摘要:

A new family of closure approximations, called orthotropic closures, is developed for modeling of flow‐induced fiber orientation. These closures approximate the fourth‐order moment tensor for fiber orientation in terms of the second‐order moment tensor. Key theoretical concepts are that any approximate fourth‐order tensor must be orthotropic, that its principal axes must match those of the second‐order tensor, and that each principal fourth‐order component is a function of just two principal values of the second‐order tensor. Examples of orthotropic closures are presented, including a simple form based on linear interpolation and a formula that is fitted to numerical solutions for the probability density function. These closures are tested against distribution function solutions in a variety of flow fields, both steady and unsteady, by integrating the orientation evolution equation. A scalar measure of the difference between the exact and approximate second‐order tensors quantifies the errors of various closures. The orthotropic fitted closure is shown to be far more accurate than any earlier closure approximation, and slightly more accurate than Verleye and Dupret’s natural closure. Approaches for further increasing the accuracy of orthotropic closures and ultimate limits to the accuracy of any closure approximation are discussed.

ISSN:0148-6055    

DOI:10.1122/1.550630

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

The apparent wall slip velocity coefficient of concentrated monodisperse suspensions of 90 μm PMMA particles in a viscous Newtonian fluid was determined experimentally in a narrow gap Couette device by measuring the particle velocities across the gap using a laser doppler anemometer system and then extrapolating the results to the two walls. The slip coefficients thereby obtained were found to be insensitive to the magnitude of the applied shear rate and to equal, approximately, λ/8 for particle concentrations φ in the range 0.45≤φ≤0.52, where λ refers to the relative effective viscosity of the suspension with respect to that of the pure fluid.

ISSN:0148-6055    

DOI:10.1122/1.550631

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

An analysis of the dynamic behavior of polymeric liquid crystals is given in terms of a second‐rank order parameter tensor describing the orientational state of the local microstructure. The continuum equations governing the dynamics of the material are analyzed under both steady‐state and transient conditions for isotropic and liquid‐crystalline fluids subjected to shear and magnetic fields. Analysis reveals that a great variety of dynamic behavior for liquid‐crystalline materials can be accommodated within the framework of a continuum theory in terms of a second‐rank order parameter tensor, and that this dynamic behavior approximates well the orientational behavior obtained with the more complex distribution function theories. Under some conditions the associated rheological behavior of the continuum theory exhibits discrepancies in the normal stress behavior compared to rheological calculations based on the distribution function theory. For simultaneous application of shear and magnetic fields, both the direction and the strength of the magnetic field play a major role in determining the dynamic system response.

ISSN:0148-6055    

DOI:10.1122/1.550633

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

The frequency‐dependent behavior of the storage modulusG′ and loss modulusG″ has been measured for an ordered latex at different volume fractions. From these measurements the volume fraction dependency of the static shear modulus was obtained. The theoretical static shear modulus has been deduced from a stress tensor expression which only takes into account the electrostatic pair interactions between nearest neighbors. The electrostatic pair interaction is modeled adequately to account for the multiparticle environment of a particle and for high surface charges. The interactions are described by the linear superposition approximation for the pair interaction energy between two particles given by Belletal. [J. Colloid Interface Sci.33, 335 (1970)]. The apparent surface potential and the effective Debije screening length used in this expression are determined from the electrostatic potential which is numerically determined from the Poisson–Boltzmann equation in a spherical cell. The theoretical model is also compared with measurements of several other investigators. Most of the experimental data can be scaled to a single mastercurve resulting from the proposed theoretical model.

ISSN:0148-6055    

DOI:10.1122/1.550634

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Laser Doppler velocimetry and flow‐induced birefringence are used to measure the rate of deformation and the principal components of the refractive index tensor in a 5% polyisobutylene (PIB) solution in tetradecane (C14) flowing along the centerplane of an abrupt 3.97:1 planar contraction. The stress optical law is used to interpret the birefringence data in terms of the normal stress difference, which is used to calculate a transient elongational viscosity defined along the centerplane. These measurements are compared directly to predictions of six multimode, differential constitutive models (Oldroyd‐B, White–Metzner, Aciernoetal., Giesekus, Bird–DeAguiar, and Phan‐Thien–Tanner) that are fit to steady and small amplitude oscillatory shear flow data for the PIB/C14 solution. The fluid exhibits slight elongational thickening followed by apparent extensional thinning at higher elongation rates. We believe that this ‘‘thinning’’ behavior is due to the decreased residence time of the polymer molecules in the high‐strain‐rate region as the flow rate (and maximum elongation rate) is increased. The nonlinear constitutive equations, except for the White–Metzner model, are virtually indistinguishable in their description of the dynamical response of the fluid in this experiment; however, the Phan‐Thien–Tanner model gives the best quantitative fit to the data. These results point to the need for experiments in which the fluid flowing along the centerline is subjected to a greater total elongational strain.

ISSN:0148-6055    

DOI:10.1122/1.550725

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

We demonstrate for the first time that the rheological parameters like the apparent viscosities and the first and second normal stress differences of suspensions of orientable particles can show chaotic behavior when the orientation vector evolves chaotically. We also demonstrate that the range of the values of the rheological parameters is about 10 000 times greater when the parameters evolve chaotically. This suggests that a wide range of properties may be obtained by small variations in controllable parameters. When coupled with suitable control of chaos algorithms, a wide range of suspension behavior is thus possible since a chaotic solution can be considered as an unlimited reservoir of periodic solutions of arbitrary period.

ISSN:0148-6055    

DOI:10.1122/1.550729

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Viscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well‐characterized solution of 5%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point‐wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow‐induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single‐ and a four‐mode Phan‐Thien and Tanner (PTT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De=1.87). Impressively good agreement was found between the predictions of the four‐mode PTT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder.

ISSN:0148-6055    

DOI:10.1122/1.550635

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

This article describes the technical performance and initial results for a new, two‐piston, ‘‘multipass rheometer.’’ Fluid is contained within a capillary by two servo‐hydraulically controlled pistons. Both steady flow and oscillatory data can be obtained from the device with mean pressure as an independent adjustable variable. Steady and oscillatory data are presented for a silicone oil and a viscoelastic solution and certain data are compared with results obtained from a Rheometrics RDS‐II mechanical spectrometer or with literature data. The results show that the multipass rheometer is capable of extending the experimental ranges of many conventional rheometers, particularly in terms of pressure control, high shear rates, and multiple, successive flow measurements.

ISSN:0148-6055    

DOI:10.1122/1.550637

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Suspensions of fumed silica exhibit a wide range of rheological properties, depending on the type of microstructure present. At high silica concentrations, the rheological behavior is ‘‘gel‐like,’’ due to the formation of a network consisting of interconnected silica flocs. When large amplitude oscillatory preshear is applied on these systems, the network linkages are disrupted, resulting in the formation of isolated flocs. In this study, we focus on the extent to which the network is restored on cessation of preshear. By applying small amplitude oscillations we can study the development of the elastic modulus (G′) with time, following disruptive shear. We find that the restoration of the network after preshear is instantaneous; however,G′ recovers to different levels depending on the amplitude of the imposed preshear strain. Contrary to expectations, larger preshear strains (which cause a greater degree of microstructural disruption) do not always lead to lower levels of recoveredG′. For strains greater than a critical value, the recoveredG′ progressively increases with increasing preshear strain. This anomalous behavior of the elastic modulus is explained in terms of microstructural rearrangements that may occur during oscillatory preshear.

ISSN:0148-6055    

DOI:10.1122/1.550638

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

In this work, slit flow of an electrorheological (ER) fluid is studied via laser Doppler anemometry under nonuniform electric‐field conditions. For that purpose, the electrodes were coated with a PVC foil. Under ac conditions the ER effect with homogeneous coating was smaller than in the case of no coating. Yet, as soon as holes were punched in the foil, the ER effect greatly increased, exceeding the effect of the uncoated electrodes. Irrespective of the type of coating applied, the electric current remained the same. This contrasts with the results under dc conditions where (i) the ER effect with coating (irrespective of the type of coating) was smaller (or even zero) than without coating and where (ii) a decrease of the ER effect always was accompanied by a decrease in electric current. No electric current implied no ER effect, irrespective of the strength of the applied electric field.

ISSN:0148-6055    

DOI:10.1122/1.550639

出版商:The Society of Rheology    

年代:1995

数据来源: AIP