(s):  
Long Range ◽  
Superposition Principle ◽  
Relaxation Times ◽  
Stellar Dynamics ◽  
Mixing Times ◽  
Spherical Shells ◽  
Phase Mixing ◽  
Long Range Interactions ◽  
System Of Particles ◽  
Classical Gravity

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of r-2force law. However, recently the interest in alternative gravities has emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an r-αforce law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent α, with small values of α corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.

scholarly journals The χ2-divergence and mixing times of quantum Markov processes

2010 ◽  
Vol 51 (12) ◽  
pp. 122201 ◽  
Author(s):  
K. Temme ◽  
M. J. Kastoryano ◽  
M. B. Ruskai ◽  
M. M. Wolf ◽  
F. Verstraete
Keyword(s):  
Markov Processes ◽  
Mixing Times ◽  
Quantum Markov Processes

Establishment of a simple method to evaluate mixing times in a plastic bag photobioreactor using image processing based on freeware tools

2021 ◽  
Author(s):  
Michael Sandmann
Keyword(s):  
Image Processing ◽  
Optical Method ◽  
Gas Flow ◽  
Mixing Time ◽  
Pearson Correlation ◽  
Mixing Times ◽  
Simple Method ◽  
Area Of Interest ◽  
Background Removal ◽  
Programming Skills

Abstract Objective The aim of this work was to develop a simple optical method to determine the mixing time in a photobioreactor. The image processing method should be based on freeware tools and should not require programming skills. Results An optical method has been established to analyze images from recorded videos of mixing experiments. The basic steps are: 1. Extraction of a sequence of images from the video file; 2. Cropping of the pictures; 3. Background removal; and 4. Image analysis and mixing time evaluation based on quantification of pixel-to-pixel heterogeneity (standard deviation over pixel intensities) within a given area of interest. The novel method was generally able to track the dependency between aeration rate and mixing time within the investigated photobioreactor. In a direct comparison, a Pearson correlation coefficient of rho = 0.9957 was obtained. Gas flow rates between 10 L h−1, and 300 L h−1 resulted from mixing times of between 48 sec and 14 sec, respectively. This simple technique is applicable even without programming skills and can be used in education within high schools and in early stages of undergraduate programs.

Difference Between Mixing Times Measured with Reversible and Irreversible Reactions

2012 ◽  
Vol 38 (1) ◽  
pp. 19-24
Author(s):  
Shunsuke Hashimoto ◽  
Akitoshi Nishimura ◽  
Yoshiro Inoue
Keyword(s):  
Mixing Times

Mixing times for the rook’s walk via path coupling

2017 ◽  
Vol 10 (1) ◽  
pp. 51-64
Author(s):  
Cam McLeman ◽  
Peter T. Otto ◽  
John Rahmani ◽  
Matthew Sutter
Keyword(s):  
Mixing Times ◽  
Path Coupling

scholarly journals Study of the Effect of a Plug with Torsion Channels on the Mixing Time in a Continuous Casting Ladle Water Model

Metals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1942
Author(s):  
Gerardo Aguilar ◽  
Gildardo Solorio-Diaz ◽  
Alicia Aguilar-Corona ◽  
José Angel Ramos-Banderas ◽  
Constantin A. Hernández ◽  
...  
Keyword(s):  
Continuous Casting ◽  
Mixing Time ◽  
Tangential Velocity ◽  
Water Model ◽  
Mixing Times ◽  
Low Velocity ◽  
Velocity Magnitude ◽  
Image Velocimetry ◽  
Casting Ladle ◽  
Upward Direction

The use of porous plugs in injecting gas through the bottom of a ladle forms vertical plumes in a very similar way to a truncated cone. The gas plume when exiting the plug has a smaller diameter compared to that formed in the upper zone of the ladle because inertial forces predominate over buoyancy forces in this zone. In addition, the magnitude of the plume velocity is concentrated in an upward direction, which increases the likelihood of low velocity zones forming near the bottom of the ladle, especially in lower corners. In this work, a plug with spiral-shaped channels with different torsion angles is proposed, with the objective that the gas, when passing through them, has a tangential velocity gain or that the velocity magnitude is distributed in the three axes and does not just focus on the upward direction, helping to decrease low velocity zones near the bottom of the ladle for better mixing times. For the experimentation, we worked in a continuous casting ladle water model with two configuration injections, which in previous works were reported as the most efficient in mixing the steel in this ladle. The results obtained using the PIV technique (particle image velocimetry) and conductimetry technique indicate that the plugs with the torsion channels at angles of 60° and 120° improve the mixing times for the two injection configurations.

scholarly journals Stationary frequencies and mixing times for neutral drift processes with spatial structure

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180238
Author(s):  
Alex McAvoy ◽  
Ben Adlam ◽  
Benjamin Allen ◽  
Martin A. Nowak
Keyword(s):  
Spatial Structure ◽  
Evolutionary Process ◽  
General Setting ◽  
Rates Of Convergence ◽  
Demographic Variables ◽  
Neutral Evolution ◽  
Mixing Times ◽  
Mutation Process ◽  
Neutral Drift ◽  
Genetic Types

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (traits), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analysing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.

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