The rheological characterisation of bread dough using capillary rheometry

An Australian hard wheat flour–water dough has been characterised using parallel plate and capillary rheometers over an extensive range of apparent shear rates (10^− 3–10³ s^− 1) relevant to process conditions. Torsional measurements showed that the shear viscosity of the dough increased with strain to a maximum value and then decreased, suggesting a breakdown of the dough structure. Both torsional and capillary experiments revealed the shear-thinning behaviour of the dough. The wall slip phenomenon in capillary rheometry was investigated and found to be diameter dependent and occurred at a critical shear stress of approximately 5–10 kPa. A two-regime power law behaviour was observed, with the power law index approximately 0.3 in the low shear rate range increasing to 0.67 in the high shear rate range. Pressure fluctuation was observed in the capillary data and increased with shear rate, in particular, at shear rates approaching 10⁴ s^− 1. The results demonstrate that capillary rheometry is a viable means of rheologically testing dough at high shear rates provided pressure fluctuation is carefully monitored and capillary rheometry corrections, including wall slip, are accounted for.     

Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Miniaturized Compression Test at Very High Strain Rates by Direct Impact

A modified miniaturized version of the Direct Impact Compression Test (DICT) technique is described in this paper. The method permits determination of the rate-sensitive plastic properties of materials up to strain rate ∼10⁵ s⁻¹. Miniaturization of the experimental setup with specimen dimensions: diameter d _S = 2.0 mm and thickness l _S = 1.0 mm, Hopkinson bar diameter 5.2 mm, with application of a novel optical arrangement in measurement of specimen strain, makes possible compression tests at strain rates from ∼10³ s⁻¹ to ∼10⁵ s⁻¹. In order to estimate the rate sensitivity of a low-alloy construction steel, quasi-static, Split Hopkinson Pressure Bar (SHPB) and DICT tests have been performed at room temperature within the rate spectrum ranging from 5*10⁻⁴ s⁻¹ to 5*10⁴ s⁻¹. Adiabatic heating and friction effects are analyzed and the final true stress versus true strain curves at different strain rates are corrected to a constant temperature and zero friction. The results have been analyzed in the form of true stress versus the logarithm of strain rate and they show two regions of a constant rate sensitivity : relatively low up to the strain rate threshold ∼50 s⁻¹, and relatively high above the threshold, up to strain rate ∼4.5*10⁴ s⁻¹.     

Three views of viscoelasticity for Cox–Merz materials

A slight rearrangement of the classical Cox and Merz rule suggests that the shear stress value of steady shear flow, , and complex modulus value of small amplitude oscillatory shear, G^∗(ω) = (G^′2 + G^″2)^1/2, are equivalent in many respects. Small changes of material structure, which express themselves most sensitively in the steady shear stress, τ, show equally pronounced in linear viscoelastic data when plotting these with G^∗ as one of the variables. An example is given to demonstrate this phenomenon: viscosity data that cover about three decades in frequency get stretched out over about nine decades in G^∗ while maintaining steep gradients in a transition region. This suggests a more effective way of exploiting the Cox–Merz rule when it is valid and exploring reasons for lack of validity when it is not. The τ −G^∗ equivalence could also further the understanding of the steady shear normal stress function as proposed by Laun.     

Small and large strain rheology of wheat gluten

 The rheological properties of wheat gluten were studied under both small and large deformation and compared with those of the parent flours. The limiting strain of linear viscoelastic behaviour of gluten doughs, 3 × 10⁻², was an order of magnitude larger than that of the flour doughs, 10⁻³. The role of starch in the lower limiting strain of flour doughs was indicated by the exponential decrease in the limiting strain of gluten-starch mixtures with greater quantities of starch. Large strain measurements showed gluten doughs possessed greater shear and elongational viscosities than flour doughs and these differences were greatest at lower shear and elongation rates (0.01 and 0.1 s⁻¹). The larger viscosities of flour and gluten doughs at the low strain rates help to stabilise and prevent the collapse of gas bubbles during bread fermentation and baking. Increasing starch levels in gluten-starch mixtures, at either constant or optimal water levels, lowered the elongational viscosity. Dynamic measurements were, however, more sensitive to the level of water added to the gluten-starch mixtures. The storage modulus decreased with increasing starch levels when constant water levels were used to prepare the mixtures, but when optimal water levels were used the storage modulus increased. Gluten and starch are major contributors to the large and small strain rheological properties of flour doughs; however, gluten-starch mixtures were unable to duplicate exactly the rheological properties of flour doughs, indicating that other flour components such as pentosans, lipids and water soluble proteins also influence dough rheology. Received: 20 March 2001 Accepted: 11 July 2001     

A shear-compression specimen for large strain testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s⁻¹), up to very high strain rates (2×10⁴s⁻¹ in the present case).     

Experimental Investigation of Strain Rate Dependence of Nanocrystalline Pt Films

A new microscale uniaxial tension experimental method was developed to investigate the strain rate dependent mechanical behavior of freestanding metallic thin films for MEMS. The method allows for highly repeatable mechanical testing of thin films for over eight orders of magnitude of strain rate. Its repeatability stems from the direct and full-field displacement measurements obtained from optical images with at least 25 nm displacement resolution. The method is demonstrated with micron-scale, 400-nm thick, freestanding nanocrystalline Pt specimens, with 25 nm grain size. The experiments were conducted in situ under an optical microscope, equipped with a digital high-speed camera, in the nominal strain rate range 10⁻⁶–10¹ s⁻¹. Full field displacements were computed by digital image correlation using a random speckle pattern generated onto the freestanding specimens. The elastic modulus of Pt, E = 182 ± 8 GPa, derived from uniaxial stress vs. strain curves, was independent of strain rate, while its Poisson’s ratio was v = 0.41 ± 0.01. Although the nanocrystalline Pt films had the elastic properties of bulk Pt, their inelastic property values were much higher than bulk and were rate-sensitive over the range of loading rates. For example, the elastic limit increased by more than 110% with increasing strain rate, and was 2–5 times higher than bulk Pt reaching 1.37 GPa at 10¹ s⁻¹.     

The motion of long bubbles through viscoelastic fluids in capillary tubes

The penetration of long gas bubble through a viscoelastic fluid in a capillary tube has been studied in order to investigate the influence of viscoelastic material properties on the hydrodynamic coating thickness and local flow kinematics. Experiments are conducted for three tailored ideal elastic (Boger) fluids, designed to exhibit similar steady shear properties but substantially different elastic material functions. This allows for the isolation of elastic and extensional material effects on the bubble penetration process. The shear and extensional rheology of the fluid is characterized using rotational and filament stretching rheometers (FSR). The fluids are designed such that the steady-state extensional viscosity measured by the FSR at a Deborah number (De) greater than 1 differs over three orders of magnitude (Trouton ratio = 10³–10⁶). The experiment set up to measure the hydrodynamic coating thickness is designed to provide accurate data over a wide range of capillary numbers (0.01 < Ca < 100). The results indicate that the coating thickness in this process increases with an increase in the extensionally thickening nature of the fluid. Experiments are also conducted using several different capillary tube diameters (0.1 < D < 1 cm), in order to compare responses at similar Ca but different flow De. Suitable scaling methods and nonlinear viscoelastic constitutive equations are explored to characterize the displacement process for polymeric fluids. Bubble tip shapes at different De are recorded using a CCD camera, and measured using an edge detection algorithm. The influence of the mixed flow field on the bubble tip shape is examined. Particle tracking velocimetry experiments are conducted to compare the influence of viscoelastic properties on the velocity field in the vicinity of the bubble tip. Local shear and extension rates are calculated in the vicinity of the bubble tip from the velocity data. The results provide quantitative information on the influence of elastic and extensional properties on the bubble penetration process in gas-assisted injection molding. The bubble shape and velocity field information provides a basis for evaluating the performance of constitutive equations in mixed flow. Received: 19 January 1999 Accepted: 30 June 1999     

The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

Recoverable deformation and morphology after uniaxial elongation of a polystyrene/linear low density polyethylene blend

The transient recoverable deformation ratio after melt elongation at various elongational rates and maximum elongations was investigated for pure polystyrene and for a 85 wt.% polystyrene/15 wt.% linear low density polyethylene (PS/LLDPE 85:15) blend at a temperature of 170 ^oC. The ratio p of the zero shear rate viscosity of LLDPE to that of PS is p = 0.059 ≈ 1:17. Retraction of the elongated LLDPE droplets back to spheres and end-pinching is observed during recovery. A simple additive rule is applied in order to extract the contribution of the recovery of the elongated droplets from the total recovery of the blend. In that way, the recoverable portion of the PS/LLDPE blend induced by the interfacial tension is determined and compared with the results of a theory based on an effective medium approximation. The effective medium approximation reproduces well the time scale of the experimental data. In addition, the trends that the recoverable deformation increases with elongational rate and maximum elongation are captured by the theoretical approach.     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

Rheology and birefringence of Fomblin YR at very high shear rates

The rheological and structural properties of perfluoropolyether (PFPE) lubricant films including viscosity, shear stress, and birefringence were measured at relatively low to extremely high shear rates using a rotational optical rheometer. The viscosity of various films with different thicknesses exhibit Newtonian behavior up to a shear rate 1 × 10⁴ s⁻¹, with a transition to shear-thinning behavior obvious at higher shear rates. Birefringence of these films was also measured for the first time, and these results indicate chain alignment with shear in the shear-thinning regime. The shear rate at which alignment occurs is similar to that of the onset of shear thinning. This correlation between chain alignment and shear thinning provides direct evidence that the ability of PFPEs to lubricate hard drives at high shear rates is a direct consequence of the ability of the applied shear field to align the molecules on a molecular level.     

Grafting of polyamide 6 on a styrene–acrylonitrile maleic anhydride terpolymer: melt rheology at the critical gel state

In this work, we studied the melt rheology of multigraft copolymers with a styrene–acrylonitrile maleic anhydride (SANMA) terpolymer backbone and randomly grafted polyamide 6 (PA 6) chains. The multi-grafted chains were formed by interfacial reactions between the maleic anhydride groups of SANMA and the amino end groups of PA 6 during melt blending. Because of the phase separation of SANMA and PA 6, the grafted SANMA backbones formed nearly circular domains which were embedded in the PA 6 melt with a diameter in the order of 20 to 40 nm. The linear viscoelastic behaviour of PA 6/SANMA blends at a sufficiently large SANMA concentration displayed the characteristics of the critical gel state, i.e. the power relations G′ ∝ G′′ ∝ ω ^0.5. In elongation, the PA 6/SANMA blend at the critical gel state showed a non-linear strain hardening behaviour already at a very small Hencky strain. In contrast to neat PA 6, the elasticity of the PA 6/SANMA blends was strongly pronounced, which was demonstrated by recovery experiments. Rheotens tests agreed with the linear viscoelastic shear oscillations and the measurements using the elongational rheometer RME. Increasing the SANMA concentration led to a larger melt strength and a reduced drawability. The occurrence of the critical gel state can be interpreted by the cooperative motion of molecules which develops between the grafted PA 6 chains of neighbouring micelle-like SANMA domains.     

Characterization of the flow properties of sodium carboxymethylcellulose via mechanical and optical techniques

Sodium carboxymethylcellulose (NaCMC) in solution represents a complex rheological system, since it forms aggregates and associations and hence higher-level structures and, depending on the synthesis, is only found in a molecularly dispersed form in exceptional cases. Rheo-mechanical investigations of the viscoelasticity showed that the Cox-Merz rule is not fulfilled. The aim was therefore to examine whether rheo-optics could be employed to provide more detailed conclusions about the parameters that influence the flow behavior of NaCMC than has hitherto been available with mechanical methods. The flow birefringence, Δn ^′, rises as the degree of polymerization increases, and exhibits the same dependence on molar mass as does the viscosity: Δn ^′∝M _w ^3.4. As the degree of polymerization increases while the shear rate remains constant, the polymer segments become more distinctly aligned in the direction of shear. Hence increasing the degree of polymerization also affects the solution structure, i.e. the interaction of the molecules with one another. The stress-optical rule only applies to a limited extent for this system. The stress-optical coefficient, C, is almost independent of the shear rate, but is strongly influenced by the concentration and attains a limiting value of 3 × 10⁻⁸ Pa⁻¹. C was determined for a polymer in dilute solution and the curve obtained also enabled transitions in the solution structure to be recognized. Received: 1 May 1998 Accepted: 5 October 1998     

Shear and elongational flow behavior of acrylic thickener solutions

We investigate the effect of hydrophobic aggregation in alkali-swellable acrylic thickener solutions on shear and extensional flow properties at technically relevant polymer concentrations using the commercial thickener Sterocoll FD as model system. Apparent molecular weight of aggregates in water is M _w  ≈ 10⁸ g/mol and decreases by more than an order of magnitude in ethanol. Zero shear viscosity η ₀ is low and shear thinning is weak compared to the high molecular weight of the aggregates. Linear viscoelastic relaxation is described by the Zimm theory up to frequencies of 10⁴ rad/s, demonstrating that no entanglements are present in these solutions. This is further supported by the concentration dependence of η ₀ and is attributed to strong association within the aggregates. Extensional flow behavior is characterized using the capillary break-up extensional rheometry technique including high-speed imaging. Solutions with ϕ ≥ 1% undergo uniform deformation and show pronounced strain hardening up to large Hencky strains. Elongational relaxation times are more than one order of magnitude lower than the longest shear relaxation times, suggesting that aggregates cannot withstand strong flows and do not contribute to the elongational viscosity.

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

Transient elongational viscosities of aqueous polyacrylamide solutions measured with an optical rheometer

An anionic polyacrylamide solution was characterized in elongational flow by combining laser-Doppler velocimetry to determine the strain rate in the flow direction and the two-color flow-induced birefringence method to measure the first normal stress difference along the axial centerline of a hyperbolic die. The elongational rate was constant along the axial centerline of the planar hyperbolic die as long as vortices at the die entrance did not occur. The transient elongational viscosity μ ⁺ was determined as a function of the elongational rate. The parameters varied are the Hencky strain rate and the polymer concentration. μ ⁺ showed a pronounced increase over the linear viscoelastic behavior above critical Hencky strains of 1.2 to 1.5; that is, a significant strain hardening could be observed for polyacrylamide solutions. This strain hardening is stronger the higher the elongational rate. A slight enhancement of strain hardening was found by increasing the concentration from 0.5 to 1 g/l. The stress optical coefficient was determined as 1.8 × 10⁻⁷ Pa⁻¹ (0.5 g/l) and 1.2 × 10⁻⁷ Pa⁻¹ (1 g/l).

Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ _xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ _xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

Synthesis and electrorheological properties of polar molecule-dominated TiO 2 particles with high yield stress

Two types of amorphous TiO₂ particles with different particle sizes were synthesized by a simple sol–gel method and were characterized by X-ray diffraction analysis, field emission scanning electron microscopy, and Fourier transform infrared spectrometry. The electrorheological (ER) results show that the TiO₂/silicone oil suspensions exhibited a remarkable ER effect. The static shear stress can be up to 130 kPa (shear rate 0.2 s^− 1) under the DC electric field of 4 kV/mm at room temperature. The polar molecules present on the particles’ surface play a decisive role for the observed giant ER effect, which arises from the alignment of polar molecules in the gap between neighboring particles.     

Bentonite slurries—zeta potential,yield stress,adsorbed additive and time-dependent behaviour

Bentonite clay is a vital ingredient of drilling mud. The time-dependent and high shear thinning yield stress behaviour of drilling mud is essential for maintaining wellbore stability and to remove cuttings, cool and clean the drill bit of debris. As-prepared 3, 5 and 7 wt.% bentonite clay slurries displayed time-dependent behaviour where the yield stress (measured after quick stirring) decreased with time of rest. An equilibrium value is reached after 24 h. Despite the low solids concentration, the yield stress is already relatively high and is displayed at all pH level. The yield stress is maximum at pH 2 and minimum at pH ∼ 7. This yield stress is due to the formation of gel structure by the swelling clay particles. However the addition of phosphate additives such as (PO₃)^19 −, (P₃O₁₀)^5 − and (P₂O₇)^4 − completely dispersed the clay slurries at pH above 6. At pH below 6, yield stress is still present but is 3-folds smaller than that of the pure bentonite slurry. With phosphate additives, the magnitude of the critical zeta potential at the complete dispersion pH is ca 48 mV. However for the pure bentonite, the slurry remained flocculated at zeta potential of >50 mV in magnitude. Interestingly, (P₂O₇)^4 − anions is more effective than the other two phosphate additives in reducing the yield stress at low pH, ∼ 2.0.