Practical Parameters for Mixing

1975 ◽  
Vol 48 (4) ◽  
pp. 577-591 ◽  
Author(s):  
P. R. Van Buskirk ◽  
S. B. Turetzky ◽  
P. F. Gunberg
Keyword(s):  
Shear Strain ◽  
Large Scale ◽  
Rate Of Change ◽  
Dimensionless Number ◽  
Die Swell ◽  
High Shear ◽  
Actual Measurement ◽  
Unit Work ◽  
Mooney Viscosity ◽  
Total Shear

Abstract (1) Compounds mixed under high-shear conditions in a laboratory Brabender Plastograph or in larger Banbury mixers can be quantitatively compared on the basis of work input per unit volume. This quantity, unit work Wu, is proposed as a useful parameter for characterizing the effects of polymer, filler, and other ingredient on mixing performance. (2) This work supports the principle that, independent of the size and speed of a mixer, there is a unique relationship between unit work and such in-process properties of the compound as Mooney viscosity, die swell, etc. It has been shown that this relationship extends to other high-shear mixers, such as the Shaw Intermix and a cam-head type Brabender Plasticorder. (3) Practical unit work ranges for passenger tire-tread mixing found typical of factory operations are: first stage, 300–800 MJ/m3; second stage, 150–400 MJ/m3; final mix, 2000–4500 MJ/m3. Mixing to these unit-work levels in the laboratory achieved mixing quality that closely duplicated large-scale high-shear mixing. (4) Process profiles (the changes of certain in-process properties such as Mooney viscosity and die swell as functions of unit work) yield additional behavior indices that are characteristic of each individual rubber—filler mixture: The viscosity-work index (VWI), for instance, reflects the rate of change in the compound viscosity with increasing unit work, while the position of the maximum in the die swell vs. unit work curve is a good indicator of the minimum unit work required to obtain low levels of undispersed carbon black. (5) A second scaling parameter, based on an expanded concept of the total shear-strain performance for Banbury-type mixers, is proposed. It offers an alternative approach to scaled mixing when the actual measurement of unit work is not convenient. The total shear-strain parameter, as derived, is a dimensionless number Γ defined as Γ = [(shear rate) (time) (volumetric throughput ratio) (land-length ratio)]. Its use implies ideal viscous flow during mixing plus an accurate knowledge of mixer rotor and chamber dimensions.

Scale-Up of Internal Mixers

1984 ◽  
Vol 57 (1) ◽  
pp. 48-54 ◽  
Author(s):  
I. Manas-Zloczower ◽  
Z. Tadmor
Keyword(s):  
Shear Strain ◽  
Scale Up ◽  
Operating Conditions ◽  
Dimensionless Number ◽  
Operational Parameters ◽  
Acceptable Error ◽  
Work Input ◽  
Unit Work ◽  
New Criterion ◽  
Total Shear

Abstract In this paper, a new criterion for scaling Banbury type internal mixers is proposed. The new criterion is a dimensionless number Xt*, representing the product of the fraction of broken agglomerates during one pass through the high shear zone of the internal mixer and the average number of passes through this zone, for a given mixing time. It can be calculated for a given system of polymer-additive from a knowledge of machine geometry and operating conditions. The dimensionless number Xt* is uniquely related to the fraction of undispersed agglomerates, ψ, which is a frequently encountered mixing quality criterion. Experimental results reported in literature, for a broad range of mixer sizes, fit, within practical acceptable error, the theoretical curve ψ versus Xt*, lending support to its validity. Moreover, the dimensionless number Xt* correlates almost linearly with the presently used scaling-up criteria, the unit work input and the total shear strain, which in turn proved to be interrelated to other properties of the compound, such as Mooney viscosity and die-swell. However, while the unit work input and the total shear strain can be used in scaling only as long as proper operating conditions are met, the dimensionless number Xt* provides a reliable scale-up criterion for a broad range of mixer sizes and geometries as well as different operational parameters. Derived from a theoretical model of dispersive mixing in internal mixers based exclusively on fundamental considerations, this new criterion can be used also for mixing cycle optimization and basic machine design.

Compound Processability and Molecular Weight Distribution of SBR

1976 ◽  
Vol 49 (2) ◽  
pp. 291-302 ◽  
Author(s):  
W. Mills ◽  
F. Giurco
Keyword(s):  
Molecular Weight ◽  
Carbon Black ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Mixing Time ◽  
Die Swell ◽  
Similar Information ◽  
Unit Work ◽  
Normal Production ◽  
Mooney Viscosity

Abstract Nonuniformities in the mixing and extrusion behavior of nominally standard grades of emulsion- and solution-polymerized oil-extended SBR are associated with variations in molecular weight distribution but are not reflected by Mooney viscosity. The variations in the samples studied were representative of normal production material. The solution-polymerized polymers characteristically exhibit wider variations in compound die swell and have generally more rapid dispersion of carbon black than comparable emulsion-polymerized polymers. This is true, regardless of whether BIT or t′ point is considered as a measure of carbon black dispersibility. Generally, increasing polydispersity increases compound die swell and retards the rate of carbon-black dispersion. Utilization of unit work instead of mixing time as a measure for torque rheometer processability gives similar information on carbon-black dispersibility. However, unit work is preferred because of the promise it holds for scaleup and interlaboratory correlation. Delta Mooney values, and to a lesser extent peak Mooney torque, provide a useful basis for predicting the mixing and extrusion behavior of oil-extended SBR. The torque rheometer t′ point recently proposed as an index for carbonblack dispersibility is also useful for predicting compound die swell.

scholarly journals Effects of Climatic Drivers and Teleconnections on Late 20th Century Trends in Spring Freshet of Four Major Arctic-Draining Rivers

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 179
Author(s):  
Roxanne Ahmed ◽  
Terry Prowse ◽  
Yonas Dibike ◽  
Barrie Bonsal
Keyword(s):  
Arctic Ocean ◽  
Large Scale ◽  
Southern Oscillation ◽  
Rate Of Change ◽  
The Arctic ◽  
Late 20Th Century ◽  
Basin Scale ◽  
The Arctic Ocean ◽  
Spring Freshet ◽  
Climatic Drivers

Spring freshet is the dominant annual discharge event in all major Arctic draining rivers with large contributions to freshwater inflow to the Arctic Ocean. Research has shown that the total freshwater influx to the Arctic Ocean has been increasing, while at the same time, the rate of change in the Arctic climate is significantly higher than in other parts of the globe. This study assesses the large-scale atmospheric and surface climatic conditions affecting the magnitude, timing and regional variability of the spring freshets by analyzing historic daily discharges from sub-basins within the four largest Arctic-draining watersheds (Mackenzie, Ob, Lena and Yenisei). Results reveal that climatic variations closely match the observed regional trends of increasing cold-season flows and earlier freshets. Flow regulation appears to suppress the effects of climatic drivers on freshet volume but does not have a significant impact on peak freshet magnitude or timing measures. Spring freshet characteristics are also influenced by El Niño-Southern Oscillation, the Pacific Decadal Oscillation, the Arctic Oscillation and the North Atlantic Oscillation, particularly in their positive phases. The majority of significant relationships are found in unregulated stations. This study provides a key insight into the climatic drivers of observed trends in freshet characteristics, whilst clarifying the effects of regulation versus climate at the sub-basin scale.

scholarly journals Equatorial ionospheric disturbance observed through a transequatorial HF propagation experiment

2006 ◽  
Vol 24 (5) ◽  
pp. 1401-1409 ◽  
Author(s):  
T. Maruyama ◽  
M. Kawamura
Keyword(s):  
Large Scale ◽  
Ionospheric Disturbance ◽  
Great Circle ◽  
Rate Of Change ◽  
Spatial Distance ◽  
Propagation Path ◽  
Multiple Signal Classification ◽  
Radio Broadcasting ◽  
Equatorial Plasma Bubbles ◽  
Propagation Experiment

Abstract. A transequatorial radio-wave propagation experiment at shortwave frequencies (HF-TEP) was done between Shepparton, Australia, and Oarai, Japan, using the radio broadcasting signals of Radio Australia. The receiving facility at Oarai was capable of direction finding based on the MUSIC (Multiple Signal Classification) algorithm. The results were plotted in azimuth-time diagrams (AT plots). During the daytime, the propagation path was close to the great circle connecting Shepparton and Oarai, thus forming a single line in the AT plots. After sunset, off-great-circle paths, or satellite traces in the AT plot, often appeared abruptly to the west and gradually returned to the great circle direction. However, there were very few signals across the great circle to the east. The off-great-circle propagation was very similar to that previously reported and was attributed to reflection by an ionospheric structure near the equator. From the rate of change in the direction, we estimated the drift velocity of the structure to range mostly from 100 to 300 m/s eastward. Multiple instances of off-great-circle propagation with a quasi-periodicity were often observed and their spatial distance in the east-west direction was within the range of large-scale traveling ionospheric disturbances (LS-TIDs). Off-great-circle propagation events were frequently observed in the equinox seasons. Because there were many morphological similarities, the events were attributed to the onset of equatorial plasma bubbles.

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence

1997 ◽  
Vol 347 ◽  
pp. 37-70 ◽  
Author(s):  
J. R. RISTORCELLI
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Single Point ◽  
Longitudinal Velocity ◽  
Rate Of Change ◽  
Constitutive Relationship ◽  
Compressible Turbulence ◽  
Velocity Correlation ◽  
Turbulent Reynolds Number ◽  
Simple Scaling

The mathematical consequences of a few simple scaling assumptions regarding the effects of compressibility are explored using a singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure–dilatation and dilatational dissipation appearing in single-point moment closures for compressible turbulence are obtained. The results obtained, in as much as they come from the same underlying procedure, represent a unified development for both dilatational covariances. While the results are expressed in the context of a statistical turbulence closure they provide, with very few phenomenological assumptions, an interesting and clear mathematical model for the ‘scalar’ effects of compressibility. For homogeneous turbulence with quasi-normal large scales the expressions derived are – in the small turbulent Mach number squared isotropic limit – exact. The expressions obtained contain constants that have a precise physical significance and are defined in terms of integrals of the longitudinal velocity correlation. The pressure–dilatation covariance is found to be a non-equilibrium phenomenon related to the time rate of change of the kinetic energy and internal energy of the turbulence; it is seen to scale with α2M2t εs [Pk/ε−1] (Sk/εs)2. Implicit in the scaling is a dependence on the square of a gradient Mach number, S[lscr ]/c. A new feature indicated by the analysis is the appearance of the Kolmogorov scaling coefficient, α, suggesting that large-scale quantities embodied in the well-established ε∼u˜3/[lscr ] relationship provide a link to the structural dependence of the effects of compressibility. The expressions for the dilatational dissipation are found to depend on the turbulent Reynolds number and scale as M4t (Sk/εs)4R−1t. The scalings for the pressure–dilatation are found to produce an excellent collapse of the pressure–dilatation data from direct numerical simulation.

High shear strain rate rheometry of polymer melts

2009 ◽  
Vol 114 (2) ◽  
pp. 864-873 ◽  
Author(s):  
A. L. Kelly ◽  
T. Gough ◽  
B. R. Whiteside ◽  
P. D. Coates
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Polymer Melts ◽  
Shear Strain Rate ◽  
High Shear

Real-Time Prediction of Choke Health Using Production Data Integrated with AI

2021 ◽  
Author(s):  
Ahmed Alghamdi ◽  
Olakunle Ayoola ◽  
Khalid Mulhem ◽  
Mutlaq Otaibi ◽  
Abdulazeez Abdulraheem
Keyword(s):  
High Pressure ◽  
Real Time ◽  
Large Scale ◽  
Production Systems ◽  
Rate Of Change ◽  
Production Data ◽  
Ann Model ◽  
Sand Production ◽  
Data Set ◽  
Pressure Drops

Abstract Chokes are an integral part of production systems and are crucial surface equipment that faces rough conditions such as high-pressure drops and erosion due to solids. Predicting choke health is usually achieved by analyzing the relationship of choke size, pressure, and flow rate. In large-scale fields, this process requires extensive-time and effort using the conventional techniques. This paper presents a real-time proactive approach to detect choke wear utilizing production data integrated with AI analytics. Flowing parameters data were collected for more than 30 gas wells. These wells are producing gas with slight solids production from a high-pressure high-temperature field. In addition, these wells are equipped with a multi-stage choke system. The approach of determining choke wear relies on training the AI model on a dataset constructed by comparison of the choke valve rate of change with respect to a smoother slope of the production rate. If the rate of change is not within a tolerated range of divergence, an abnormal choke behavior is detected. The data set was divided into 70% for training and 30% for testing. Artificial Neural Network (ANN) was trained on data that has the following inputs: gas specific gravity, upstream & downstream pressure and temperature, and choke size. This ANN model achieved a correlation coefficient above 0.9 with an excellent prediction on the data points exhibiting normal or abnormal choke behaviors. Piloting this application on large fields, where manual analysis is often impractical, saves a substantial man-hour and generates significant cost-avoidance. Areas for improvement in such an application depends on equipping the ANN network with long-term production profile prediction abilities, such as water production, and this analysis relies on having an accurate reading from the venturi meters, which is often the case in single-phase flow. The application of this AI-driven analytics provides tremendous improvement for remote offshore production operations surveillance. The novel approach presented in this paper capitalizes on the AI analytics for estimating proactively detecting choke health conditions. The advantages of such a model are that it harnesses AI analytics to help operators improve asset integrity and production monitoring compliance. In addition, this approach can be expanded to estimate sand production as choke wear is a strong function of sand production.

The Simulation of Aggregated Colloids Under Flow

1992 ◽  
Vol 289 ◽  
Author(s):  
John R. Melrose
Keyword(s):  
Shear Rate ◽  
Large Scale ◽  
Shear Thinning ◽  
High Shear ◽  
Shear Rates ◽  
Rouse Model ◽  
High Shear Rates ◽  
Structural Breakdown ◽  
Large Scale Simulations ◽  
Low Shear

AbstractAn overview is given of theories of aggregates under flow. These generally assume some sort of structural breakdown as the shear rate is increased. Models vary with both the rigidity of the bonding and the level of treatment of hydrodynamics. Results are presented for simulations of a Rouse model of non-rigid, (i.e. central force) weakly bonded aggregates. In large scale simulations different structures are observed at low and high shear rates. The change from one structure to another is associated with a change in the rate of shear thinning. The model captures low shear rate features of real systems absent in previous models: this feature is ascribed to agglomerate deformations. Quantitatively, the model is two orders of magnitude out from experiment but some scaling is possible.

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