Entropic Measures of Mixing Tailored for Various Applications

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

doi:10.1063/1.1766518

Cited by 9 publications

(10 citation statements)

References 7 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method presented here is a development of that presented in [53] for the study of chaotic micromixers. Similar works include [52] for polymer processing using the Renyi entropy, whereas other works using the Shannon entropy include [54] for a single screw extruder, [13] for a helical pipe, [55] for the right coronary artery and [56] for nasal cavities.…”

Section: Entropic Measure Of Mixingmentioning

confidence: 99%

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Gambaruto

Moura

Sequeira

2010

Numer Methods Biomed Eng

View full text Add to dashboard Cite

SUMMARYWith growing focus on patient-specific studies, little attempt has yet been made to quantify the modelling uncertainty. Here uncertainty in both geometry definition obtained from in vivo magnetic resonance imaging scans and mathematical models for blood are considered for a peripheral bypass graft. The approximate error bounds in computed measures are quantified from the flow field in steady state simulations with rigid walls assumption.A brief outline of the medical image filtering and segmentation procedures is given, as well as virtual model reconstruction and surface smoothing. Diversities in these methods lead to variants of the virtual model definition, where the mean differences are within a pixel size. The blood is described here by either a Newtonian or a non-Newtonian Carreau constitutive model.The impact of the uncertainty is considered with respect to clinically relevant data such as wall shear stress. This parameter is locally very sensitive to the surface definition; however, variability in the topology has an effect on the core flow field and measures to study the flow structures are detailed and comparison performed. Integrated effect of the Lagrangian dynamics of the flow is presented in the form of stir mixing, which also has a strong clinical relevance.

show abstract

Section: Entropic Measure Of Mixingmentioning

confidence: 99%

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Gambaruto

Moura

Sequeira

2010

Numer Methods Biomed Eng

View full text Add to dashboard Cite

show abstract

“…The current algorithm has been adopted from the work of [16] who use a related idea of using entropy to obtain an index of dispersion for measuring the dispersion of multiple species of particulate matter in a medium. However, the details involved in adapting the concept of Shannon entropy to measure SWNT dispersion are different from [16] and are described later in this section.…”

Section: Image Analysis Techniquementioning

confidence: 99%

“…However, the details involved in adapting the concept of Shannon entropy to measure SWNT dispersion are different from [16] and are described later in this section. The authors are not aware of any such method for quantifying the dispersion of SWNTs in epoxy.…”

Section: Image Analysis Techniquementioning

confidence: 99%

Synthesis of ZnO Nanorods by Laser Ablation of ZnO and Zn Targets in He and O₂ Background Gas

Okada¹,

Kawashima²,

Nakata³

et al. 2005

Jpn. J. Appl. Phys.

View full text Add to dashboard Cite

A new continuous impingement mixing process has been used to disperse unpurified single-walled carbon nanotubes (SWNTs) in a Shell EPON-862/EpiCURE system. Composites with up to 0.2 wt% loading of SWNTs were prepared by this process. The hydrodynamic dispersion of SWNTs was found to depend on the non-dimensional Curtet number (C t ). Dispersion was evaluated by analyzing SEM images of the fracture surface using an image processing technique based on the concept of Shannon entropy. Electrical conductivity of these composites was greatly enhanced when compared with the plain material. The behavior of electrical conductivity as a function of dispersion was found to be in accordance with results from the image processing technique, and was also used to estimate the sedimentation of SWNTs.

show abstract

“…In contrast, Guida et al (2010) used conditional entropy to introduce a mixing measure of the flow itself, independent of any scalar distribution. They independently developed the same idea previously presented by Alemaskin et al (2004).…”

Section: Introductionmentioning

confidence: 99%

“…At first glance, the global mixing measure proposed by Alemaskin et al (2004) and Guida et al (2010) is the most similar to the ICI proposed here. It is independent of any scalar distribution and is defined as the average of Shannon's conditional entropy.…”

Section: Introductionmentioning

confidence: 99%

Flow complexity in open systems: interlacing complexity index based on mutual information

et al. 2017

View full text Add to dashboard Cite

Flow complexity is related to a number of phenomena in science and engineering, which has been approached from the perspective of chaotic dynamical systems, ergodic processes, or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolutions, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon's mutual information (MI), and inspired by an analogy between inlet-outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver, and communication channel are played, respectively, by the inlet, the outlet, and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross section used to parameterize them, valid for any type of mass-preserving flow.

show abstract

Entropic Measures of Mixing Tailored for Various Applications

Cited by 9 publications

References 7 publications

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Synthesis of ZnO Nanorods by Laser Ablation of ZnO and Zn Targets in He and O₂ Background Gas

Flow complexity in open systems: interlacing complexity index based on mutual information

Contact Info

Product

Resources

About

Entropic Measures of Mixing Tailored for Various Applications

Cited by 9 publications

References 7 publications

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty

Synthesis of ZnO Nanorods by Laser Ablation of ZnO and Zn Targets in He and O2 Background Gas

Flow complexity in open systems: interlacing complexity index based on mutual information

Contact Info

Product

Resources

About

Synthesis of ZnO Nanorods by Laser Ablation of ZnO and Zn Targets in He and O₂ Background Gas