Rheology of physically evolving suspensions

The objective of this work was to investigate the modeling of the whole dynamic rheological behavior of physically evolving suspensions (e.g., polyvinyl chloride plastisols). The evolutions of the complex viscosity with time (isothermal) and with temperature (non-isothermal) were analyzed. To understand the physically involved phenomena, the determination of relationships between the solid volume fraction evolution and the rheological behavior was investigated. Firstly, the evolution of the volume fraction in relation with the variation of radii particle suspensions using a modified Avrami equation was determined. Actually, the rheological study of this physically evolving system is far too complicated due to the many factors involved in the evolving process. Consequently, a phenomenological law using Carreau–Yasuda equation and percolation laws combined with the evolution of the solid volume fraction is investigated to obtain the modeling of the whole dynamic rheological behavior at any frequency and temperature.     

Dehnviskosität von Kautschukmischungen

It is shown that the extensional viscosity measured by uniaxial stretch may give useful information as to the processability of rubber compounds. A simple apparatus was constructed to measure this rheological property at constant rate of strain. The influence of rubber type, filler, aging, mastication and degree of crosslinking on the reduced stress is represented by diagrams. No steady-state extensional viscosity was obtained for highly filled rubber compounds. It was found that the flow behaviour of rubber compounds can be better characterized with an extensional rheometer than with a high-pressure capillary rheometer.

     

Small-diameter parallel plate rheometry: a simple technique for measuring rheological properties of glass-forming liquids in shear

The rheological characterization of glass-forming liquids is challenging due to their extreme temperature dependence and high stiffness at low temperatures. This study focuses on the special precautions that need to be taken to accommodate high sample stiffness and torsional instrument compliance in shear rheological experiments. The measurement errors due to the instrument compliance can be avoided by employing small-diameter parallel plate (SDPP) rheometry in combination of numerical instrument compliance corrections. Measurements of that type demonstrate that accurate and reliable rheological data can be obtained by SDPP rheometry despite unusually small diameter-to-gap (d/h) ratios. Specimen preparation for SDPP requires special attention, but then experiments show excellent repeatability. Advantages and some current applications of SDPP rheometry are briefly reviewed. SDPP rheometry is seen as a simple and versatile way to measure rheological properties of glass-forming liquids especially near their glass transition temperature.     

Determination of flow activation energy at viscosity maximum for spherical and wormlike micelles of different lengths and flexibility

Steady shear rheological measurements were carried out on aqueous solutions containing 15 mM cetyltrimethylammonium bromide (CTABr) and a constant value of [MX] and temperature for MX = 2,3-; 2,4-; 2,5-; 2,6-; 3,4-; and 3,5-Cl₂BzNa with Bz^?representing C₆H₃CO_2?. Plots of zero shear viscosity (η ₀) vs. [MX] at 35 °C and 15 mM CTABr show the presence of single maximum and double maxima for MX = 2,3- and 3,5-Cl₂BzNa, respectively. Turbidity data (absorbance at 600 nm vs. [MX]) coupled with η ₀vs. [MX] data at 35 °C reveal indirectly the presence of vesicles along with wormlike micelles (WM) at MX / CTABr > 0. 7 for MX = 3,5-Cl₂BzNa. Temperature dependence of η ₀in the vicinity of the viscosity maximum shows nonlinear and linear Arrhenius behavior, within the temperature range of 20–55 °C, for MX = 2,3-; 2,4-; 2,5-; 3,4-; and 3,5-Cl₂BzNa, respectively. The values of η ₀, $\dot {\gamma }_{\text {cr}} $ (critical shear rate), and flow activation energy correlate with CTABr micellar binding constants of counterions.     

Temperature dependence of the viscosity of highly starch-filled poly(hydroxy ester ether) biodegradable composites

 The temperature dependence of the viscosity of starch-filled poly(hydroxy ester ether) (PHEE) biodegradable composites was analyzed using Arrhenius and WLF equations. Corn starch/PHEE materials were extruded using a twin screw extruder with starch volume fractions from 0.27 to 0.66. Dynamic strain sweep measurements were carried out at 10 rad/s at six different temperatures from 100 °C to 150 °C. Both Arrhenius and WLF equations model equally well the temperature effect on viscosity of PHEE and starch/PHEE composites with starch volume fractions up to 0.36. Arrhenius equation with stress correction describes the stress dependence of viscosity of starch/PHEE composites with higher starch volume fractions. The activation energy using both Arrhenius equation and Arrhenius equation with stress correction is 62.7 kJ/mol for pure PHEE and starch/PHEE composites. Received: 10 September 1999 Accepted: 27 March 2000     

Passive Scalar Transport in a Turbulent Cylinder Wake in the Presence of a Downstream Cylinder

This work aims to investigate how the presence of a downstream cylinder affects the passive scalar transport in a cylinder wake. The wake was generated by two tandem brass circular cylinders of the same diameter (d). The cylinder centre-to-centre spacing L/d was 1.3, 2.5 and 4.0, respectively, covering the three typical flow regimes of this flow. The upstream cylinder was slightly heated. Measurements were conducted at x/d= 10 and Re (≡ dU _∞/ν, where U _∞ is the free-stream velocity and ν is the kinematic viscosity of fluid) = 7000. A three-wire probe consisting of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations, while an X-wire provided a phase reference. The phase-averaged velocity vectors and vorticity display single vortex street behind the downstream cylinder, irrespective of the flow regimes. However, the detailed flow structure exhibits strong dependence on L/d in terms of the Strouhal number, the vortex strength and its downstream evolution. This naturally affects passive scalar transport. The coherent and incoherent heat flux vectors show significant variation for different L/d.     

Localisation of optimal perturbations in variable viscosity channel flow

We discuss how a variable fluid viscosity affects the nonmodal stability characteristics of the pressure driven flow between two parallel walls maintained at different temperatures. In this work, we specify the fluid viscosity to be a function of the fluid temperature. We employ an Arrhenius model to model the viscosity of water, and Sutherland’s law to model the viscosity of air. We impose a stable density stratification, and find that strong density stratification can suppress optimal transient growth regardless of how strong the viscosity variation is. Some studies have been inclined to neglect viscosity stratification, since the changes in levels of optimal growth, when compared to the uniform viscosity case, are often not too significant. In this article, we show significant localisation of optimal perturbation energy in the less viscous region, a feature that is not observed in uniform viscosity flows. This can have a bearing on the route to turbulence in these systems.     

Diffusionally assisted grain-boundary sliding and viscoelasticity of polycrystals

Motivated by recent attenuation experiments on finely grained samples, we reanalyse the Raj-Ashby model of grain-boundary sliding. Two linearly elastic layers having finite thickness and identical elastic constants are separated by an interface (grain boundary) whose location is a given periodic function of position. Dissipation is confined to that interfacial region. It is caused by two mechanisms: a slip (boundary sliding) viscosity, and grain-boundary diffusion, with corresponding Maxwell relaxation times t_v and t_d. Owing to the assumption of a given, time-independent interface, the resulting boundary-value problem (b.v.p.) is linear and time-separable. The response to time-periodic forcing depends on angular frequency ω, on the ratio M=t_v/t_d of Maxwell times, and on the characteristic interface slope. The b.v.p. is solved using a perturbation method valid for small slopes. To relate features of the mechanical loss spectrum previously studied in isolation, we first discuss the solution as a function of M. Motivated by experiments, we then emphasize the case M?1 in which the relaxation times are widely separated. The loss spectrum then always has two major features: a frequency band 1?ωt_d?M^-1 within which the loss varies relatively weakly with ω; and a loss maximum at ωt_d∼M^-1 due to the slip viscosity. If corners on the interface are sufficiently rounded, those two universal features are separated by a third feature: between them, there is a strong minimum whose location is (entirely) independent of slip viscosity. The existence of that minimum has not previously been reported. These features are likely to occur even in solutions for finite interface slopes, because they are a consequence of the separation of timescales. The precise form of the spectrum in the weakly varying band must, however, be slope-dependent because it is controlled by stress singularities occurring at corners, and the strength of those singularities depends on the angle subtended by the corner.     

Mean flow characteristics of a 3D turbulent wall jet over an isothermal and an insulating flat surface

An experimental study was carried out on the mean aerodynamic and heat-exchange characteristics of a weaklyheated air jet flowing over an isothermal and an insulating flat surface. The jet issued from a contracting profiled rectangular nozzle (39×22 m² outlet) at 30 m/sec velocity (Re _d =~5.5×10⁴) and incidence angle α₀, π/12, π/6, π/4. It was established that as α₀ increases, so do the decay rates of the axial velocity and temperature along the jet axis as well as the jet width, while the jet thickness decreases. Parallel examination of an in sulating and an isothermal surface permitted separation of the heat-exchange process between the jet and the surrounding medium, from that between the jet and the wall surface-with the conclusion tha tin the isothermal case, the exchange with the surface intensifies as α₀ increases.     

Linear viscoelastic models: Part IV. From molecular dynamics to temperature and viscoelastic relations using control theory

Viscoelasticity and temperature dependences are explained using molecular dynamics and control theory. We have previously (Borg and Pääkkönen, 2009 [1], [2], [3]) applied control theory to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD), and here these topics are discussed more generally. In this paper we show the direct simple relation to molecular dynamics using structural models comprising dumb-bells (Bird et al., 1987 [4]) with internal viscosity and elasticity in a statistical tube. The dumb-bell model is used to obtain the linear relation to the elasticity P′ value of function P′(ω) and the relation to the viscosity P″ value of function P″(ω) from chain friction. The applied principle is also valid for the relaxation modulus or shear viscosity. A new principle is presented for obtaining absolute values such as zero viscosity by modelling, which is first used to obtain absolute values for a target point at a high rate for unentangled chains (since close relaxed states of chain topology are much more complicated). An analytical model for the temperature dependency of viscoelastic flows is presented, which is many times more accurate than WLF or Arrhenius equations. Control theory and variations of tube diameter as a function of temperature gives linear relation between chain dynamics and viscoelastic properties. New compact formulas are presented to simultaneously model different polymer flows and temperatures. We have also found that the MWDs computed from the relaxation modulus or complex and the shear viscosity are not temperature sensitive, in contrast to what time–temperature superposition (TTS) suggests, although absolute viscoelastic values make them appear very temperature-dependent. TTS is verified for thermorheologically simple materials, and the reasons for it not holding are explained.     

Dynamic rheological analysis of the gelation behaviour of waxy crude oils

In this work we have characterised the viscoelastic behaviour of paraffin crystals in three different complex crude oils, close to the gelation threshold and after curing the gels under quiescent isothermal conditions, by means of oscillatory shear measurements. An increase in gelation temperature is observed with increasing oils molecular weight. The interactions between wax crystals and the formation of the space-filling network of interlocking wax crystals are thus facilitated by the presence of paraffins with higher molecular weight. The apparent gelation time, obtained from isothermal curing experiments, decreases as the curing temperature was decreased, and it is highly temperature-dependent.The presence and the importance of the ageing of the wax were established under isothermal conditions. It must result from a coarsening of the crystallites presents in the oil and it is, more important, close to the gel point where its full development is very slow taking several days to occur. After ageing the gels, the connective domains or junction zones linking the crystal arrays fail when relatively small strains are applied to the system and the mechanical spectra of the gels reveal an imperfect elastic network, typical rheological characteristics of a particle gel. Despite the compositional differences among the samples, the similarity of their mechanical behaviour is quite remarkable indicating that in all cases the gel-like organisation of the waxy material results from the formation of identical structures in the different oils, which is related not only to the wax content but also to the presence of other material that may reduce the crystallinity of the structure.The low fractal dimensionality obtained indicates elongated substructures. These results, together with the very high elastic modulus obtained at low volume fractions of crystallised material, are indicative of network structures with high degree of porosity: a lattice of wax crystals with large spaces among them filled by the oil and non-precipitated material.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

磨合过程对流体润滑性能影响的数值分析数学模型

建立了非牛顿流体热弹流润滑数学模型,对重载条件下磨合过程进行数值分析,在考虑具有粘塑性本构的非牛顿流体时,采用了高效粘度法对建立的方程进行了解算。结果表明,热解的摩擦系数明显低于等温解的摩擦系数,当进一步考虑流体的非牛顿效应时,不仅温升的结果更为符合实际,摩擦系数也更接近试验结果。     

Viscoelastic properties of a silicone resin during crosslinking

Viscoelastic properties of a silicone resin crosslinked at various extents were characterised by means of rheology. The influence of temperature on the viscoelastic properties of the material as-delivered and in a state pre-crosslinked approximately to the gel point has been investigated by dynamic-mechanical measurements. While the glass transition temperature is increased by the crosslinking, no changes of the free volume fraction at T _g and its thermal expansion coefficient were observed. Taking the different glass transition temperatures into account, it could be shown that the corresponding WLF-parameters are the same. The molar mass and, hence, the viscosity of the material can be increased by a heat treatment. The dependence of the zero shear-rate viscosity on the weight average molar mass indicates that the existence of entanglements of the polymer molecules is not very probable.     

Influence of rheological properties of bitumen emulsions on the performance of surface dressing systems

Three bitumen emulsions, used in road surface dressing construction, one conventional and two polymer modified, have been tested in a CarriMed rheometer to determine their rheological properties G ^* and . These properties were determined over a temperature range and curing time conditions that resemble those experienced in-situ upon laying. A tensile loading test called the Pull-Off Test was developed to determine the adhesive strength of surface dressing systems and was used to study the influence of temperature and curing time on the strength development of dressing systems containing the three emulsions in question. To establish reliability criteria for the developed test, its parameters were correlated with the G ^* values of the emulsions evaluated under similar temperature and curing time conditions.     

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.     

Rheological properties of lightly crosslinked carboxy copolymers in aqueous solutions

The rheological properties of a series of lightly crosslinked carboxy copolymers in aqueous solutions have been evaluated in steady shear and dynamic oscillatory modes. Viscosity profiles and the behavior of storage modulus are related to the chemical composition of the copolymers and their crosslinking density. A maximum in viscosity and in storage modulus which depends on the type of crosslinking agent used is explained by a combination of a chain entanglement mechanism and a closely-packed spheres model. The recovery of viscosity and storage modulus after shearing is very fast and is related to the very fast rearrangement of the microgel structure as a function of time.     

Meltblown fibers: Influence of viscosity and elasticity on diameter distribution

Both melt viscosity (η_o) and elasticity (correlated here with the longest melt relaxation time λ₁) were found to control the diameter distribution of meltblown fibers. Fibers were formed by melt blowing binary polystyrene (PS) blends containing widely differing component molecular weights using a custom-built laboratory apparatus. Varying the concentration and molecular weight of a high molecular weight PS provided independent control over η_o and λ₁. These rheological parameters influence the average diameter (d_av) and the distribution of diameters (coefficient of variation, CV) of meltblown fibers in different ways. Increasing η_o leads to an increase in d_av but has little impact on CV. On the other hand, increasing λ₁ beyond a threshold value reduces CV while simultaneously increasing d_av. A one-dimensional slender-jet theoretical model with both upper convected Maxwell and Phan–Thien and Tanner constitutive equations was developed to investigate the influence of viscoelasticity and processing parameters on the properties of meltblown fibers. This model predicts a strong dependence of fiber diameter on the air shear stress and variations in fiber diameter with viscoelasticity that are in qualitative agreement with the experimental results. We believe these results suggest that carefully controlling the viscoelastic profile of polymers used in melt blowing is a viable approach for producing nanofibers with narrow fiber diameter distributions using current commercial equipment.     

Rheology of crosslinking poly vinyl alcohol systems during film formation and gelation

Gelation of crosslinking polymers, with ionic groups, is of interest in membrane processing of these materials. The gelation of polyvinyl alcohol in the presence of an ionic crosslinker, sulfosuccinic acid, was monitored through rheological measurements. The evolution of rheological material functions during film formation, which involves solvent evaporation and crosslinking, was observed at different polymer and crosslinker concentrations. Relative effect of water evaporation leading to physical gelation and the chemical crosslinking was examined. To understand the effect of crosslinker type, the rheology of nonionic crosslinker, glutaraldehyde was also examined. The gel points as well as network parameters for these covalent networking systems were different and depended on crosslinker type and polymer/crosslinker concentrations. However, qualitative evolution of rheological behavior during film formation was largely similar, demonstrating the dominating effect of solvent evaporation. Crosslinking in the absence of solvent evaporation was examined at different temperatures. It can be concluded that similar mechanism was involved, independent of temperature, in the temperature range of interest. The effect of crosslinker concentration on evolution of rheological properties near gelation was insignificant for ionic crosslinker though marginally significant for nonionic crosslinker.     

Numerical investigation of pyrolysis of a Loy Yang coal in a lab-scale furnace at elevated pressures

A computational fluid dynamics (CFD) model of the pyrolysis of a Loy Yang low-rank coal in a pressurised drop tube furnace (pdtf) was undertaken evaluating Arrhenius reaction rate constants. The paper also presents predictions of an isothermal flow through the drop tube furnace. In this study, a pdtf reactor operated at pressures up to 15 bar and at a temperature of 1,173 K with particle heating rates of approximately 10⁵ K s^?1 was used. The CFD model consists of two geometrical sections; flow straightner and injector. The single reaction and two competing reaction models were employed for this numerical investigation of the pyrolysis process. The results are validated against the available experimental data in terms of velocity profiles for the drop tube furnace and the particle mass loss versus particle residence times. The isothermal flow results showed reasonable agreement with the available experimental data at different locations from the injector tip. The predicted results of both the single reaction and competing reaction modes showed slightly different results. In addition, several reaction rate constants were tested and validated against the available experimental data. The most accurate results were being Badzioch and Hawksley (Ind Eng Chem Process Des Dev 9:521–530, 1970) with a single reaction model and Ubhayakar et al. (Symp (Int) Combust 16:427–436, 1977) for two competing reactions. These numerical results can provide useful information towards future modelling of the behaviour of Loy Yang coal in a full scale tangentially-fired furnace.