Index for Simultaneous Dispersive and Distributive Mixing Characterization in Processing Equipment

Alemaskin, Kirill; Manas–Zloczowe, I.; Kaufman, Miron

doi:10.3139/217.1843

Cited by 15 publications

(7 citation statements)

References 21 publications

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“…Furthermore, the dispersion state was evaluated by using Shannon entropy according to the literature. [ 24,25 ] The Shannon entropy

Ψ

is defined by Equation (3),

Ψ goodbreak= goodbreak- \sum_{c = 1}^{C} p_{c} \frac{\sum_{j = 1}^{M} p_{j / c} \ln p_{j / c}}{\ln M} goodbreak= goodbreak- \sum_{c = 1}^{C} p_{c} S_{c}

where

C

is the total number of species, the index

c

indicates each species,

M

is the total number of subregions (bins), the index

j

indicates the nominal number of bins,

p_{c}

is the sum of agglomerate areas in species

c

divided by the total area of all agglomerates, and

p_{j / c}

is the probability of finding an agglomerate in bin

j

conditional on being of species

c

. In this study, the species were categorized by area in pixel 2 into eight species (10 0 –10 0.5 , 10 0.5 –10 1 , 10 1 –10 1.5 , 10 1.5 –10 2 , 10 2 –10 2.5 , 10 2.5 –10 3 , 10 3 –10 3.5 , 10 3.5 –10 4 pixel 2 ).…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, the dispersion state was evaluated by using Shannon entropy according to the literature. [24,25] The Shannon entropy Ψ is defined by Equation (3),…”

Section: Characterization Of Dispersion Statementioning

confidence: 99%

“…Furthermore, the quantification of the dispersion state of nanofillers is also an important topic. Alemaskin et al [ 24 ] and Rohm et al [ 25 ] adopted Shannon entropy analysis to quantitatively characterize the dispersion level in a polymer matrix. Thus, in this study, the Shannon entropy was used to evaluate the dispersion state.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A modified blister mixing element for generating extensional flow in a twin‐screw extruder: Process characterization and dispersion state of carbon nanotubes in cyclo‐olefin polymer

Matsumoto

Tanaka

2022

Polymer Engineering & Sci

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This study aimed to improve the dispersion state of single-walled carbon nanotubes (SWCNTs) in a cyclo-olefin polymer (COP) matrix by introducing extensional flow during the compounding through a twin-screw extruder (TSE). A modified mixing element with multiple holes, called a fixed blister disc (XBD), was developed. To describe the mixing performance of XBD, the flow state was characterized via numerical simulation and acquisition of process data such as pressure drop (ΔP) at XBD and specific mechanical energy (SME), while the operational conditions of TSE were varied. The dispersion state of SWCNTs was evaluated from the viewpoint of the melt viscoelastic property, surface resistivity of extruded samples and mechanical properties of injection molded samples. Furthermore, the dispersion morphology was observed via optical microscopy and scanning electron microscopy. As a result, the mixing performance of XBD was improved by increasing the ratio of throughputs Q to screw speed N s (Q/N s ) since ΔP, which is related to extensional stress, was increased. However, the trade-off relationship between ΔP and SME was confirmed versus Q/N s . Although the dispersion state at the submicron level was markedly improved with higher SME inputs, higher ΔP reduced the largest agglomerate size and improved dispersion uniformity. Consequently, the mechanical properties were improved significantly.

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“…Furthermore, the dispersion state was evaluated by using Shannon entropy according to the literature. [ 24,25 ] The Shannon entropy

Ψ

is defined by Equation (3),

Ψ goodbreak= goodbreak- \sum_{c = 1}^{C} p_{c} \frac{\sum_{j = 1}^{M} p_{j / c} \ln p_{j / c}}{\ln M} goodbreak= goodbreak- \sum_{c = 1}^{C} p_{c} S_{c}

where

C

is the total number of species, the index

c

indicates each species,

M

is the total number of subregions (bins), the index

j

indicates the nominal number of bins,

p_{c}

is the sum of agglomerate areas in species

c

divided by the total area of all agglomerates, and

p_{j / c}

is the probability of finding an agglomerate in bin

j

conditional on being of species

c

Section: Methodsmentioning

confidence: 99%

“…Furthermore, the dispersion state was evaluated by using Shannon entropy according to the literature. [24,25] The Shannon entropy Ψ is defined by Equation (3),…”

Section: Characterization Of Dispersion Statementioning

confidence: 99%

See 1 more Smart Citation

A modified blister mixing element for generating extensional flow in a twin‐screw extruder: Process characterization and dispersion state of carbon nanotubes in cyclo‐olefin polymer

Matsumoto

Tanaka

2022

Polymer Engineering & Sci

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show abstract

“…We assume continuous feeding of particles at the extruder entrance and thus steady-state conditions for all the results presented in this work. Details of the numerical simulations and the particle tracking algorithm are given in Reference [5].…”

Section: Entropic Characterization Of Simultaneous Dispersive and Dismentioning

confidence: 99%

Entropic Measures of Mixing Tailored for Various Applications

Alemaskin¹,

Camesasca²,

Manas‐Zloczower³

et al. 2004

AIP Conference Proceedings

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Abstract.Mixing is an important component in most processing operations including but not limited to polymer processing. Generically, mixing refers to the system capability to reduce composition nonuniformity. Since the entropy is the rigorous measure of disorder or system homogeneity, we will explore in this presentation various ways to employ the entropy to characterize the state of mixing in a multi-component system. The various species can be initially present in the system or they can evolve as a result of a dispersive mixing operation involving a cohesive minor component.

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“…A few authors have also proposed the use of mixing indices to straightforwardly characterize the extent of distributive or dispersive mixing, as these would facilitate direct comparisons between different operating conditions, screw profiles, and material properties. Average particle/droplet size relative to the initial size, number-average diameter [ 22 , 23 ], relative flow strength [ 24 ], shear stress distribution [ 25 , 26 ], and cumulative area ratio [ 27 , 28 ] have been routinely used as indicators of dispersive mixing, whereas Shannon entropy [ 29 ] was suggested as a measure of distributive mixing. Nevertheless, these indices require either lengthy experimental characterization or computationally demanding calculations.…”

Section: Introductionmentioning

confidence: 99%

On-Line Optical Monitoring of the Mixing Performance in Co-Rotating Twin-Screw Extruders

2022

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The use of real-time techniques to evaluate the global mixing performance of co-rotating twin-screw extruders is well consolidated, but much less is reported on the specific contribution of individual screw zones. This work uses on-line flow turbidity and birefringence to ascertain the mixing performance of kneading blocks with different geometries. For this purpose, one of the barrel segments of the extruder was modified in order to incorporate four sampling devices and slit dies containing optical windows were attached to them. The experiments consisted in reaching steady extrusion and then adding a small amount of tracer. Upon opening each sampling device, material was laterally detoured from the local screw channel, and its turbidity and birefringence were measured by the optical detector. Residence time distribution curves (RTD) were obtained at various axial positions along three different kneading blocks and under a range of screw speeds. It is hypothesized that K, a parameter related to the area under each RTD curve, is a good indicator of dispersive mixing, whereas variance can be used to assess distributive mixing. The experimental data confirmed that these mixing indices are sensitive to changes in processing conditions, and that they translate the expected behavior of each kneading block geometry.

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Index for Simultaneous Dispersive and Distributive Mixing Characterization in Processing Equipment

Cited by 15 publications

References 21 publications

A modified blister mixing element for generating extensional flow in a twin‐screw extruder: Process characterization and dispersion state of carbon nanotubes in cyclo‐olefin polymer

A modified blister mixing element for generating extensional flow in a twin‐screw extruder: Process characterization and dispersion state of carbon nanotubes in cyclo‐olefin polymer

Entropic Measures of Mixing Tailored for Various Applications

On-Line Optical Monitoring of the Mixing Performance in Co-Rotating Twin-Screw Extruders

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