An experimental study of food melt rheology

The shear viscosity of commercial maize grits, potato powder and a low density polyethylene has been measured under a range of extrusion processing conditions using an extruder-fed slit die viscometer and a capillary rheometer. The results show the strong dependence of the viscosity of food melts on the processing history undergone during extrusion. To this end, the shear viscosity data for the food materials have been fitted to relationships including the effects of temperature, shear rate and moisture. The effect of the shear processing history on the viscosity has been represented by a power-law relationship with extruder screw speed.     

Linear and non-linear rheology of linear polydisperse polyethylene

Rheological techniques, size-exclusion chromatography, and molecular spectroscopy are the most widely used tools for describing polymer molecular structure in polyolefins. The detection of long-chain branching, and to some extent, its quantification, have been based on quantifying the deviation of polyethylene??s (PE) rheological behavior from that of a linear reference. Although metallocene-based PE has been extensively studied, linear polydisperse originating from Ziegler or Chromium-based catalysts are not often thoroughly considered, despite their high industrial importance. Within this work, we study the linear and non-linear rheology of a set of polydisperse PEs, for which the topological linearity is confirmed by GPC-MALLS measurements. Thus, we can safely quantify the effect of broad molecular weight distribution, high and ultra-high molecular weight fractions on rheological quantities and model parameters. Specifically, the zero-shear viscosity, ?? ₀ vs. M _w, relaxation spectra, phase lag vs. the complex modulus plot (van Gurp?CPalmen method) were applied and significant deviations from the ??rheologically linear?? behavior were observed, attributed only to M _w, M _z and polydispersity. Since the elongational viscosity was typical of linear PE, large-amplitude oscillatory shear and FT-Rheology were applied to quantify the non-linear rheological behavior. The latter was described by a single parameter, $Q=I_{3/1}/\gamma_0^2$ , which for linear polydisperse PE was correlated to the high molecular weight fraction and was constant over a broad range of applied Deborah numbers for the respective excitation frequencies. Since we need to correlate structural features such as broad MWD and HMW to polymer performance under processing conditions, we have to extend the analysis of linear rheological parameters, such as zero-shear viscosity, to non-linear parameters, e.g., the Q parameter quantified and used here.     

Extensional rheology of a shear-thickening cornstarch and water suspension

A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.     

An experimental study of food melt rheology. II. End pressure effects

A twin-screw extruder-fed slit die viscometer (SDV) and a piston capillary rheometer have been used to measure the end pressure losses of a low density polyethylene, maize grits and potato powder. The entrance and exit pressure losses have been measured as a function of extrusion conditions. The entrance pressure losses were found to be less than 10% of the total pressure drop in the SDV for LDPE and maize grits. For the potato material, this loss was found to be as large as 58%. The exit pressures for the potato were between 10–20% of the total pressure drop compared to negligible values for the maize and LDPE. Various approaches due to Bagley, Han and Cogswell were used to investigate the elastic properties of these materials.     

An experimental study of the effective thermal conductivity of a sheared suspension of rigid spheres

An experimental study was conducted to measure the effective thermal conductivity of a sheared suspension of rigid spherical particles. The objective was to verify the theoretical prediction of Leal (1973) for a dilute suspension undergoing shear at low particle Peclet number, and to extend the range of the experiments to conditions beyond the scope of the theory. Surprisingly, reasonable agreement with the theoretical prediction was observed even for suspensions of moderate concentrations (volume fraction ≤ 0.25) and higher Peclet numbers [Pe 0(1)]. The trend of the data, however, verifies the obvious fact that the theory does not completely describe the transport behavior at higher concentrations and Peclet numbers. The range of quantitative applicability of Leal's result is apparently only for Pe < 0.01 and < 0.01, but the changes in the effective thermal conductivity in this domain were too small to be measured in our apparatus.     

An experimental study of electrorheological fluid flow through a packed bed of glass beads

This paper shows that pressure drop-flow rate performance of an electrorheological (ER) fluid flowing through a packed bed of glass beads is consistent with a modified Ergun equation for yield stress flow through a packed bed. ER fluids are of scientific and engineering interest due to the sensitivity of their rheological properties on the applied electric field. As far as we know ER fluids have not been studied for flows through porous media. In this work a silica particle–silicone oil suspension is pumped through a rectangular packed bed of glass beads with applied electric fields. The silica particles are observed to form fibrous structures parallel to the electric field that stretch between the beads and extend between the electrodes. The pressure drop-flow rate performance agrees well with the expected performance calculated from a modified Ergun equation for a yield stress fluid flow through the packed bed with the viscosity and yield stress as functions of the applied electric field.     

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.     

Nonlinear rheology of a concentrated spherical silica suspension:

Time-dependent nonlinear flow behavior was investigated for a model hard-sphere suspension, a 50 wt% suspension of spherical silica particles (radius = 40 nm; effective volume fraction = 0.53) in a 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The suspension had two stress components, the Brownian stress ^B and the hydrodynamic stress ^H After start-up of flow at various shear rates , the viscosity growth function ₊ (t, ) was measured with time t until it reached the steady state. The viscosity decay function _– (t, ) was measured after cessation of flow from the steady as well as transient states. At low where the steady state viscosity ( ) exhibited the shear-thinning, the _– (t, ) and ⁺ (t, ) data were quantitatively described with a BKZ constitutive equation utilizing data for nonlinear relaxation moduli G (t, ). This result enabled us to attribute the thinning behavior to the decrease of the Brownian contribution ^B = ^B / (considered in the BKZ equation through damping of G (t, )). On the other hand, at high where ( ) exhibited the thickening, the BKZ prediction largely deviated from the ₊ (t, ) and ₊ (t, ) data, the latter obtained after cessation of steady flow. This result suggested that the thickening was due to an enhancement of the hydrodynamic contribution ^H = ^H / (not considered in the BKZ equation). However, when the flow was stopped at the transient state and only a small strain (<0.2) was applied, ^H was hardly enhanced and the _– (t, ) data agreed with the BKZ prediction. Correspondingly, the onset of thickening of ₊ (t, ) was characterized with a -insensitive strain ( 0.2). On the basis of these results, the enhancement of ^H (thickening mechanism) was related to dynamic clustering of the particles that took place only when the strain applied through the fast flow was larger than a characteristic strain necessary for close approach/collision of the particles.     

An experimental study of a high-rise building model in tornado-like winds

An experimental study was conducted to quantify the characteristics of wake vortex and flow structures around a high-rise building model as well as the resultant wind loads (both forces and moments) acting on the test model in tornado-like winds. In addition to measuring wind loads acting on the tested high-rise building model using a high-sensitivity load cell, a digital Particle Image Velocimetry (PIV) system was used to conduct detailed flow field measurements to quantify the evolution of the unsteady vortex and turbulent flow structures around the test model in tornado-like winds. The measurement results revealed clearly that the evolution of the wake vortex and turbulent flow structures around the test model as well as the resultant wind loads induced by tornado-like winds were significantly different from those in conventional straight-line winds. The detailed flow field measurements were correlated with the wind load measurement data to elucidate the underlying physics to gain further insight into the flow-structure interactions between the tested high-rise building model and tornado-like vortex. The new findings derived from the present study could be used to provide more accurate prediction of wind damage potential to built environment with the ultimate goal of reducing life loss, injury casualty, and economic loss that results from tornados.     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

An experimental evaluation of the behaviour of mono and polydisperse polystyrenes in Cross-Slot flow

The behaviour of a number of mono and polydisperse polystyrenes are probed experimentally in complex extensional flow within a Cross-Slot geometry using flow-induced birefringence. Polystyrenes with similar molecular weight (M _w) and increasing polydispersity (PD) illustrated the effect of PD on the principal stress difference (PSD) pattern in extensional flow. Monodisperse materials exhibited only slight asymmetry at moderate flowrates, although increased asymmetry and cusping was observed at high flowrates. The response of monodisperse materials of different M _w at various flowrates is presented and characterised by Weissenberg numbers for both chain stretch and orientation using a theory for linear entangled polymers. The comparison of stress profiles against Weissenberg number for each process is used to determine whether the PSD pattern observed is independent of M _w and elucidate which relaxation mechanism is dominant in the flow regimes probed. For monodisperse materials, at equivalent chain orientation Weissenberg number (We _τd), different molecular weight materials were seen to exhibit similar steady state PSD patterns independent of We _τR (chain stretch We). Whilst no obvious critical Weissenberg number (We) was found for the onset of increased asymmetry and cusping, it was found to occur in the “orientating flow without chain stretch” regime.     

Random close packing and relative viscosity of multimodal suspensions

Multimodal suspensions, consisting of non-colloidal spherical particles and a Newtonian matrix, are considered. A new differential (or multi-scale mean field approach) model for the relative viscosity of multimodal suspensions has been developed. The problem of the random close packing fraction of the solid phase is also investigated. We suppose that the multimodal suspension has a dominant large particle composition and that the smaller particles are embedded in the empty space between the larger particles. The relative viscosity model can therefore be based on the theory of monomodal suspensions. Experimental data of Eveson are compared to the predictions given by using three different models of monomodal suspensions respectively. The Maron–Pierce approach appears to give the best agreement with Eveson’s experiments. However, due to experimental uncertainties, we recommend that the Mendoza and Santamaria-Holek (MSH) formula be adopted.     

A study of the glass transition temperature of asphalts and their viscosity

Summary The glass transition temperatures (T _g ) of asphalt samples of different origins and penetration grades were determined by differential scanning calorimetry (DSC-2). TheT _g values of samples originating from two sources decreased with increasing penetration whereas those of samples from a third source were identical at all values of penetration. Substituting theseT _g data and values of the universal as well as the optimized constantsC ₁ andC ₂ in the Williams-Landel-Ferry equation, viscosities were calculated for each of the samples and compared with the corresponding experimental results. The universal values forC ₁ andC ₂ yielded viscosities which were far removed from the experimental data while the optimized values produced much better results.

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Zusammenfassung Die GlasübergangstemperaturenT _g von Asphaltproben verschiedener Herkunft und Penetrationsgrade wurden mit einem Differentialkalorimeter (DSC-2) bestimmt. DieT _g -Werte von Proben aus zwei Quellen nahmen mit wachsendem Penetrationsgrad ab, wohingegen diese bei Proben aus einer dritten Quelle bei allen Penetrationsgraden gleich blieben. Durch Einsetzen dieserT _g -Daten in die Williams-Landel-Ferry-Gleichung wurden sowohl unter Verwendung von universellen als auch von optimierten Werten der KonstantenC ₁ undC ₂ die Viskositäten der verschiedenen Proben berechnet und mit den experimentell gefundenen Daten verglichen. Die universellen Werte ergaben Viskositäten, die große Unterschiede zu den gemessenen aufwiesen, während man bei Verwendung der optimierten Werte eine weitaus bessere Übereinstimmung erhielt.

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With 2 figures and 10 tables     

On the viscosity of a concentrated suspension of solid spheres

Explanations of the very high viscosities of concentrated suspensions of spheres based on the dissipation in squeezing flow between particles pairs are shown to be in error. The dissipation in pair interactions is always of the order of that generated by shearing motions, and this dissipation is of too low an order in concentration for single pair interactions to explain the observed viscosities.     

A smoothed particle hydrodynamics-based fluid model with a spatially dependent viscosity: application to flow of a suspension with a non-Newtonian fluid matrix

A smoothed particle hydrodynamics approach is utilized to model a non-Newtonian fluid with a spatially varying viscosity. In the limit of constant viscosity, this approach recovers an earlier model for Newtonian fluids of Español and Revenga (Phys Rev E 67:026705, 2003). Results are compared with numerical solutions of the general Navier–Strokes equation using the “regularized” Bingham model of Papanastasiou (J Rheol 31:385–404, 1987) that has a shear-rate-dependent viscosity. As an application of this model, the effect of having a non-Newtonian fluid matrix, with a shear-rate-dependent viscosity in a moderately dense suspension, is examined. Simulation results are then compared with experiments on mono-size silica spheres in a shear-thinning fluid and for sand in a calcium carbonate paste. Excellent agreement is found between simulation and experiment. These results indicate that measurements of the shear viscosity of simple shear-rate-dependent non-Newtonian fluids may be used in simulation to predict the viscosity of concentrated suspensions having the same matrix fluid.     

An experimental study of flow-induced fiber orientation and concentration distributions in a concentrated suspension flow through a slit channel containing a cylinder

Flow-induced fiber orientation and concentration distributions were measured in a concentrated fiber suspension (CFS) and a dilute one (DFS). The channel has a thin slit geometry containing a circular cylinder. In the previous work, many researchers have qualitatively studied fiber orientation and concentration distributions in injection-molded products of fiber-reinforced plastics. In the present work, however, they are quantitatively estimated by direct observation of fibers in the concentrated suspension flow. For the CFS, some fibers rotate in an expansion part between the channel wall and the circular cylinder, and the fiber orientation becomes almost random state. On the other hand, fibers are perfectly aligned along the flow direction owing to the elongational flow near the centerline downstream of the cylinder. The fiber concentration has a flat distribution except near the channel wall and the centerline. For the DFS a minimum in the fiber concentration distribution was clearly observed on the centerline, and two peaks beside the centerline and near the channel wall. This characteristic distribution is caused by the fiber-wall and fiber-cylinder interactions. It is found that the obstacle such as the circular cylinder in the channel significantly affects the fiber orientation downstream of the obstacle for the CFD, while it affects the fiber concentration distribution for the DFS.