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The rheology of noncolloidal suspensions in superposed simple shearing and oscillatory shearing was explored. With a Newtonian matrix fluid, one would expect that G′ would be zero in an oscillatory flow, but this was not found; the action of Coulomb friction between the particles appears to cause an increment of G′ at lower frequencies. To understand this frictional effect, measurements of small and medium strain oscillatory flows, up to 10% strain magnitude, were made. The matrix fluid was 12 Pa s silicone oil, and the polystyrene spheres were on average 40.3 μm in diameter. Hysteresis during tests with varying strain amplitudes was more dominant in the storage modulus than in the loss modulus, and, at a 50% volume fraction, the effect was severe. Because of the observed tendency to hysteresis, the oscillatory flow was then combined with a parallel steady shear flow to try to control or eliminate hysteresis. The hysteresis appears to be a frictional effect, and it was reduced under superposed shearing. The effect of variable oscillatory shear stress and steady shear stress was studied, and a model was proposed for the superposed storage modulus, loss modulus, and shear viscosity responses. Frictional effects are considered in the proposed model, and one observes a generally satisfactory fit to the experimental data. From the model, the average friction coefficient is shown to be less at higher frequencies due to higher relative rubbing speeds and better lubrication between the particles. Clearly, suspension rheology is dominated by friction and is essentially a study in tribology.

This review deals with non-Brownian (noncolloidal) suspension rheology; experimental and computational works are compared where possible. The matrix fluids are non-Newtonian, and the rigid particles have an aspect ratio close to one. Volume fractions of 0.5 and below are considered. Shearing and extensional flows are discussed; the former are fairly well understood but the latter are not prominent in the literature. Unsteady and oscillatory flows are surveyed. A comparison of Newtonian and viscoelastic suspension rheology is made, and some aspects of finding constitutive models for these suspensions are discussed. While progress has been made, it appears that satisfying agreement between computation and experiment is rare. More attention to rheological and frictional modeling is needed, and improved computational methods need to be developed.

We study the rheology of a non-colloidal suspension of rigid spherical particles interacting with a viscoelastic matrix. Three-dimensional numerical simulations under shear flow are performed using the smoothed particle hydrodynamics method and compared with experimental data available in the literature using different constant-viscosity elastic Boger fluids. The rheological properties of the Boger matrices are matched in simulation under viscometric flow conditions. Suspension rheology under dilute to semi-concentrated conditions (i.e. up to solid volume fraction $\unicode[STIX]{x1D719}=0.3$) is explored. It is found that at small Deborah numbers $De$ (based on the macroscopic imposed shear rate), relative suspension viscosities $\unicode[STIX]{x1D702}_{r}$ exhibit a plateau at every concentration investigated. By increasing $De$, shear thickening is observed, which is related to the extensional thickening of the underlying viscoelastic matrix. Under dilute conditions ($\unicode[STIX]{x1D719}=0.05$), numerical results for $\unicode[STIX]{x1D702}_{r}$ agree quantitatively with experimental data in both the $De$ and $\unicode[STIX]{x1D719}$ dependences. Even under dilute conditions, simulations of full many-particle systems with no a priori specification of their spatial distribution need to be considered to recover precisely experimental values. By increasing the solid volume fraction towards $\unicode[STIX]{x1D719}=0.3$, despite the fact that the trend is well captured, the agreement remains qualitative with discrepancies arising in the absolute values of $\unicode[STIX]{x1D702}_{r}$ obtained from simulations and experiments but also with large deviations existing among different experiments. With regard to the specific mechanism of elastic thickening, the microstructural analysis shows that elastic thickening correlates well with the average viscoelastic dissipation function $\unicode[STIX]{x1D703}^{elast}$, requiring a scaling as $\langle \unicode[STIX]{x1D703}^{elast}\rangle \sim De^{\unicode[STIX]{x1D6FC}}$ with $\unicode[STIX]{x1D6FC}\geqslant 2$ to take place. Locally, despite the fact that regions of large polymer stretching (and viscoelastic dissipation) can occur everywhere in the domain, flow regions uniquely responsible for the elastic thickening are well correlated to areas with significant extensional component.

We explore the effect of deliberately increased particle roughness on the rheology of noncolloidal suspensions of spheres, both in Newtonian (polydimethylsiloxane or silicone oil) and non-Newtonian (Boger fluid) matrices. The object of the experiment is to change only the roughness of the spheres, while leaving the density and the material of the particles unchanged, so as to isolate the effect of roughness on rheology. Two sphere materials, polystyrene (PS) and polymethylmethacrylate (PMMA) were used. The PS spheres were of 40 and 80 μm nominal diameters, and the PMMA spheres were 40 μm in diameter. Roughness ratios (average roughness/sphere radius) of 0.1%–5% were explored. With silicone matrices, there was up to 50% increase in viscosity with a 50% volume fraction suspension and an increase in the normal stress differences of a similar magnitude. Two polybutene-based Boger fluids were also used. The increases of viscosity with the polybutene matrices were somewhat larger than those with the Newtonian matrix; at 40% volume concentration, we saw approximately a 35% increase in viscosity with a roughness ratio of 5.3%. We compared the experimental results with computations for spheres in Newtonian matrices, and we found reasonable agreement with the computations of Mari et al. [J. Rheol. 58, 1693–1724 (2014)] if a friction coefficient of about 0.5 was assumed. We conclude that friction and roughness must be considered in computational work, or no agreement with experiment will be found. We suggest that the shear-thinning seen with Newtonian matrices is due to a lessening of friction with shear rate. We also show that the unexpected success of the Maron–Pierce formula for Newtonian suspensions is due to the fact that it mimics well a frictional suspension with a friction coefficient of ∼0.5.

The analytical solution of the Stokes-Darcy equations is derived for a Newtonian, statistically homogenous, suspension with non-Brownian (non-colloidal) rigid spherical particles. Navier-type linear slip over the surface of the particles is applied. The mathematical model is based on Brinkman's (1949) original idea for the viscous force exerted by a flowing fluid on a dense swarm of spherical particles. First, the equations are solved analytically for the pressure-driven and uniform flow of the suspension. Self-consistency of the model allows for the evaluation of the resistance parameter as function of the volume fraction of the solid phase and the dimensionless slip coefficient. The results show that for fixed solid concentration, the drag force on each particle decreases due to the slippage of the fluid over its surface. Consequently, the resistance parameter decreases compared to the classic no-slip case. However, in all cases, divergence of the resistance parameter occurs as the solid volume fraction approaches the value 2/3 which is very close to the maximum volume fraction 0.637( ≈ 2/π)for random close packing of spherical particles. The analysis is also performed for steady shear and steady uniaxial elongational flows and exact analytical solutions for the velocity and the pressure are derived. Then, a volume average of the total stress tensor in the suspension allows for the analytical evaluation of the shear and elongational viscosities of the complex flow system. Limiting expressions for the no-slip and perfect slip cases are also found and discussed.

Experiments and computations were carried out to explore the origins of shear-thinning in non-colloidal suspensions. Two grades of polydimethylsiloxane (silicone oil) and a glycerine/water mixture were used as matrices for the suspensions. The particles were 40 μm diameter polystyrene (PS) and polymethyl methacrylate (PMMA) spheres. We concentrated on 40% volume fraction suspensions where shear-thinning was clear. The silicone oil matrices were nearly Newtonian: at 24 °C the viscosity of the 1.15 Pa s sample showed a 2% drop in viscosity a shear rate of about 3000 s−1, the 13.2 Pa s sample showed a drop of 2% at a shear rate of approximately 100 s−1, and the glycerine/water sample appeared to be Newtonian at least up to 104 s−1. Mild shear-thinning was seen with all suspensions, beginning at shear rates of order 0.1–1 s−1, followed by a rapid reduction of torque in the parallel-plate system at shear rates of 14, 150 and 1000 s−1 respectively with the three matrices. These rapid reductions are ascribed to edge effects. Matching smoothed particle hydrodynamics (SPH) simulations were made. The silicone matrix viscosities were modelled by a Carreau–Yasuda (CY) fit up to shear rates of order 107 s−1. The agreement between computations and experiments is generally good for 40% volume fraction suspensions up to the shear rate where edge effects intervene in the experiments- there are no edge effects in the simulations. This confirms the suggestion by Vazquez-Quesada et al. [1] that ‘hidden’ high shear rates between particles, where the non-Newtonian matrix viscosity comes into play, can result in shear-thinning at the macroscopic level. For the glycerine/water matrix at low shear rates this mechanism does not apply and a separate mechanism based on variable interparticle friction is suggested; the two mechanisms can co-exist.

Two fundamental test systems were used to evaluate the visco-elastic properties of doughs from wheat samples of three varieties grown at four distinct sites. For comparison, tests were also performed with traditional equipment, namely the Mixograph, an extension tester and a Farinograph-type small-scale recording mixer. Uniaxial dough elongation (with an Instron) produced results similar to the conventional extension tester, except that results were provided in fundamental units (Pascals), the critical value recorded being the elongational stress at maximum strain. Stress relaxation measurements were performed following a small initial shear strain. With this method, it was possible to distinguish between the viscosity and the elastic components of dough visco-elasticity. In all the tests the extra dough-strength properties were evident for the variety (Guardian) that had the 5 + 10 glutenin subunits, in contrast to the other two with the 2 + 12 combination of subunits.

We have measured the viscometric functions (η, N1, and N2) for a suspension of noncolloidal spherical particles in a Boger fluid matrix. The polymethyl methacrylate particles were nominally 40 μm in size, and the matrix fluid was similar to that used by Zarraga et al. [J. Rheol. 45, 1065–1084 (2001)]. The volume concentrations (ϕ) ranged from 5% to 40%, and a combination of the open trough and parallel-plate methods was used. The viscosity did not shear-thin for higher concentrations, unlike the Newtonian matrix case; for the larger concentrations we saw a mild shear-thickening. This is in agreement with the work of Zarraga et al. [J. Rheol. 45, 1065–1084 (2001)] and Scirocco et al. [J. Rheol. 49, 551–567 (2005)]. N2 was always negative, and its magnitude increased with concentration. N1 was initially positive as in the matrix fluid, but for ϕ>0.3, it became negative, similar to the result of Aral and Kalyon [J. Rheol. 41, 599–620 (1997)]; also, we found, at a constant shear stress, that |N2/N1| was great...

We present the results of measuring the three viscometric functions [the relative viscosity ηr, and the first (N1) and second (N2) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of ηr and N1−N2 were made with a parallel-plate rheometer, while we used the open semicircular trough method to give N2 directly. With the trough method measurements of N2 could be made down to a 10% concentration (φ=0.1); measurements were continued up to 45% concentration. The trough surface shows visually that N2 is directly proportional to the shear stress τ, and the measurements of N2 agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for N1 show greater scatter. In the range 0.1≤φ≤0.45, our best estimate of N2/τ is −4.4φ3 and that of N1/τ is −0.8φ3. Hence, the magnitude of N2 is much greater than that o...

A red blood cell (RBC) in a microfluidic channel is highly interesting for scientists in various fields of research on biological systems. This system has been studied extensively by empirical, analytical, and numerical methods. Nonetheless, research of predicting the behavior of an RBC in a microchannel is still an interesting area. The complications arise from deformation of an RBC and interactions among the surrounding fluid, wall, and RBCs. In this study, a pressure-driven RBC in a microchannel was simulated with a three-dimensional lattice Boltzmann method of an immersed boundary. First, the effect of boundary thickness on the interaction between the wall and cell was analyzed by measuring the time of passage through the narrow channel. Second, the effect of volume conservation stiffness was studied. Finally, the effect of global area stiffness was analyzed.

Shear thinning-a reduction in suspension viscosity with increasing shear rates-is understood to arise in colloidal systems from a decrease in the relative contribution of entropic forces. The shear-thinning phenomenon has also been often reported in experiments with noncolloidal systems at high volume fractions. However its origin is an open theoretical question and the behavior is difficult to reproduce in numerical simulations where shear thickening is typically observed instead. In this letter we propose a non-Newtonian model of interparticle lubrication forces to explain shear thinning in noncolloidal suspensions. We show that hidden shear-thinning effects of the suspending medium, which occur at shear rates orders of magnitude larger than the range investigated experimentally, lead to significant shear thinning of the overall suspension at much smaller shear rates. At high particle volume fractions the local shear rates experienced by the fluid situated in the narrow gaps between particles are much larger than the averaged shear rate of the whole suspension. This allows the suspending medium to probe its high-shear non-Newtonian regime and it means that the matrix fluid rheology must be considered over a wide range of shear rates.

A viscosity-oriented, flow-induced crystallization model is used to predict the rate of crystal layer growth in a tube at high shear rates. A combined strain and strain rate dependence of the enhancement of crystallization kinetics was proposed that showed excellent agreement with viscosity measurements at low deformation rates in simple shear, and it is here considered in the more complex Poiseuille flow. Suspension mechanics is used to link the relative crystalline volume fraction to the viscosity of the semicrystalline polymer. The microstructure is directly related to the thermomechanical histories and this was accounted for in the total volume fraction using the Avrami-Kolmogorov model. The key characteristic of our model is the coupling of the flow history to induced crystallization and the linkage of the flow-enhanced nucleation with viscosity. In this way, the flow is described in terms of changes in crystallization due to changes in rheological behavior. A finite volume numerical treatment was employed using the ANSYS CFX software to model the layer growth. The model is further tested with the presence of an organic nucleating agent in which the sensitivity of the rheological properties of the pigment–polymer blend to stress and temperature was evident. Reasonable agreement with experiments was observed. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers

We refer to the elongational testing of bread dough using a constant strain rate and specimens of varying initial diameter. Previously we found that 5 mm diameter specimens showed a much larger tensile stress for a given strain and strain rate than larger (20 mm diameter) specimens [Tanner et al., in Proceedings of the 5th International Symposium on Food Rheology and Structure, edited by P. Fischer, M. Pollard, and E. J. Windhab (ETH, Zurich, 2009), pp. 348–351]. It is important to understand this result because if it is true it is not possible to write a simple constitutive equation for the dough. In this paper, we examine the roles of ambient humidity and method of specimen preparation. The latter factor was seen to be crucial to obtaining consistent results in elongational testing of dough with different size specimens; it seems essential to limit pretest deformation to a Hencky strain of about 0.5 (extension ratio of about 1.6). Ambient humidity variations also affected the results, but the apparent shift with diameter was much smaller.

A new differential (or multi-scale, mean field approach) model for the relative viscosity of bimodal suspensions is discussed in this paper. Solid spherical particles with a bimodal size distribution in a Newtonian solvent are considered. The problem of random close packing for a bidisperse system is studied. The bounds on volume fractions are given by

The rheological behaviour of a 58 vol.% dispersion of styrene/acrylate particles in ethylene glycol was investigated using a plate-on-plate rheometer. Experimental results showed that the concentrated polymer dispersion exhibited a strong shear-thickening transition under both steady shear and dynamic oscillatory conditions. The low-frequency dynamic oscillatory behaviour could be reasonably interpreted in terms of the steady shear behaviour. Accordingly, the critical dynamic shear rate \( \dot{\gamma }_{{{\text{c\_d}}}} , \) agreed well with the critical shear rate obtained in steady flow \( \dot{\gamma }_{{{\text{c\_s}}}} , \) where \( \dot{\gamma }_{{{\text{c\_d}}}} \) was calculated as the maximum shear rate by the critical dynamic shear strain γc and the frequency ω, i.e. \( \dot{\gamma }_{{{\text{c\_d}}}} = \omega \gamma_{\text{c}} . \) However, during high-frequency dynamic oscillation, it was observed that the shear thickening occurred only when an apparent critical shear strain was reached, which could not be fully explained by the wall-slipping effect. Based on freeze fracture microscopic observations, the effect of the micro-sized flocculation of particles on the rheology of concentrated dispersions was also discussed.

It has been suggested that isothermal flow-induced crystallization is linked jointly to shear strain and strain-rate. By combining continuum mechanics methods and experimental results, an invariant general strain-rate-strain model for some crystallizing polymers, applicable to all flows, is constructed. Examples show the great differences of response in shear and elongation; at a given rate elongation is the more powerful promoter of crystallinity.

There are many curious phenomena when very thin lubricant films interact with sliding surfaces. It is difficult to do experiments on these nano-thickness films, and here we describe the use of non-equilibrium molecular dynamics (MD) to investigate friction in alkane lubricant layers. The pronounced increase of viscosity in layers of thickness seven molecules and less enables an increased load capacity to be sustained in such films. We also demonstrate the existence of a newly-discovered low-friction regime.

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the straightforward implementation of multiple boundary conditions. The performance of the proposed method is investigated by considering several biharmonic problems of first and second kinds; more accurate results and higher convergence rates are achieved than with conventional differential methods.

Purpose – To present a new collocation method for numerically solving partial differential equations (PDEs) in rectangular domains.Design/methodology/approach – The proposed method is based on a Cartesian grid and a 1D integrated‐radial‐basis‐function scheme. The employment of integration to construct the RBF approximations representing the field variables facilitates a fast convergence rate, while the use of a 1D interpolation scheme leads to considerable economy in forming the system matrix and improvement in the condition number of RBF matrices over a 2D interpolation scheme.Findings – The proposed method is verified by considering several test problems governed by second‐ and fourth‐order PDEs; very accurate solutions are achieved using relatively coarse grids.Research limitations/implications – Only 1D and 2D formulations are presented, but we believe that extension to 3D problems can be carried out straightforwardly. Further, development is needed for the case of non‐rectangular domains.Originality/...

This paper reports a new boundary-integral-equation method (BIEM) for numerically solving biharmonic problems with Dirichlet boundary conditions. For the solution of these problems in convex polygons, it was found that the accuracy of the conventional BIEM is significantly reduced, and spurious oscillatory behaviour is often observed in the boundary solutions especially for areas near corners (Mai-Duy N, Tanner RI. An effective high order interpolation scheme in BIEM for biharmonic boundary value problems. Eng Anal Bound Elem 2005;29:210–23). In this study, a new treatment for these difficulties is proposed. The unknown functions in boundary integrals are approximated using a domain-type interpolation scheme rather than traditional boundary-type interpolation schemes. Two test problems are considered to validate the formulation and to demonstrate the attractiveness of the proposed method.

We consider the drawing of slender optical fibres containing an axial hole, which is initially circular and is not necessarily coaxial with the fibre. A Newtonian creeping flow analysis is used to show that changes in hole shape from circular occur when the hole is not on the fibre axis, but these changes only appear in proportion to the square of the slenderness ratio of the fibre. The final oval shape predicted compares qualitatively with experiments on polymethyl-methacrylate fibres.

It has been suggested that isothermal flow-induced crystallization is jointly linked to strain and strain rate. Here we test this idea further by studying some results of Bove and Nobile on isotactic poly (1-butene). We also present some new experimental results on polypropylene in finite amplitude sinusoidal oscillation. The ranges of strain amplitude and frequency are from 0.1% to 10% and from 0.1 to 30 Hz, respectively. The experimental data are compared with the results calculated by using a multimode PTT model with a suspension-based theory; both strain and strain rate are involved in the flow-induced crystallization. A fairly good agreement between experiments and calculations has been observed. We conclude that a simple strain plus strain-rate function gives a reasonable description of flow-induced crystallization at low shear rates. POLYM. ENG. SCI. 46:659–669, 2006. © 2006 Society of Plastics Engineers

The properties of a surfactant salt obtained by neutralizing oleic acid with an ethoxylated stearylamine were determined in blends of water and propylene glycol. The adsorption of this surfactant salt onto the surface of a commercial TiO(2) dispersed in blends of water and propylene glycol was studied using a rheometer. At low propylene glycol content the dispersions exhibited Newtonian behavior, but became shear-thinning fluids with high viscosity at propylene glycol contents above a critical concentration. The observed behavior is consistent with a model involving a surfactant bilayer below the critical point, moving to a monolayer above the critical point. The high viscosity above the critical point is generated by reversible flocculation via hydrophobic forces. The viscosity of the dispersion flocculated by the hydrophobic forces was found to be much higher than that caused by flocculation via van der Waals forces in the absence of surfactant. Changing both the total concentration of the surfactant in the dispersion and the dispersion temperature resulted in a reversible transition between the bilayer and the monolayer. Although the surfactant was always above its critical micelle concentration (CMC) the amount on the particle surface varied appreciably with both propylene glycol and surfactant concentration.

A numerical study on the transient flow of a viscoelastic fluid is presented. The numerical framework is that of Smoothed Particle Hydrodynamics (SPH) already used by Ellero et al. in previous simulations of Non-Newtonian flows [J. Non-Newtonian Fluid. Mech. 105 (2002) 35–51]. In particular, the start-up flow between parallel plates is simulated for an Oldroyd-B and UCM fluid at low Reynolds number. Results for a Newtonian fluid are also shown for comparison. The numerical results are presented and compared with available theoretical solutions, showing a very good agreement. In particular, the simulations of an Oldroyd-B fluid have been found to be stable and accurate for a wide range of the Weissenberg number. In the case of a UCM fluid, the absence of a viscous term in the momentum equation makes its numerical modelling harder. Namely, the process is characterised by a travelling damped wave, which, if not accurately resolved, can lead to the rapid growth of small oscillations in time eventually causing divergence. On the other hand, if specifically dealing with transient flow problems, stabilising techniques such as BSD, EVSS or AVSS can not be used either; whenever used in conjunction with decoupled solution algorithms, they give an excessive oversmoothing in the results which deteriorates the final accuracy. In this work, we consider an exact SPH discretisation of the hyperbolic equation characterising the UCM model. SPH simulations are finally performed for different Weissenberg numbers showing very promising results. Finally, a discussion on the SPH treatment of the boundary conditions for general hydrodynamics problems is also outlined following the approach of ‘SPH boundary particles’ introduced by Morris for the simulations of low Reynolds number flows.

This paper presents an effective high order boundary integral equation method (BIEM) for the solution of biharmonic equations. All boundary values including geometries are approximated by high order radial basis function networks (RBFNs) rather than the conventional low order Lagrange interpolation schemes. For a better quality of approximation, the networks representing the boundary values and their derivatives are constructed by using integration processes. Prior conversions of network weights into nodal variable values are employed in order to form a square system of equations. Numerical results show that the proposed BIEM attains a great improvement in solution accuracy, convergence rate and computational efficiency over the linear- and quadratic-BIEMs.

This paper is concerned with the application of radial basis function networks (RBFNs) for solving non-Newtonian fluid flow problems. Indirect RBFNs, which are based on an integration process, are employed to represent the solution variables; the governing differential equations are discretized by means of point collocation. To enhance numerical stability, stress-splitting techniques are utilized. The proposed method is verified through the computation of the rectilinear and non-rectilinear flows in a straight duct and the axisymmetric flow in an undulating tube using Newtonian, power-law, Criminale-Ericksen-Filbey (CEF) and Oldroyd-B models. The obtained results are in good agreement with the analytic and benchmark solutions.

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.

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.

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.

The flow of a viscoelastic fluid through a corrugated tube is important both for modeling the flow of polymeric fluids through porous media and for testing numerical methods in non‐Newtonian fluid mechanics. In this paper the boundary element method is used to solve this flow problem for various geometries. Newtonian, Maxwell, Oldroyd‐B, and modified Phan‐Thien–Tanner (MPTT) constitutive equations were used. The periodicity of the flow was guaranteed by treating the periodic conditions as parts of the system of equations. The effect of mesh refinement was considered and in some cases this was found to be negligible. The results are generally in good agreement with other investigators up to a Weissenberg number of about 6. After this point no convergence was reached with the present discretization. For the Maxwell and Oldroyd‐B fluids, the change in the flow resistance is small (∼5% decrease) as the Weissenberg number increases. An increase in the flow resistance with the Weissenberg number was observed in the MPTT fluid when the rheological parameter ζ≠0.

In this paper, we report on molecular dynamics simulation studies of thin dodecane films confined between mica surfaces. On confinement, the film undergoes a surface-mediated transition into a novel phase characterized by tetratic orientational order. The rheology of this ordered film is governed by slip planes and, at low shear rates, stick-slip behavior observable under steady shear rates. Melting of these films was observed either on heating or on exceeding a critical shear rate. Evidence is presented that this tetratic film is not the true equilibrium state; rather, a state characterized by nematic order and very low viscosities is found to be more stable.

Some new (boundary‐element) computations of the flow over a slot are reported. By studying the Maxwell model, we find the hole pressure effect is −0.24N1 for this case, which is close to the −0.25N1 result for a second‐order fluid. We believe this accurate result at low Weissenberg numbers is due to the use of tractions as primitive variables in the calculations; this avoids the need to add separately the pressure and extra stress tensors as is usually the case in other numerical methods. Using a modified Phan‐Thien‐Tanner model we were able to perform computations which are a very good fit to the experimental data of Pike and Baird for polystyrene. Various parameters were changed in the MPTT model, and we confirm the approximate validity of the Higashitani‐Pritchard analysis.

The design of wire-coating dies is described using finite element numerical analysis as a guide. Finite elements are able to accommodate awkward geometries and non-Newtonian fluid properties in a realistic manner, and produce streamline and stress patterns within the die. Two basic die geometries are examined and a new design which eliminates recirculation within the die is proposed.

This paper extends Petrie's work on film-blowing to cover viscoelastic non-isothermal flow for both the convected Maxwell and the Leonov models. Good agreement with experimental data is shown for the former. The calculations are highly unstable, however, and it is difficult to obtain convergence with arbitrary values of the film-blowing parameters. The general effect of viscoelasticity is to stiffen the film and restrain the increase in bubble diameter. There is some difference between bubble shapes generated using the Maxwell and Leonov constitutive models but the temperature variation of properties is seen as the dominant effect, The Leonov model tends not to be stiff enough in its response to the present flow, which is purely extensional and good agreement with experiment was not obtained. For the Maxwell model the relevant mean relaxation time must be used for good agreement between experiment and calculation.

Using a combination of boundary element methods, finite element methods and streamline tracking for stresses, we explore the coupling between temperature‐induced swelling and stress‐induced swelling for materials with temperature‐dependent properties and a single relaxation time. One sees an interactive effect; the temperature‐ and stress‐induced swellings are not simply additive. The change of swelling shape is also noticeable. Calculations are reported for a temperature‐dependent Maxwell model up to a Weissenberg number of 1.5, and Weissenberg numbers up to 4.0 with the PTT model; Peclet numbers up to 200 are considered.

A survey of constitutive equations for application to superposed simple and time-dependent shearing is made. Few of the equations so far proposed are capable of showing the experimentally observed cut-off of relaxation processes with rates less than the simple shearing rate. Using rubber-like elasticity theory as a guide, and introducing the concept of network rupture at a given strain magnitude, an integral-type constitutive equation is proposed. This model shows the observed type of behaviour in the combined flow, reasonable numerical agreement for normal stress data in simple shearing and qualitative agreement with the scanty data for extensional flow. Since the numerical quantities occurring in the constitutive equation may be found from dynamic small-strain shear measurements and viscometric flows only, some predictive ability is displayed. Further generalizations and the application of the experimental results to dynamically loaded bearings are also discussed.

The apparent instability of some otherwise useful rate-type fluid equations for superposed simple shear and time-dependent shear is demonstrated. This type of instability appears to reduce the value of rate-type equations for describing polymer fluids.

Reasonable agreement between an Oldroyd -type theory and experiment for helical flows of viscoelastic fluids was found. However, it was not found possible to predict accurately the experimental drag on a sphere using “constants” found from helical flow tests. It is concluded that the flow curve of the Oldroyd fluid is unrealistic and must be modified for practical use. A scheme is suggested which would allow the interpretation of any set of data given the flow curves, normal stresses and relaxation spectrum from experiments. It is suggested that few engineering calculations will need the simultaneous consideration of all the factors mentioned above and separate cases are considered. For the case of unsteady flows where normal stress effects are unimportant, the modified Oldroyd equation will be simple and useful; for more complex cases it may not be the simplest approach. Some remarks on the practical use and meaning of falling-ball tests in non-Newtonian fluids are also given.