Quantifying Fluid Mixing with the Shannon Entropy

Camesasca, Marco; Kaufman, Miron; Manas‐Zloczower, Ica

doi:10.1002/mats.200600037

Cited by 98 publications

(74 citation statements)

References 33 publications

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“…Global Shannon entropy (GSE) whose value ranges from 0 to 1 is a commonly used entropic measure and has been applied in many fields, such as Camesasca [15] and Guida [16] to assess mixing quality in material processing. Under complete spatial randomness, the probability of particles in each quadrat is the same, and thus GSE=1.…”

Section: Particle Number and Area Indexmentioning

confidence: 99%

An Image-Based Approach for Modeling the Copper Particle Uniformity in Formulation Design of Copper-Coated Graphite

Liu¹,

Huang²

2015

IJCA

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Section: Particle Number and Area Indexmentioning

confidence: 99%

An Image-Based Approach for Modeling the Copper Particle Uniformity in Formulation Design of Copper-Coated Graphite

Liu¹,

Huang²

2015

IJCA

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“…Following [34][35][36], the following probabilities are used to express the entropy S as a sum of conditional entropies:…”

Section: -P3mentioning

confidence: 99%

Assessment of mixing in passive microchannels with fractal surface patterning

Fodor

Itomlenskis

Kaufman

2009

Eur. Phys. J. Appl. Phys.

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Abstract. We explore numerically the feasibility of enhancing the mixing capability of microchannels by employing the Weierstrass fractal function to generate a pattern of V-shaped ridges on the channel floor. Motivated by experimental limitations such as the finite resolution (∼10 µm) associated with rapid prototyping through soft lithography techniques, we study the influence on the quality of mixing of having finite width ridges. The mixing capability of the designs studied is evaluated using an entropic measure and the designs are optimized with respect to: the distances between the ridges and the position range of their tip along the width of the channels. The results are evaluated with respect to the benchmarks established by the very successful staggered herring bone (SHB) design. We find that the use of a non periodic protocol to generate the geometry of the bottom surface of the microchannels can lead to consistently larger entropic mixing indices than in cyclic structures. Furthermore, since the optimization curves (mixing index vs. geometric parameters) are broader at the maximum for fractal microchannels than for their SHB counterparts, the microchannel designs using the Weierstrass fractal function are less sensitive to experimental uncertainties. PACS

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“…In addition, several methods have been developed to quantify mixing (Poincaré maps, periodic point analysis, Lyapunov exponents, etc.) [10].…”

Section: Introductionmentioning

confidence: 99%

CFD Based Qualification of Mixing Efficiency of Stirred Vessels

Till

Molnár²,

Egedy

et al. 2018

Period. Polytech. Chem. Eng.

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In this work, we focus on the most crucial units in a chemical technology, the chemical reactors. Using a commercially available CFD software package, COMSOL Multiphysics, 3D mathematical models of a batch reactor with different impeller geometries have been investigated. The reasonable agreement between the experimental and simulation results indicates the validity of the developed CFD model. The effect of the impeller design, e. g. number of blades on the mixing efficiency is evaluated based on the simulation studies.The proposed measure to determine the energy efficiency of mixing (i. e. mixing index) is based on the calculated velocity field and energy usage. The information about the homogeneity of the mixed phase in the system can be extracted from the developed velocity field. Hence, we proposed histograms of velocity fluctuations on a logarithmic scale as an efficient tool to measure the achieved homogeneity of the phase in case of different impellers and rotational speeds. IntroductionDuring the last few decades, computational fluid dynamics (CFD) method has become a very powerful tool in the process industry primarily to analyse the hydrodynamic behavior. In general, CFD methods rely on the numerical solution of the Navier-Stokes equations, thus flow velocity, velocity magnitudes, and pressure values can be calculated in the geometric space investigated. A particularly significant benefit of the CFD simulators is that they can include entire apparatuses in three dimensions, regarding either single phase or multiphase systems [1,2]. This property of the CFD simulators makes them useful in a large number of research areas, including the study of mixing phenomena. Fluid mixing is a fundamental operation in the chemical process industry and the stirred tank or autoclave is a commonly used reactor type in many kinds of chemical technologies; therefore these systems are well described. Regardless, when it comes to design work, simple experimental correlations are still commonly used, e.g. Reynolds number, Froude number, power number or the Euler number which is derived from the previous ones. This approach has its limitations when it comes to the design of stirred vessels with complex internal structure.

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Quantifying Fluid Mixing with the Shannon Entropy

Cited by 98 publications

References 33 publications

An Image-Based Approach for Modeling the Copper Particle Uniformity in Formulation Design of Copper-Coated Graphite

An Image-Based Approach for Modeling the Copper Particle Uniformity in Formulation Design of Copper-Coated Graphite

Assessment of mixing in passive microchannels with fractal surface patterning

CFD Based Qualification of Mixing Efficiency of Stirred Vessels

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