The viscosity-volume fraction relation for suspensions of rod-like particles by falling-ball rheometry

1989 ◽  
Vol 202 ◽  
pp. 217-232 ◽  
Author(s):  
William J. Milliken ◽  
Moshe Gottlieb ◽  
Alan L. Graham ◽  
Lisa A. Mondy ◽  
Robert L. Powell
Keyword(s):  
Volume Fraction ◽  
Fibre Length ◽  
Relative Viscosity ◽  
Ball Bearings ◽  
Specific Viscosity ◽  
Volume Fractions ◽  
Ball Size ◽  
Theoretical Predictions ◽  
Constant Viscosity ◽  
Good Agreement

The relative viscosities of suspensions of randomly oriented rods in a Newtonian fluid were measured using falling-ball rheometry. The rods were monodisperse and sufficiently large to render colloidal and Brownian forces negligible. Steel and brass ball bearings were dropped along the centreline of cylindrical columns containing the suspensions. The terminal velocities of the falling balls were measured and used to determine the average viscosities of the suspensions. The suspensions behaved as Newtonian fluids in that they were characterized by a constant viscosity. They exhibited a linear relative viscosity-volume fraction relationship for volume fractions less than 0.125, and, for volume fractions between 0.125 and 0.2315, the specific viscosity increased with the cube of the volume fraction. The relative viscosity was found to be independent of falling-ball size for a ratio of falling ball to fibre length greater than 0.3. It was found to be independent of the diameter of the containing cylindrical column for a ratio of column diameter to fibre length greater than 3.2. The value determined for the intrinsic viscosity is in good agreement with theoretical predictions for suspensions of randomly oriented rods.

scholarly journals Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells

2019 ◽  
Vol 872 ◽  
pp. 818-848 ◽  
Author(s):  
Naoki Takeishi ◽  
Marco E. Rosti ◽  
Yohsuke Imai ◽  
Shigeo Wada ◽  
Luca Brandt
Keyword(s):  
Red Blood Cells ◽  
Intrinsic Viscosity ◽  
Blood Cells ◽  
Volume Fraction ◽  
Relative Viscosity ◽  
Shear Plane ◽  
Constitutive Law ◽  
Stable Mode ◽  
Volume Fractions ◽  
Wide Range

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modelled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma,$\unicode[STIX]{x1D706}=0.1$–10, for volume fractions up to$\unicode[STIX]{x1D719}=0.41$and for different capillary numbers ($Ca$). Our numerical results show that an RBC at low$Ca$tends to orient to the shear plane and exhibits so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As$Ca$increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allow RBCs to exhibit tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modelling the relative viscosity as a polynomial function of$\unicode[STIX]{x1D719}$cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of a deformed RBC. We find that the relative viscosity successfully collapses on a single nonlinear curve independently of$\unicode[STIX]{x1D706}$except for the case with$Ca\geqslant 0.4$, where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.

Flow Characteristics of Aluminium Oxide Nanofluids

2009 ◽  
Author(s):  
Vanessa M. Egan ◽  
Patrick A. Walsh ◽  
Edmond J. Walsh
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Volume Fraction ◽  
Relative Viscosity ◽  
Flow Characteristics ◽  
Aluminium Oxide ◽  
Nanoparticle Size ◽  
Rotational Viscometer ◽  
Volume Fractions ◽  
Viscosity Measurements

The current study is an investigation in the flow characteristics of aluminium oxide nanofluids. Relative viscosity measurements are obtained for varying volume fractions using both a rotational viscometer and an experimental setup designed for pressure drop measurements in tubes. The effect of nanoparticle size and preparation method is also investigated as predispersed nanofluids of nominal particle size 10nm and 50nm are compared with each other and with a fluid mixed from Al2O3 nanopowder. Volume fractions of between 1% and 7% were tested. The first method employed to obtain viscosities is based on the Hagen-Poiseuille equation for laminar pipe flow, where pressure drop measurement and flow rate measurements are used to determine relative viscosities of various nanofluids samples. Viscosity measurements were also obtained for a number of solutions on a rotational viscometer and compared to the latter and existing models available in the literature. Overall, it was found during experimentation that the relationship between pressure and flow rate for the various nanofluids was linear indicating that the fluids were Newtonian in nature. An increase in viscosity was recorded for increasing volume fraction; however this was seen to be negligible for volume fractions lower than 1%. Overall it was also seen that both methods of determining relative viscosity were in good agreement. There was not a clear indication of the effect of nanoparticle size on the relative viscosity however the nanofluids formulated from purchased Al2O3 powder resulted in a considerably lower relative viscosity when compared to both nanofluids purchased pre-dispersed from suppliers.

Scaling Behavior of the Complex Conductivity of Graphite-Boron Nitride Percolation Systems

1997 ◽  
Vol 500 ◽  
Author(s):  
Jungie Wu ◽  
D S McLachlan
Keyword(s):  
Boron Nitride ◽  
Volume Fraction ◽  
Hexagonal Boron Nitride ◽  
Imaginary Component ◽  
Frequency Range ◽  
Critical Volume Fraction ◽  
Theoretical Predictions ◽  
Continuous Curves ◽  
Large Frequency ◽  
Good Agreement

ABSTRACTMeasurements of both components of the complex AC conductivity σ*m of continuum percolation systems, based on Graphite and hexagonal Boron Nitride, over a large frequency range, for samples near the conductor insulator composition, are reported. The results of the real part of σ*m (σmr) above the critical volume fraction (φc) and the imaginary component (σmi = iωεoεmr) below φo are shown to have the correct power law dispersion behavior, but only if the non-universal exponents measured in previously described DC experiments are used. It is also shown that all the results can be scaled, as is predicted by percolation theory, so as to lie on two continuous curves, one below and one above φc. Unfortunately the actual ωc values used to scale the experimental results are found not to be in good agreement with theoretical predictions.

scholarly journals Volume Fractions of Tantalum Carbides Deduced from the Ta Contents in the Matrix of Three 1250°C–Aged Cobalt–Based Alloys; Comparison with Thermodynamic Calculations

2020 ◽  
pp. 53-61
Author(s):  
Patrice Berthod
Keyword(s):  
High Temperature ◽  
Volume Fraction ◽  
Thermodynamic Calculations ◽  
Chemical Compositions ◽  
Volume Fractions ◽  
Tantalum Carbides ◽  
Mass Fractions ◽  
The Matrix ◽  
Electron Imaging ◽  
Good Agreement

Some superalloys for service at high temperature under stresses are strengthened by tantalum carbides. Their creep resistance depends on the quantity of TaC and this is the reason why it is often important to control the volume fraction of these carbides in the microstructure. Metallographic preparation followed by electron imaging and surface fraction measurements by image analysis is a frequent way for that. Another possibility is to deduce the mass fraction of TaC, and after their volume fraction, from the chemical composition of the matrix when the alloys are only double–phased, on the {matrix + TaC} type. In this work three alloys – chemically designed to be made exclusively of matrix and TaC – were elaborated and isothermally exposed to an elevated temperature for a duration long enough to allow the alloys being at their thermodynamic equilibria. The chemical compositions of the alloy and of its matrix were measured and the results allowed evaluating their TaC mass fractions which were converted in volume fractions. The obtained TaC fractions were compared to results issued from thermodynamic calculations. Good agreement was found for the three alloys, and this allowed to exploit the used software and thermodynamic database to explore further the microstructures at the same high temperature, notably to know the conditions on the Co, Ni, Cr, Ta and C contents to keep the {matrix + TaC} structure and to avoid any possible partial melting.

scholarly journals A Generalized Approach for Evaluating the Mechanical Properties of Polymer Nanocomposites Reinforced with Spherical Fillers

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 830
Author(s):  
Julio Cesar Martinez-Garcia ◽  
Alexandre Serraïma-Ferrer ◽  
Aitor Lopeandía-Fernández ◽  
Marco Lattuada ◽  
Janak Sapkota ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Polymeric Nanocomposites ◽  
Mechanical Reinforcement ◽  
Future Studies ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Filler Network ◽  
New Research ◽  
Good Agreement ◽  
Research Avenue

In this work, the effective mechanical reinforcement of polymeric nanocomposites containing spherical particle fillers is predicted based on a generalized analytical three-phase-series-parallel model, considering the concepts of percolation and the interfacial glassy region. While the concept of percolation is solely taken as a contribution of the filler-network, we herein show that the glassy interphase between filler and matrix, which is often in the nanometers range, is also to be considered while interpreting enhanced mechanical properties of particulate filled polymeric nanocomposites. To demonstrate the relevance of the proposed generalized equation, we have fitted several experimental results which show a good agreement with theoretical predictions. Thus, the approach presented here can be valuable to elucidate new possible conceptual routes for the creation of new materials with fundamental technological applications and can open a new research avenue for future studies.

scholarly journals Heat Treatment Evaluation for the Camshafts Production of ADI Low Alloyed with Vanadium

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1036
Author(s):  
Eduardo Colin García ◽  
Alejandro Cruz Ramírez ◽  
Guillermo Reyes Castellanos ◽  
José Federico Chávez Alcalá ◽  
Jaime Téllez Ramírez ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Tensile Strength ◽  
Ductile Iron ◽  
Volume Fraction ◽  
Energy Impact ◽  
Treatment Conditions ◽  
Mold Casting ◽  
Grade 3 ◽  
Good Agreement

Ductile iron camshafts low alloyed with 0.2 and 0.3 wt % vanadium were produced by one of the largest manufacturers of the ductile iron camshafts in México “ARBOMEX S.A de C.V” by a phenolic urethane no-bake sand mold casting method. During functioning, camshafts are subject to bending and torsional stresses, and the lobe surfaces are highly loaded. Thus, high toughness and wear resistance are essential for this component. In this work, two austempering ductile iron heat treatments were evaluated to increase the mechanical properties of tensile strength, hardness, and toughness of the ductile iron camshaft low alloyed with vanadium. The austempering process was held at 265 and 305 °C and austempering times of 30, 60, 90, and 120 min. The volume fraction of high-carbon austenite was determined for the heat treatment conditions by XRD measurements. The ausferritic matrix was determined in 90 min for both austempering temperatures, having a good agreement with the microstructural and hardness evolution as the austempering time increased. The mechanical properties of tensile strength, hardness, and toughness were evaluated from samples obtained from the camshaft and the standard Keel block. The highest mechanical properties were obtained for the austempering heat treatment of 265 °C for 90 min for the ADI containing 0.3 wt % V. The tensile and yield strength were 1200 and 1051 MPa, respectively, while the hardness and the energy impact values were of 47 HRC and 26 J; these values are in the range expected for an ADI grade 3.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

scholarly journals A Micro-mechanical Investigation of Empirical Models for the Effective Properties of Aligned Short-Fibre Composites

1995 ◽  
Vol 4 (1) ◽  
pp. 096369359500400
Author(s):  
T.D. Papathanasiou
Keyword(s):  
Aspect Ratio ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Fibre Volume ◽  
Short Fibre ◽  
Computational Results ◽  
Volume Fractions ◽  
Fibre Composites ◽  
Effective Tensile Modulus ◽  
Fibre Aspect Ratio

The predictions of the Halpin equation concerning the effect of fibre volume fraction and fibre aspect ratio on the effective tensile modulus of uniaxially aligned short-fibre composites are compared with computational experiments on three-dimensional, multiparticle composite samples. The method of boundary elements is used to model the mechanical behaviour of composite specimens consisting of up to 40 discrete aligned fibres randomly dispersed in an elastic matrix. Statistical averages of computational results relating the effective tensile modulus to the aspect ratio and volume fraction of the fibres are found to agree very well with the predictions of the Halpin equation for fibre aspect ratio up to 10 and fibre volume fractions up to 20%. Computational results seem to indicate that the predictions of the Halpin equation fall bellow those of micro-mechanical models at higher volume fractions.

The Reduction of Bias Error in Transfer Function Estimates Using FFT-Based Analyzers

1984 ◽  
Vol 106 (1) ◽  
pp. 29-35 ◽  
Author(s):  
P. Cawley
Keyword(s):  
Transfer Function ◽  
Random Excitation ◽  
Analogue Computer ◽  
Bias Error ◽  
Testing Time ◽  
Theoretical Predictions ◽  
Set Up ◽  
Modal Mass ◽  
Time Required ◽  
Good Agreement

The susceptibility to bias error of two methods for computing transfer (frequency response) functions from spectra produced by FFT-based analyzers using random excitation has been investigated. Results from tests with an FFT analyzer on a single degree-of-freedom system set up on an analogue computer show good agreement with the theoretical predictions. It has been shown that, around resonance, the bias error in the transfer function estimate H2 (Syy/Sxy*) is considerably less than that in the more commonly used estimate, H1 (Sxy/Sxx). The record length, and hence the testing time, required for a given accuracy is reduced by over 50 percent if the H2 calculation procedure is used. The analysis has also shown that if shaker excitation is used on lightly damped structures with low modal mass, it is important to minimize the mass of the force gage and the moving element of the shaker.

Estimation of Interlayer Thickness in Inorganic Particulate-Filled Polymer Composites

2011 ◽  
Vol 24 (6) ◽  
pp. 777-788 ◽  
Author(s):  
J.Z. Liang
Keyword(s):  
Polymer Composites ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Interfacial Structure ◽  
Interlayer Thickness ◽  
Filled Polymer ◽  
Mechanical And Physical Properties ◽  
The Relationship ◽  
Good Agreement

The structure of the interlayer between matrix and inclusions affect directly the mechanical and physical properties of inorganic particulate-filled polymer composites. The interlayer thickness is an important parameter for characterization of the interfacial structure. The effects of the interlayer between the filler particles and matrix on the mechanical properties of polymer composites were analyzed in this article. On the basis of a simplified model of interlayer, an expression for estimating the interlayer thickness ([Formula: see text]) was proposed. In addition, the relationship between the [Formula: see text] and the particle size and its concentration was discussed. The results showed that the calculations of the [Formula: see text] and thickness/particle diameter ratio ([Formula: see text]) increased nonlinearly with an increase of the volume fraction of the inclusions. Moreover, the predictions of [Formula: see text] and the relevant data reported in literature were compared, and good agreement was found between them.

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