Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
124
result(s) for
"Normal stress difference"
Sort by:
Assessing the practical utility of the hole-pressure method for the in-line rheological characterization of polymer melts
The most promising method capable of providing accurate measurements of the first and second normal-stress differences in shear flows at shear rates typical of polymer processing is the so-called hole-pressure method, but its use has not been as widespread as would be expected, namely due to the experimental difficulties associated with performing such experiments accurately. In this work, we use a small-scale modular slit die to assess the practical utility of the method for in-line monitoring of polymer melt flow. We provide a quantitative analysis of intrinsic error sources and use state-of-the-art data acquisition tools to minimize errors associated with pressure transducers. Our results demonstrate that the method can be used to accurately measure the viscosity and first normal-stress difference in melts but probably not the second normal-stress difference because the intrinsic errors are too high, even when the influence of all the potential error sources is minimized or eliminated.
Journal Article
The normal stress behaviour of suspensions with viscoelastic matrix fluids
We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented.
Journal Article
A shear rheometer for measuring shear stress and both normal stress differences in polymer melts simultaneously: the MTR 25
The MTR 25 is a multitask rheometer (for shear and squeeze flow) with 25 kg of normal force and a partitioned plate. Torque and normal force are measured at both, the inner disk and the outer ring of the plate. The first and second normal stress differences can be determined from a single test. The axial stiffness is high (10
7
N/m) by using rigid springs and strain gauges for the load cell. Monodisperse polystyrene (
M
w
= 206 kg/mol, 180°C) has been sheared in the range from 0.05 to 47 s
− 1
. The viscosity and first normal stress difference are highly reproducible. The second normal stress difference scatters and mirrors the instability at the rim. A critical comparison is made between the MTR 25 method and the single transducer evaluation method (RMS 800 method, Schweizer, Rheol Acta 41:337–344,
2002
): Both yield excellent and coinciding viscosity and first normal stress difference data. The RMS 800 method gives more stable second normal stress difference data, since the normal force from the outer ring, which is influenced by edge fracture, is not used. Data for the RMS 800 method can be acquired on the MTR 25. The high normal force capacity permits larger samples and higher shear rates than on the RMS 800.
Journal Article
Measurement of the first and second normal stress differences in a polystyrene melt with a cone and partitioned plate tool
Step shear rate experiments in the range of (0.14
Journal Article
Comparison of shear viscosity and normal stress measurements by rotational and on-line slit rheometers with tube model predictions
In-extruder measurements of shear viscosity and normal stresses are important as these measurement techniques allow determining the rheological state of the polymer melt at processing conditions up to high shear rates. However, validation of viscosity and normal stress data obtained by in-line slit rheometers at high shear rates is difficult due to a lack of overlap of the in-line data and the off-line measurements by rotational rheometers limited to lower shear rates. Here, shear viscosity and normal stress data measured in-line at large shear rates during extrusion and off-line at low shear rates are compared to predictions of the Doi-Edwards model and the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model using linear-viscoelastic off-line small amplitude oscillating shear data of two polystyrenes and a low-density polyethylene as input parameters. For polystyrene, the results of this investigation do not only validate the experimental data obtained by rotational as well as slit-die rheometry, but also demonstrate the agreement between experiments and models up to very high shear rates, which were not experimentally accessible earlier. The low-density polyethylene shows a more complex behaviour, which follows the HMMSF model at low shear rates, but approaches the Doi-Edwards model at high shear rates.
Journal Article
Measuring and assessing first and second normal stress differences of polymeric fluids with a modular cone-partitioned plate geometry
We propose a simple, robust method to measure both the first and second normal stress differences of polymers, hence obtaining the full set of viscometric material functions in nonlinear shear flow. The method is based on the use of a modular cone-partitioned plate (CPP) setup with two different diameters of the inner plate, mounted on a rotational strain-controlled rheometer. The use of CPP allows extending the measured range of shear rates without edge fracture problems. The main advantage of such a protocol is that it overcomes limitations of previous approaches based on CPP (moderate temperatures not exceeding 120 °C, multiple measurements of samples with different volume) and yields data over a wide temperature range by performing a two-step measurement on two different samples with the same volume. The method was tested with two entangled polystyrene solutions at elevated temperatures, and the results were favorably compared with both the limited literature data on the second normal stress difference and the predictions obtained with a recent tube-based model of entangled polymers accounting for shear flow-induced molecular tumbling. Limitations and possible improvements of the proposed simple experimental protocol are also discussed.
Graphical abstract
The effects of edge fracture in start-up shear experiments can be circumvented with the use of a cone-partitioned plate (CPP) geometry. Such a device consists of an inner measuring plate surrounded by an outer nonmeasuring corona. The radius of the sample exceeds that of the measuring plate so that the measured volume is not affected by edge instability. However, the measured first normal stress difference is an apparent one (
N
app,1
), owing to the contribution of the nonmeasured part of the sample. The figure depicts a schematic design of a modular CPP geometry. Such a fixture is built in a way that the inner tool and the outer partition can be easily replaced, in order to have different measuring diameters (i.e., 6 and 10 mm). From the corresponding signals of the
N
app,1
, the effective first and second normal stress differences can be calculated.
Journal Article
Anisotropic swim stress in active matter with nematic order
Active Brownian particles (ABPs) transmit a swim pressure swim = n ζ D swim to the container boundaries, where ζ is the drag coefficient, Dswim is the swim diffusivity and n is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress swim = − n ζ D swim , which is related to the anisotropic swim diffusivity D swim . We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems. The anisotropy, defined as the ratio of the maximum to the minimum of the three principal stresses, is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure swim = − ( swim n ) n on a wall with normal vector n , and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components-the normal stress difference-generates a net flow of ABPs along the wall, which is a generic property of active matter systems.
Journal Article
Flow and rheology of frictional elongated grains
The rheology of a 3-dimensional granular system consisting of frictional elongated particles was investigated by means of discrete element model calculations. A homogenous shear flow of frictional spherocyliders was simulated, and a number of rheological quantities were calculated. In the framework of the μ(I) rheology, the effective friction was found to be a non-monotonic function of the aspect ratio for interparticle friction coefficient μp ≲ 0.4, while it was an increasing function for larger μp. We reveal the microscopic origin of this peculiar non-monotonic behaviour. We show the non-trivial dependence of the velocity fluctuations on the dissipation regime, and trace back the behaviour of the normal stress differences to particle-level quantities.
Journal Article
Prediction of Normal Stress Difference and Relaxation Modulus of Polylactic Acid/Calcium Phosphate Nanocomposites
New research is being conducted to better understand the relationship between mechanical characteristics and strain rate in polymeric materials. In this study, calcium phosphate nanoparticles were incorporated into polylactic acid using ultrasonic vibration-assisted melt mixing, and the samples were cast under vacuum. The normal stress difference and relaxation modulus for the Polylactic acid/Calcium phosphate nanocomposites were calculated using the experimentally measured value of viscoelastic properties. The dependency of normal stress difference and relaxation modulus on different parameters was also shown for the validation of the expressions. The first normal stress difference and relaxation modulus were predicted based on the frequency dependence viscoelastic characteristics of polylactic acid/calcium phosphate nanocomposites. The first normal stress difference increases with shear rate and reaches a plateau at lower shear rates. The value of the first normal stress differential increases with calcium phosphate nanoparticle concentration, demonstrating that calcium phosphate promotes elasticity. The relaxation modulus falls as shear rates increase while increasing with calcium phosphate nanoparticle concentration. However, the incorporation of the calcium phosphate nanoparticle to polylactic acid increases the relaxation modulus because of polymer-filler interaction.
Journal Article
A technical note on large normal-stress differences observed in a novel self-assembling functionalized dipeptide surfactant solution
A number of functionalised dipeptides self-assemble in water under specific conditions to give micellar aggregates. The micellar aggregates formed depend on the exact molecular structure and are important to understand as they control the properties both of the micellar phase and also of the gel phase which can be formed from these precursor solutions. Here, we investigate the rheological properties of a functionalised dipeptide which behaves as a surfactant at high pH. This solution has been shown previously to exhibit very “stringy” behaviour, and this has previously been characterised using capillary breakup extensional rheometry (CaBER). In the current technical note, we extend the rheological characterisation of an exemplar precursor solution via small-amplitude oscillatory shear and steady shear. Using a cone-and-plate geometry and a dedicated protocol, we can measure the first normal-stress difference
N
1
and using a parallel-plate geometry to also measure (
N
1
-
N
2
), subsequently determining the second normal-stress difference
N
2
. In so doing, we confirm that these systems are highly elastic, e.g. for shear rates greater than ~ 30 s
−1
, corresponding to a Weissenberg number based on the longest relaxation time ~ 330,
N
1
> 10τ where τ is the shear stress, and also, we find that
N
2
can be significant, is negative and approximately equal in magnitude to ~ 0.36 ± 0.05
N
1
. Significant uncertainties associated with the normal-stress difference data led to us using a range of different rheometers (and geometries) and highlight the issues with determining
N
2
using this two-measurement approach. Despite these uncertainties, the non-negligible value of the second-normal stress difference is demonstrated for these fluids.
Journal Article