Effective moduli of particulate solids: Lubrication approximation method

To efficiently calculate the effective properties of a composite, which consists of rigid spherical inclusions not necessarily of the same sizes in a homogeneous isotropic elastic matrix, a method based on the lubrication forces between neighbouring particles has been developed. The method is used to evaluate the effective Lamé moduli and the Poisson's ratio of the composite, for the particles in random configurations and in cubic lattices. A good agreement with experimental results given by Smith (1975) for particles in random configurations is observed, and also the numerical results on the effective moduli agree well with the results given by Nunan & Keller (1984) for particles in cubic lattices.     

Criteria of negative wake generation behind a cylinder

It was demonstrated by simulation in our previous study that both the normal stress and its gradient are responsible for the negative wake generation (overshoot in the axial velocity) and streamline shifting. Extensional properties of the fluids dominate the generation of the negative wake, while other factors strengthen or weaken the formation of velocity overshoot. In this study, the criteria for the negative wake generation are discussed in detail for various fluid models, including the PTT, the FENE-CR, the FENE-P, and the Giesekus models. With the FENE-CR fluid, it is easier to generate negative wake than with the FENE-P fluid. This confirms that the constant shear viscosity FENE-CR fluid enhances the velocity overshoot, and that the shear-thinning viscosity FENE-P fluid delays the negative wake generation. The Giesekus fluid has a similar behaviour to the PTT fluid with regarding to the critical conditions of negative wake generation when appropriate fluid parameters are selected. The mechanism of wall proximity in enhancing the negative wake generation is also demonstrated with the analysis for the first time.     

Negative wake in the uniform flow past a cylinder

The upstream/downstream streamline shift and the associated negative wake generation (streamwise velocity overshoot in the wake) in a viscoelastic flow past a cylinder are studied in this paper, for the Oldroyd-B, UCM, PTT, and FENE-CR fluids, using the Discrete Elastic Viscous Split Stress Vorticity (DEVSS-ω) scheme (Dou HS, Phan-Thien N (1999). The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation. J Non-Newtonian Fluid Mech 87:47–73). The numerical algorithm is a parallelized unstructured Finite Volume Method (FVM), running under a distributed computing environment through the Parallel Virtual Machine (PVM) library. It is demonstrated that both the normal stress and its gradient are responsible for the negative wake generation and streamline shifting. Fluid extensional rheology plays an important role in the generation of the negative wake. The negative wake can occur in flows where the fluid extensional viscosity does not increase rapidly with strain rate. The formation of the negative wake does not depend on whether the streamlines undergo an upstream or a downstream shift. Shear-thinning viscosity weakens the velocity overshoot and while shear-thinning first normal stress coefficient enhances the velocity overshoot. Wall proximity is not necessary for the velocity overshoot; however, it enhances the strength of the negative wake. For the Oldroyd-B fluid, the ratio of the solvent viscosity to the zero-shear viscosity plays an important role in the streamline shift. In addition, mesh dependent behaviour of normal stresses along the centreline at high De in most cylinder/sphere simulations is due to the convection of normal stress from the cylinder to the wake, which results in the maximum of the normal stress being located off the centreline by a short distance at high De.     

On the stability of the torsional flow of a class of Oldroyd-type fluids

It is shown that the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid. Furthermore, it is shown by a linearized stability analysis and by numerical integration, that the basic flow is unstable at high Weissenberg numbers. An Oldroyd fluid which has a negative second-normal stress coefficient is found to be more stable than one with zero (or positive) second-normal stress coefficient in this flow.     

The squeezing flow of a model suspension fluid

The paper is concerned with the squeezing flow of a model suspension fluid. The numerical solution obtained by a time-dependent Boundary Element Method is compared to an asymptotic solution at large radius. It is found that the kinematics are Newtonian in character, and the fibres quickly align themselves radially. Consequently, the squeezing force is only weakly dependent on the initial orientations of the fibres and the device can be used for measuring the effective viscosity of the suspension. The effective viscosity found from the squeezing flow agrees surprisingly well with experimental data and numerical data derived from the falling sphere geometry at low volume fractions ( < 0.1).     

Flow enhancement mechanisms of a pulsating flow of non-Newtonian liquids

Summary The pipe flow of non-Newtonian liquids under a fluctuating pressure gradient is considered. Adopting a generalized Maxwell model with full relaxation spectrum and considering only weak-sense stationary pressure-gradient noises, it is shown that there are two mechanisms involved in the flow enhancement: an inelastic and a dynamic mechanism. Both depend on the shear-thinning properties of the liquid in steady and oscillatory flows. For one-frequency pressuregradient noises, the flow enhancement increases with increasing frequency of fluctuation if the modulus of the complex viscosity is a decreasing function of the frequency. Since almost all polymeric liquids are shear-thinning in oscillatory shear flows, this investigation serves as a possible explanation for the data collected byBarnes, Townsend andWalters (1971). This, however, does not necessarily ensure that the constitutive model adopted in this study is free of defect in a general flow field.

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Zusammenfassung Es wird die Rohrströmung einer nicht-newtonschen Flüssigkeit bei fluktuierendem Druckgefälle betrachtet. Für ein verallgemeinertes Maxwell-Modell mit beliebigem Relaxations-Spektrum wird bei Beschränkung auf kleine Schwankungen des Druckgradienten um einen stationären Mittelwert gezeigt, daß zwei Mechanismen zur Steigerung des Durchflusses beitragen, ein unelastischer und ein dynamischer Mechanismus. Beide hängen von den Scherentzähungs-Eigenschaften der Flüssigkeit bei stationären und oszillierenden Beanspruchungen ab. Für eine harmonisch-periodische Druckstörung nimmt die Durchflußsteigerung mit wachsender Schwankungsfrequenz zu, wenn der Betrag der komplexen Viskosität eine mit der Frequenz abnehmende Funktion darstellt. Da nahezu alle Polymerflüssigkeiten bei oszillierenden Scherströmungen Scherentzähung aufweisen, liefert diese Untersuchung eine mögliche Erklärung für die vonBarnes, Townsend undWalters (1971) zusammengestellten Ergebnisse. Dies bedeutet aber nicht notwendigerweise, daß das hier angenommene Modell auch für die Beschreibung allgemeinerer Strömungsfelder angemessen ist.

     

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     

Viscosity of concentrated suspensions of spheres

Difficulties associated with the viscosity measurement of concentrated suspensions of particulate solids in a liquid solvent can effectively be overcome with the falling needle technique reported here. The comparison of the settling (terminal) velocity of a given needle in a Newtonian solvent, with its terminal velocity in a suspension, yields the suspension viscosity ratio directly. The van den Brule and Jongschaap constitutive model describes our high concentration data best. Falling sphere data (diameter of sphere/diameter of suspended particle 10) agree well with the falling needle data over the whole range (up to 40%) of solids concentrations used in our tests.In the opaque suspensions used, the passage of sedimenting needles and spheres was initially observed radiographically. Later tests used a more convenient technique using an inductance coil particle detector driven by a Colpitts oscillator.     

A remark on the monomial conjecture and Cohen-Macaulay canonical modules

In this paper, some sufficient conditions for rings and modules to satisfy the monomial conjecture are given. A characterization of Cohen-Macaulay canonical modules is presented.