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The high molecular weight glutenin subunits (HMW-GS) play an important role in governing the functional properties of wheat dough. To understand the role of HMW-GS in defining the basic and applied rheological parameters and end-use quality of wheat dough, it is essential to conduct a systematic study where the effect of different HMW-GS are determined. This study focuses on the effect of HMW-GS on basic rheological properties. Eight wheat lines derived from cvs. Olympic and Gabo were used in this study. One line contained HMW-GS coded by all three loci, three lines were each null at one of the loci, three lines were null at two of the loci and one line null at all three loci. The flour protein level of all samples was adjusted to a constant 9% by adding starch. In another set of experiments, in addition to the flour protein content being held at 9%, the glutenin-to-gliadin ratio was maintained at 0.62 by adding gliadin. Rheological properties such as elongational, dynamic, and shear viscometric ...

The events during solidification of flowing polymers are extremely complex, often involving partial crystallization. Many processes may need consideration of viscoelastic effects, but here we present an elementary viscous model of solidification rheology based on suspension theory, with application to some recent slow-shearing experiments. It is shown that neither a simple dependence of crystallinity on shear rate nor total shear describes the results, but that a scaling law is evident.

A selection of four commercial flours has been subjected to extensive rheological measurements as part of a comprehensive program of wheat improvement. The results have been used to determine which of the many types of rheological measurements provide significant discrimination between various types of modern baker's flours (including biscuit flours) and to procure data suitable for use in mathematical models describing the dough rheology. The rheological measurements undertaken include oscillatory shear at low amplitude, steady shear at a low shear rate, stress relaxation and extensional viscosity testing. Although oscillatory shear data show minor differences between these flours, the other tests show significant variations and these provide very good discrimination between the different flour types in comparison with conventional dough testing (e.g. by the extensograph). The current dough rheological measurements provide further insight into molecular structure. In the future, mathematical (constitutive) models are expected to provide a means of predicting processing and baking behaviour of bread dough.

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.

Some h-p finite element computations have been carried out to obtain solutions for fully developed laminar flows in curved pipes with curvature ratios from 0.001 to 0.5. An Oldroyd-3-constant model is used to represent the viscoelastic fluid, which includes the upper-convected Maxwell (UCM) model and the Oldroyd-B model as special cases. With this model we can examine separately the effects of the fluid inertia, and the first and second normal-stress differences. From analysis of the global torque and force balances, three criteria are proposed for this problem to estimate the errors in the computations. Moreover, the finite element solutions are accurately confirmed by the perturbation solutions of Robertson & Muller (1996) in the cases of small Reynolds/Deborah numbers.Our numerical solutions and an order-of-magnitude analysis of the governing equations elucidate the mechanism of the secondary flow in the absence of second normal-stress difference. For Newtonian flow, the pressure gradient near the wall region is the driving force for the secondary flow; for creeping viscoelastic flow, the combination of large axial normal stress with streamline curvature, the so-called hoop stress near the wall, promotes a secondary flow in the same direction as the inertial secondary flow, despite the adverse pressure gradient there; in the case of inertial viscoelastic flow, both the larger axial normal stress and the smaller inertia near the wall promote the secondary flow.For both Newtonian and viscoelastic fluids the secondary volumetric fluxes per unit of work consumption and per unit of axial volumetric flux first increase then decrease as the Reynolds/Deborah number increases; this behaviour should be of interest in engineering applications.Typical negative values of second normal-stress difference can drastically suppress the secondary flow and in the case of small curvature ratios, make the flow approximate the corresponding Poiseuille flow in a straight pipe. The viscoelasticity of Oldroyd-B fluid causes drag enhancement compared to Newtonian flow. Adding a typical negative second normal-stress difference produces large drag reductions for a small curvature ratio δ = 0.01; however, for a large curvature ratio δ = 0.2, although the secondary flows are also drastically attenuated by the second normal-stress difference, the flow resistance remains considerably higher than in Newtonian flow.It was observed that for the UCM and Oldroyd-B models, the limiting Deborah numbers met in our steady solution calculations obey the same scaling criterion as proposed by McKinley et al. (1996) for elastic instabilities; we present an intriguing problem on the relation between the Newton iteration for steady solutions and the linear stability analyses.

This is a study on the tangential flow and advective mixing of viscoplastic fluids (Bingham plastics) between two eccentric, alternately rotating cylinders. Two geometrical configurations and various rotation modes are considered for a relatively large range of the yield stress. The hp-type finite element method with the mixed formulation is used to solve for the steady velocity and pressure fields. The bi-viscosity and the Papanastasiou models agree quantitatively with each other in predicting the velocity fields and the practically unyielded zones. However, the Papanastasiou model is more robust and economic than the bi-viscosity model in the computation using Newton iteration. In the steady flows, in addition to the motionless zones, we have discovered some plugs with rigid rotation, including rotating plugs stuck onto the outer cylinder and rotating, even counter-rotating, plugs disconnected from both cylinders. The unsteady, periodic flow is composed of a sequence of the steady flows, which is valid in the creeping flow regime. The characteristics of advective mixing in these flows have been studied by analysing the asymptotic coverages of a passive tracer, the distributions of the lineal stretching in the flow and the variations of the mean stretching of the flow with time. The tracer coverage is intuitive but qualitative and, occasionally, it depends on the initial location of the tracer. On the other hand, the distribution of stretching is quantitative and more reliable in reflecting the mixing characteristics. Interestingly, the zones of the lowest stretching in the distribution graphs are remarkably well matched with the regular zones in the tracer-coverage graphs. Furthermore, the mixing efficiency proposed by Ottino (1989) is used to characterize the advective mixing in the two geometrical configurations with various rotation modes. It is important to realize that, for plastic fluids, a major barrier to effective mixing is the unyielded fluid plugs which are controlled by the yield stress and geometrical configurations. Therefore, when designing an eccentric helical annular mixer it is important to pay attention first to the geometric issues then to the operating issues.

Large-amplitude oscillatory shearing flow data are reported for a wheat-flour dough, which is highly shear-thinning in its dynamic data. The large-amplitude data are analysed using a recently proposed constitutive equation for bread dough, in which dough is considered as a solid-like material. It is found that the model predictions agree well with experimental data, giving a certain degree of confidence in the constitutive equation. Furthermore, the markedly non-linear response of the material, even at as low an amplitude as 0.05, is mainly due to the strain softening behaviour of the material; and this non-linearity cannot be predicted by a model with shear rate dependent parameters alone.

In this paper, we are concerned with the effect of fluid elasticity and shear-thinning viscosity on the chaotic mixing of the flow between two eccentric, alternately rotating cylinders. We employ the well-developed h-p finite element method to achieve a high accuracy and efficiency in calculating steady solutions, and a full unsteady algorithm for creeping viscoelastic flows to study the transient process in this periodic viscoelastic flow. Since the distribution of periodic points of the viscoelastic flow is not symmetric, we have developed a domain-search algorithm based on Newton iteration for locating the periodic points. With the piecewise-steady approximation, our computation for the upper-convected Maxwell fluid predicts no noticeable changes of the advected coverage of a passive tracer from Newtonian flow, with elasticity levels up to a Deborah number of 1.0. The stretching of the fluid elements, quantified by the geometrical mean of the spatial distribution, remains exponential up to a Deborah number of 6.0, with only slight changes from Newtonian flow. On the other hand, the shear-thinning viscosity, modelled by the Carreau equation, has a large impact on both the advection of a passive tracer and the mean stretching of the fluid elements. The creeping, unsteady computations show that the transient period of the velocity is much shorter than the transient period of the stress, and from a pragmatic point of view, this transient process caused by stress relaxation due to sudden switches of the cylinder rotation can be neglected for predicting the advective mixing in this time- periodic flow. The periodic points found up to second order and their eigenvalues are indeed very informative in understanding the chaotic mixing patterns and the qualitative changes of the mean stretching of the fluid elements. The comparison between our computations and those of Niederkorn & Ottino (1993) reveals the importance of reducing the discretization error in the computation of chaotic mixing. The causes of the discrepancy between our prediction of the tracer advection and Niederkorn & Ottino's (1993) experiment are discussed, in which the influence of the shear-thinning first normal stress difference is carefully examined. The discussion leads to questions on whether small elasticity of the fluid has a large effect on the chaotic mixing in this periodic flow.

Aiming at simulating the viscoelastic flow problems involving three-dimensional, time-dependent complex flow, a fully three-dimensional (3D) numerical method using an implicit finite volume formulation is developed in the cylindrical coordinate system. We focus our attention on the well known swirling flows in a confined cylinder with a rotating bottom lid, and through careful comparisons with the available experimental results, the suitability of different constitutive models used to describe viscoelastic fluids is evaluated. Three difficulties arising from the coordinate transformation in a structured mesh system are removed by some simple, but effective measures. With this method, the velocity fields measured in experiments are accurately predicted, and the development of vortex breakdown in terms of Reynolds number (Re) and the height to radius ratio (H/R), as well as the time, observed in experimental visualisations are exactly reproduced for Newtonian flows. The influence of elasticity on the vertex breakdown processes is investigated for the low viscosity dilute polyacrylamide (PAA) solutions described by the upper converted Maxwell (UCM) model. It is confirmed numerically that the existence domain of vortex breakdown occurs at significantly greater Re than that for Newtonian solvent of similar shear viscosity. It seems that the centrifugal force leading to vortex breakdown in Newtonian fluids is balanced by the normal stresses in elastic fluids. As a result, vortex breakdown would be significantly delayed in terms of Re or even suppressed with increasing elasticities. Numerical simulations of the steady swirling flow involving viscoelastic fluids with a high constant viscosity (low Re) shows that the flow field could partially or entirely reversed depending on the level of fluid elasticity. Our numerical results demonstrate that at a low value of Re, for the fluids with a medium high elasticity characterized by the elastic number El = O(1), an elastic ‘ring’ vortex is developing and growing with increasing elasticities at the edge of the rotating lid, and trying to push the Newtonian vortex to the radial centre of the rotating lid, and finally it occupies the whole flow domain at a certain level of elasticity. It is also found that a small weak edge ring vortex appears at the edge of the rigid cover and counter-rotates with the main vortex when the aspect ratio H/R ≥ 1, and its size tends to increase with increasing H/R. The double-cell flow structure for strong shear-thinning viscoelastic fluids observed in visualisation has been successfully predicted numerically by using the simplified Phen-Thien–Tanner (SPTT) model. With steady-state calculations, at a given inertia level, when the flow field is dominated by elasticity, we found that there is a small counter-rotating central ring vortex appears around the centre of the rotating lid, which was usually reported as a sign of instability of the flow field in experimental work. In the second part of this work, we will focus on the numerical inspection of the highly unsteady spiral vortex flows of viscoelastic fluids observed in experiments by using time-dependent calculations, thus, checking the stability criterion of McKinley et al. [G.H. Mckinley, P. Pakdeland, A. Oztekin, J. Non-Newtonian Fluid Mech. 67 (1996) 19–47], and evaluating the suitability of different constitutive equations.

The elastic viscous split stress formulation (EVSS) and the discrete EVSS formulation (DEVSS) are effective in stabilizing numerical simulations of viscoelastic flows and have been widely used. Following the concept of Galerkin least-square perturbations proposed by Hughes et al. [Comput. Meth. Appl. Mech. Eng. 73 (1989) 173–189] and Franca et al. [SIAM J. Numer. Anal. 28(6) (1991) 1680–1697; Comput . Meth. Appl. Mech. Eng. 99 (1992) 209–233; Ibid. 104 (1993) 31–48] we are able to give the DEVSS formulation a new explanation as a perturbation to the Galerkin method based on the strain-rate residual, and furthermore, introduce another stabilized formulation, here named as MIX1, based on the incompressibility residual of the finite element discretizations. The three formulations (EVSS, DEVSS, MIX1), combined with a h–p type finite element algorithm that employs the SUPG technique to solve the viscoelastic constitutive equations are then tested on three benchmark problems: the flow of the upper-convected Maxwell fluid between eccentric cylinders, the flow of the Maxwell fluid around a sphere in a tube and the flow of the Maxwell and Oldroyd-B fluids around a cylinder in a channel. The results are checked with previous published works; good agreement is observed. Our numerical experiments convincingly demonstrate that the MIX1 is an accurate algorithm and convergent in terms of the p-extension, it has the same level of stability and robustness as the DEVSS method and is superior to the EVSS method in some respects. More important is that with MIX1 method one needs not solve for the strain-rate tensor as in EVSS and DEVSS methods, therefore, the CPU time consumption in the MIX1 method especially when using a coupled iteration scheme can be radically reduced. The success of the MIX1 method presents a challenge to the widely accepted concept of making the momentum equation explicitly elliptic.

A molecular dynamics simulation of a thin liquid film as it is sheared between two planar walls is reported. The model liquid is composed of linear chain molecules of hexadecane (C16H34) with intramolecular architecture such as bond stretching, angle bending and dihedral potentials included in the model. Designing a model that can mimic the planar shear flow enables us to study important questions on the effects of the wall properties on the slip between the liquid film and the wall. Different properties of the wall such as wall density, wall stiffness and wall–fluid interaction strength have been studied to determine the slip between the wall and fluid. The slip has been investigated for strong and weak adsorbing surfaces at various shear rates. The results emphasize the importance of adsorption on the degree of slip. The dependence of slip on the film thickness is also demonstrated.

In this work the rheological and structural properties of n-hexadecane have been studied by molecular dynamics simulation. The model consists of two structured atomic walls between which the fluid is sheared by moving the walls in opposite directions. The fluid consists of chains of n-hexadecane molecules. Each molecule has 16 interaction sites where each site on the molecule represents a CH2 or CH3 group. The Lennard–Jones potential governs the intermolecular interactions. Stretching, angular and torsional potentials are used for the intramolecular interactions to preserve the integrity of the molecules. An isothermal simulation of the Couette shear flow is conducted to reveal the rheological properties of n-hexadecane at high Weissenberg numbers in films as thin as 1 nm. The results obtained show an increase in the average viscosity of hexadecane as the film thickness is decreased to scales comparable to the molecular diameter of the chain segments. These results agree with recent experimental findings for very thin films, revealing shear thinning and normal stress difference effects which are an indication of non-Newtonian behaviour. Structural properties such as the density profiles, bond angle and dihedral angle distribution functions and average end-to-end distance of the molecules are obtained for films of different thickness and at different shear rates. The effects of the wall–fluid interaction strength on the fluid properties are also investigated in different adsorption limits. It seems that adsorption is a determining factor in the properties of these ultrathin films. The results indicate different shear responses depending on the adsorption limit of the surface.

A numerical study focusing on the macroscopic flow patterns and the Lagrangian unsteady extensional flow behaviour of a viscoelastic fluid in a rectangular duct with a sudden contraction is carried out using a three-dimensional (3-D) finite volume method (FVM). The flow geometry consists of an upstream duct with a square cross-section and a smaller downstream duct with a square or a rectangular cross-section, which corresponds to the so-called „square/square” (Sq/Sq) contraction and the planar contraction, respectively. The Phan-Thien Tanner (PTT) model, including the upper convected Maxwell (UCM) model as a special case, is adopted for the viscoelastic fluid description. Different vortex features observed experimentally in the two different types of contraction flows for the same fluid are predicted. It is found numerically that the macroscopic flow features are well correlated to the fluid‘s Lagrangian unsteady extensional behaviour in the Sq/Sq (or similarly in the axi-symmetric) contraction flow. In the planar contraction flow, however, the predicted Lagrangian unsteady extensional behaviour is different from its steady-state case, and no direct correlation can be made. The large transient extensional stress and the bounded transient extensional viscosity in the planar contraction flow may be responsible for the differences in the vortex patterns in the two contraction flows of viscoelastic fluid with a constant viscosity.

We present in this paper a fully three dimensional (3D) convergent numerical study of planar viscoelastic contraction flows. A 3D finite volume method (FVM) with the primary variable elastic viscous split stress (EVSS) formulation is employed, and a very efficient 3D block solver coupled with block correction is developed to speed up the convergence rate. Full 3D simulations of viscoelastic flows in 4:1 planar abrupt contractions are carried out using experimental conditions. Upstream vortex patterns comparable with the existing flow visualisation observations are captured using the upper convected Maxwell model for a Boger fluid and the Phan-Thien–Tanner model for a shear thinning fluid. Comprehensive comparisons between numerical simulation results and data measured in the dynamic fields in a 4:1 planar abrupt contraction are made, and the results indicate that the experimental measurements can be quantitatively reproduced if the fluid is well characterised by an appropriate viscoelastic model. It is confirmed numerically that the shear thinning of the fluid reduces the intensity of the singularity of viscoelastic flow near the re-entrant corner. With the Oldroyd-B model, by extensive computations on successively refined meshes with the minimum dimensionless size being 0.16–0.014 on the contraction plane in 2D configuration, it is revealed that, although the asymptotic flow behavior near the re-entrant corner and the build-up of the overall pressure and extensional stresses as well as the kinematic behavior along the centreline are insensitive to mesh refinement, completely different vortex activities may be predicted if the mesh is not sufficiently fine. It is verified numerically that, depending on the flow inertia and rheological properties of fluids, both the lip vortex mechanism and the corner vortex mechanism may be responsible for the vortex activities of viscoelastic fluids in 4:1 planar contraction flow, and the elasticity number E and Mach number M of the flow can be used to determine the vortex mechanism approximately. It is clear that the development process of the vortex activities could be underestimated with 2D simplification, and overpredicted with the creeping flow assumption, particularly when Re>0.5. Therefore, in planar contraction flow analyses, numerical artifacts may be produced with a coarse mesh, and 2D flow simulation is only a good approximation to the fully 3D flow if the upstream aspect ratio W/H in the experiment is at least 10.

In this paper we present the molecular dynamics simulations of thin fluids films sheared in Couette flow geometry between two structured plane walls. An NVT ensemble of atoms was chosen and simulation conducted in isothermal conditions. To keep the temperature at the required level a Gaussian thermostat was employed. This method was shown to be superior to the simple velocity rescaling method, especially at high shear rates. The Gaussian thermostat method gave results for viscosity in good agreement with the results of other researchers who used the reservoir method. The results for density and velocity profiles were obtained for a wide range of simulation parameters. The effects of shear rate and wall-fluid interaction strength were investigated in detail over a wide range of parameters. The material functions and normal stress differences were also obtained and the effects of shear rate and wall strength parameter on these properties were studied. The effect of film thickness on the viscosity was investigated and was compared with what we found for bulk fluid using the SLLOD algorithm. the existence of a non-Newtonian region with shear-thinning effect is found and examined for various films. The results suggest an increase in viscosity for thinner films in the Newtonian regime, though this is valid only for a limited range of wall-fluid interaction strength. A decrease in viscosity was also observed when the attraction force of the wall was increased.

The swelling of an extrudate initially performing a fully-developed tube flow is reconsidered for a wide class of constitutive equations, including PTT, pom–pom and general network type models. The results confirm and extend the original analysis; the limitations are also discussed.

We report an adaptive viscoelastic stress splitting (AVSS) scheme, which was found to be extremely robust in the numerical simulation of viscoelastic flow involving steep stress boundary layers. The scheme is different from the elastic viscous split stress (EVSS) in that the local Newtonian component is allowed to depend adaptively on the magnitude of the local elastic stress. Two decoupled versions of the scheme were implemented for the Upper Convected Maxwell (UCM) model: the streamline integration (AVSS/SI), and the streamline upwind Petrov-Galerkin (AVSS/SUPG) methods of integrating the stress. The implementations were benchmarked against the known analytic Poiseuille solution, and no upper limiting Weissenberg number was found (the computation was stopped at Weissenberg number of O (10 4 )). The flow past a sphere in a tube was solved next, giving convergent results up to a Weissenberg number of 3.2 with the AVSS/SI and 1.55 with the AVSS/SUPG (both were decoupled schemes; without the adaptive scheme, the limiting Weissenberg number for the decoupled streamline integration method was about 0.3). These results show that the decoupled AVSS is more stable than the corresponding EVSS, and the SI is more robust than SUPG in solving the constitutive equation of hyperbolic type. In addition, we found a very long stress wake behind the sphere, and a weak vortex in the rear stagnation region at a Weissenberg number above W i of about 1.6, which does not seem to increase in size or strength with increasing W i .

This paper reports a convergent numerical algorithm for the Upper-Convected Maxwell (UCM) fluid between two eccentric cylinders at various eccentricity ratios (ϵ); the outer cylinder is stationary, and the inner one rotating. The problem is solved by an unstructured control volume method (UCV), which is designed for a general viscoelastic flow problem with an arbitrary computational domain. A self-consistent false diffusion technique and an iteration scheme are used in combination to solve the problem. The computations of the UCM fluid using the numerical algorithm are carried out to a higher value of the Deborah number (De) at each eccentricity tested than hitherto possible with previous numerical simulations. The solutions are compared with previous numerical results, confirming the effectiveness of the UCV method as a general technique for solving viscoelastic flow problems.

The extrudate swell of a viscoelastic fluid through an orifice die is investigated by using a mixed finite element and a streamline integration method (FESIM), using a version of the K-BKZ model. The free surface calculation is based on a local mass conservation scheme and an approximate numerical treatment for the contact point movement of the free surface. The numerical results show a vortex growth and an increasing swelling ratio with the Weissenberg number. Convergence with mesh refinement is demonstrated, even at a high Weissenberg number of O(587), where the swelling ratio reaches a value of about 360%. In addition, it is found that the effective flow channel at the entrance region next to the orifice die is reduced due to the enhanced vortex growth, which may be a source of flow instability.

In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them. To solve the coupled governing equation system, an implicit finite volume method based on the SIMPLEST algorithm, which is applicable for both time-dependent and steady-state flow computations, has been developed and extended for viscoelastic flow computations by applying the decoupled techniques. The main feature of the method is to split the solution process into a series of steps in which the continuity of the flow field is enforced by solving a Poisson's equation for the pressure, and at the end of the steps, both the pressure and velocity fields are made to satisfy one and the same momentum equation. For viscoelastic flow computations, artificial diffusion terms are introduced on both sides of the discretized constitutive equations to improve numerical stability. It is found that there are in total two vortices in each quadrant of the pipe at different aspect ratios (from 1 to 16), and at each ratio the pattern of secondary flows takes the same form for different material parameters, but their strength is very sensitive to the viscoelastic material parameters. Numerical results indicate that the presence of secondary flow strongly depends on the primary flow rate and the elasticity of the fluid, namely, the first and the second normal stress differences as well as their functional departure from the constant multiple viscosity.

The flow of the Oldroyd-B fluid between two opposing orifices is simulated using a finite element method in which the non-Newtonian stress is solved by integrating the strain history along the streamlines. The energy analysis of Mackay et al. [J. Rheol., 39 (1994) 1–14] is investigated by dividing the rate of energy dissipated into three parts, due to the first normal stress difference N1, the shear stress τrz and the second normal stress difference N2. The numerical results show that the flow between two opposing orifices, an unsteady elongational flow in a Lagrangian sense, could serve as a reasonable approximation to the steady-state uniaxial elongational flow when the dimensionless gap Z0/R0 is of the order one. At larger gaps, the error can be several hundred percent. Other flow configurations are also investigated using the same numerical method, demonstrating that pressure drop measurement does not always yield a good approximation to the tensile force generated in a nearly elongational flow.

Raymond John Stalker was born in Dimboola, Victoria on 6 August 1930 and died in Brisbane on 9 February 2014. He had a distinguished academic career at the Australian National University in Canberra and at the University of Queensland. His work on hypersonic flow was universally recognized, and the ‘Stalker Tube' facilities he pioneered were able to reach unprecedented flow speeds and were reproduced in many laboratories around the world.

Robert William Bilger was born in Rustenburg, in the North-west Province of South Africa on 22 April 1935 and died in Sydney, New South Wales, on 2 October 2015. He had a distinguished academic career at the University of Sydney. His most important contribution to combustion research was the pioneering of conditional moment closure methods as a reliable predictive tool for turbulent reacting flows. He also made significant contributions to environmental flows and combustion chemistry.

Consistency of dough properties is an important requirement of millers and bakers. Attempts to achieve this aim by prior testing (prediction) of grain samples might become unnecessary if varieties could be identified that are largely tolerant to the effects of growth conditions on dough quality. Three commercial Australian wheat varieties (Janz, EGA Gregory and LongReach Guardian) were grown in four different locations in New South Wales, Australia. Their dough quality was evaluated by several small-scale methods to determine the extent to which the varieties differed in dough quality due to variations in growth conditions. Of these varieties, LongReach Guardian showed stability of dough quality irrespective of growth conditions as indicated by the results of SIG testing, of ten-gram Mixograph, extension testing and of fundamental dough testing, based on G(1) and Hencky strain. This pilot-scale experiment indicates that there is significant promise in breeding varieties for tolerance to the effects of growth conditions on dough quality.

A Phan-Thien- Tanner (PTT) integral model which is exactly equivalent to the usual differential form is used with a new numerical scheme to simulate the Poiseuille flow of PTT fluids and the steady motion of a sphere along the axis of a cylinder. The exact solution for the Poiseuille flow of a PTT fluid presented here can be used to determine the rheological parameters, as well as to test numerical schemes and codes. With this scheme, convergent simulation results for flow past sphere are obtained to Wi, (Weissenberg number) = 0.5, when ϵ =0.02, and up to Wi=2.9, when ϵ =0.25, for the finest mesh used (M4). The tube diameter is twice the sphere diameter in all cases. The mesh refinement results exhibit good convergence properties. All of the curves of the dimensionless drag force versus Wi for three different meshes are close to each other right up to where the numerical simulation diverges. There is no upturn in the drag for these results. The numerical simulation results for the dimensionless drag forces are in good agreement with those obtained by other methods using the differential form of the PTT model. One of the interesting features of the non-Newtonian stress field is the minimum value of τzz, which is negative, appearing in the downstream region near the rear stagnation point, rather than at the upstream region near the front stagnation point as usually happens for UCM fluids. For the PTT fluid, above some level of viscoelasticity, a negative value of velocity component Vz appears downstream near the rear stagnation point, which tells us there must be a vortex behind the sphere, although it is very weak at the Weissenberg numbers we have reached. We also find that the numerical method, solving the non-Newtonian extra stress based on the strain history calculation along the streamline, is an accurate scheme, which captures well the thin stress boundary layers and high stress regions The stress calculated by streamline integration is often very sensitive to small changes in kinematics, which poses a big challenge to computational stability

We consider the numerical simulation of the combined drawing and radial expansion of a thick tube, which is a possible model for continuous tube-making. Both Newtonian and visco-elastic cases are considered. Mesh refinement studies show convergence; to stabilize the computations we have introduced relaxation factors. The main difficulty here is in finding the region of contact with the sizing die, as well as the form of the free surface. It was found that the extra stress component, τθθ, is most helpful in considering the characteristics of tube expansion. The maximum value of τθθ occurs near the outer wall of the exit of the annular die for Newtonian flow and near the interface for K-BKZ liquids. Both for Newtonian and K-BKZ liquids the extra stress component τθθ in the expansion region, not including the vicinity of the exit of the die, develops from the inner free surface toward the outer free surface. The pressure value needed for tube expansion increases and then decreases as the expansion ratio R0/RW increases.

We discuss a finite volume method for computing solutions of steady incompressible viscoelastic fluid flows. A fourth-order Runge-Kutta method is used in the explicit time-stepping scheme. The computations are carried out mainly on unstructured grids on Newtonian, inelastic and differential-type constitutive equations, which include the Oldroyd-B and the upper-convected Maxwell models. The performance of the scheme on unstructured grids is investigated, with particular reference to the stick-slip problem for the modified upper-convected Maxwell fluid. The results are compared with those obtained by using the finite element method whenever possible.

It is known that the dimension of an injection-molded product, as it cools after the molding process, is usually different from the corresponding dimension of the mold cavity. The geometric reduction in the size of the part is referred to as mold shrinkage, or as-molded shrinkage, or simply shrinkage. According to ASTM standards (ASTM D955-08), shrinkage is measured 24–48 h after demolding. Warpage, or warping, is the distortion induced by the inhomogeneous shrinkage. According to Austin (1991) and Shoemaker (2006), variations in shrinkage can be further classified into three types: (i) shrinkage difference in different directions due to the material anisotropy; (ii) shrinkage variations from region to region in the part due to non-uniform pressure and temperature distributions over the part; (iii) non-uniform shrinkage across the thickness due to the differential cooling on opposing mold faces.

Most injection-molded parts are thin walled, i.e., they have a small thickness compared to other typical dimensions. Therefore, one can reduce the three-dimensional flow to a simpler two-dimensional problem, using the lubrication approximation (Richardson 1972). We consider a polymer flow through a thin cavity with a slowly varying gap-wise dimension and arbitrary in-plane dimensions. Assume that x1, x2 are the planar coordinates, x3 is the gap-wise direction coordinate. The flow occurs between two walls at \( x_{3} = \pm h/2 \). Adjacent to each wall there is a frozen layer of the solidified polymer so that the polymer melt flows between two solid–liquid interfaces at \( x_{3} = s^{ - } (x_{1} ,x_{2} ){\text{ and }}x_{3} = s^{ + } (x_{1} ,x_{2} ) \) (see Fig. 3.1). Open image in new window Fig. 3.1 Definition of the local coordinate system for mold cavity

The term “rheology” dates back to 1929 (Tanner and Walters 1998) and is used to describe the mechanical response of materials. Polymeric materials generally show a more complex response than classical Newtonian fluids or linear viscoelastic bodies. Nevertheless, the kinematics and the conservation laws are the same for all bodies. The presentation here is condensed; one may consult other books for amplification (Bird et al. 1987a; Huilgol and Phan-Thien 1997; Tanner 2000). We begin with kinematics.

A sustained industrial interest has been shown in fiber-filled polymers. When fibers are combined with a polymer matrix that provides cohesion, the fibers become the load bearing component of the composite, and enhance the strength and stiffness of the material. Many articles made from the fiber-reinforced composites are produced by injection molding or compression molding. The thermo-mechanical properties of the end-product highly depend on the fiber orientation distribution induced by the flow of fiber suspension during processing. Therefore, the flow of fiber suspensions needs to be understood in order to predict the fiber orientation distribution and its effects on the end properties of the products.

The J -integral technique was originally developed as a method of looking at energy release rates in cracked solids. It seems adaptable to non-Newtonian fluids, and here the use of J -integral methods for inelastic stick-slip and edge flows is demonstrated. This enables one to predict the strength and form of the singularity from simple integrals over the main flow; this method has been used to correct the numerical estimate of singularity strength in Richardson's Newtonian analysis. The intensification of stress and/or velocity gradients due to viscosity variations is shown using a biviscosity model. Intensity factors connected to the easily computed J -integrals are found for power-law fluid singularities both for the stick-slip and edge flow cases. Consideration of various viscoelastic models in the stick-slip flow shows that (i) the second-order model leads to non-integrable wall forces; (ii) the singularity in the Oldroyd-B case cannot generally be Newtonian in form; (iii) the Phan-Thien-Tanner (PTT) model does not lead to a separable singularity of simple form; (iv) the Maxwell case is unresolved, but no flow may exist. Acceptable solutions for edge flows, by contrast, exist for all cases except the second-order model.

An algorithm for generating unstructured tetrahedral meshes by the advancing front technique is presented. Emphasis is placed on the construction of tetrahedral elements. Several measures are employed to prevent difficult situations. A control line/surface scheme is used to specify element size. Numerical examples are provided to show the performance of the algorithm.

There are few computations of polymer forming processes which include compressibility. Here we estimate the effect of compressibility in Newtonian and PTT fluids on extrudate swell and stick-flip flow. Changes of the order of a few per cent occur in swelling, which is in accord with expectations.

The present paper considers the problem of predicting motionless regions and true plug (constant velocity areas where the stress is below the yield stress) regimes for fully three-dimensional Bingham plastic flows. Numerical solutions are obtained using a finite-element biviscosity formulation. Comparisons are drawn to alternative numerical approximations and a review of common finite elements is made with a view to finding accurate, stable and economical schemes. A number of elements are compared and we conclude that some of the Fortin elements are most useful on the grounds of computational overhead and solution accuracy. These are used to investigate axial flows of a Bingham body in an annulus. Finally, we show that the numerical solutions of the axial flow of a Bingham plastic in a narrow eccentric annulus show good agreement with observations and theoretical predictions.

Polyvinyl chloride (PVC) is widely used in industry, but it is difficult to find any extensive discussion of theological relations that describe it. The present paper discusses the behaviour of rigid PVC in extensional deformations at various temperatures. In the tests, a step elongation was applied at an initial time, then after a delay the specimen was cut, permitting recoil. Both linear and nonlinear strain regimes were studied; the linear relaxation properties (relaxation function, storage modulus) were cross-checked with eccentric-disk measurements. In the non-linear strain regime a single-integral constitutive equation of the KBKZ Wagner type was used. Separability of time and strain effects was demonstrated in our tests and so a “damping function” could be found which was only a function of strain. Video recordings of recoil were made, and detailed predictions of the strain-time behaviour were checked against experiments.

The flow along the centreline behind a falling sphere in Maxwell-type fluids is analysed using a finite difference and a path integration scheme. If the flow is unbounded, then there is no limiting Weissenberg number. This conclusion, at least to a Weissenberg number of the order 10, follows from our numerical data; analytical indications are that no limiting values exist at any Weissenberg number, either with the Maxwell, Oldroyd-B, or PTT (Phan-Thien-Tanner) models.

This paper presents a comparative study of several computational schemes which have been proposed for solving Oldroyd-Maxwell type viscoelastic constitutive equations, including a Fourier mode method, finite differences, Galerkin, streamline-upwind/Petrov Galerkin (SUPG) and the SU scheme of Marchai and Crochet. A one-dimensional steady, simplified version of the constitutive equation is the main vehicle for study. We conclude: (i) The SU method is exceptional in that it is not a method of weighted residuals. As a consequence the SU method is not able to give exact results to a simple sinusoidal excitation problem for which Galerkin and SUPG methods are exact. (ii) For general meshes, a theoretical analysis shows that the error in slope (dτ/dx) with the SU method is of order 1 at high Weissenberg numbers. When uniform meshes are used it is of O(h). The solution errors are predicted to be of order h12 and h for unequal and equal meshes respectively. (iii) The above results are compared with an upwinded difference scheme; the right-hand side terms are not accurately treated by the SU method when the mesh is of varying size. (iv) For equal meshes, the sizes of the errors are illustrated by two examples. Considering the axial stress on the axis of a sphere (Newtonian velocity field) we find that with about 9000 equal linear elements, at a Weissenberg number of four, the SU procedure is in error for the maximum stress by about 5%; with 1000 equal elements it is in error by over 300%; the error is about 50h for 9000 elements where h ≈ 10−3. Other methods have much smaller errors. Finally, some suggestions are made for improving the accuracy of the SU scheme and some results are quoted for one-dimensional problems with sinusoidal forcing.

The present paper considers the problem of predicting extrudate shapes from asymmetrical dies for Newtonian fluids. The flow is fully three-dimensional and an exploration of finite elements is made with a view to finding accurate, stable and economical schemes. A number of elements are compared and we conclude that some of the Fortin elements are most useful on the grounds of computational overhead and solution accuracy. These are used to investigate some symmetrical (square dies) and asymmetrical (unequal lip) planar and general L-shaped die flows. Finally, we show that in an unconstrained extrudate the final shape must be such that particles describe a helix in space; special cases include circular flow and rectilinear flow.

In this paper, we extend the explicitly elliptic momentum equation (EEME) formulation to a class of constitutive equations of the Maxwell type without the Newtonian solvent viscosity and apply it to a simplified Phan-Thien-Tanner (PTT) model. In the coupled finite element approach, the Galerkin method is applied to the modified momentum equations and the continuity equation, while the streamline upwind Petrov/Galerkin method is applied to the constitutive equations. The program is used to study the flow past a sphere placed at the centreline in a cylindrical tube using unstructured meshes. Our numerical results for the Maxwell model agree excellently with previous results from Lunsmann et al. (1989) up to a Weissenberg number of 2. New results for the PTT model are presented up to a Weissenberg number of about 4.5. It is found that the flow exhibits shear thinning behaviour in the drag force versus the Weissenberg number. The drag behaviour is remarkably similar to the viscosity flow curve.

Numerical solutions are presented for the flow past a sphere placed at the centreline of a cylindrical tube for Reynolds numbers ranging from 0 to 150, using a boundary element method. Fluids are modelled by a variety of constitutive equations including the Newtonian, the Carreau and the Phan-Thien-Tanner models. The influence of inertia, shear-thinning and fluid elasticity on the flow field, drag and the pressure drop force-drag ratio is examined. Some results are compared with available experimental data.

Wheat flour dough is an example of a soft solid material consisting of a gluten (rubbery) network with starch particles as a filler. The volume fraction of the starch filler is high‐typically 60%. A computer‐friendly constitutive model has been lacking for this type of material and here we report on progress towards finding such a model. The model must describe the response to small strains, simple shearing starting from rest, simple elongation, biaxial straining, recoil and various other transient flows. A viscoelastic Lodge‐type model involving a damage function. which depends on strain from an initial reference state fits the given data well, and it is also able to predict the thickness at exit from dough sheeting, which has been a long‐standing unsolved puzzle. The model also shows an apparent rate‐dependent yield stress, although no explicit yield stress is built into the model. This behaviour agrees with the early (1934) observations of Schofield and Scott Blair on dough recoil after unloading.

The hypotheses of separability and irreversibility, which have greatly improved the accuracy of constitutive models of the KBKZ type are tested in reversing step shear and elongational deformations. A reversing double-step deformation is a severe test for constitutive models and a new rheometer has been developed to perform this type of deformation, both in shear and elongation, in a single machine.