Sedimentation of particles in shear flows of viscoelastic fluids

An experimental investigation of sedimentation of single particles and concentrated suspensions in Couette flows of viscous and viscoelastic fluids is presented. With the passage from viscous to viscoelastic fluids, a slowing down of the sedimentation was observed. The sedimentation of suspensions in viscoelastic fluids accelerated with increase in the suspension concentration. The development of instabilities during the sedimentation was detected.     

Viscous dissipation with fluid inertia in oscillatory shear flow

For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry.     

Dispersion of linear gravity waves on a viscoelastic fluid in an horizontal canal

A characteristic equation is derived that describes the spatial decay of linear surface gravity waves on Maxwell fluids. Except at small frequencies, the derived dispersion relation is different from the temporal decay dispersion relation which is normally studied within fluid mechanics. The implications for waves on viscous Newtonian fluids using the two different dispersion relations is briefly discussed. The wave number is measured experimentally as function of the frequency in a horizontal canal. Seven Newtonian fluids and four viscoelastic liquids with constant viscosity have been used in the experiments. The spatial decay theory for Newtonian fluids fits well to the experimental data. The model and experiments are used to determine limits for the Maxwell fluid time numbers for the four viscoelastic liquids. As a result of low viscosity it was not possible within this study to obtain these time numbers from oscillatory experiments. Therefore, a comparison of surface gravity wave experiments with theory is applicable as a method to evaluate memory times of low viscosity viscoelastic fluids.     

Aging, rejuvenation, and thixotropy in yielding magnetorheological fluids

The yielding behavior of dilute magnetorheological (MR) fluids has been investigated using creep–recovery tests. At very low stress levels, MR fluids behave in the linear viscoelastic regime as demonstrated by the fact that the instantaneous strain equals the instantaneous (elastic) recovery. In this region, gap-spanning field-induced structures support the stress levels applied. Upon increasing the stress value, the MR fluid evolves towards a nonlinear viscoelastic response. Here, the retarded elastic and viscous strain decrease, and the plastic contribution to the instantaneous strain grows probably due to the appearance of unattached field-induced structures. A larger stress value results in a viscoplastic solid behavior with negligible retarded and viscous strain and a fully plastic instantaneous strain. Finally, a plastic fluid behavior is found when the stress value is larger than the so-called yield stress. MR fluids exhibit an intermediate behavior between non-thixotropic (simple) and highly thixotropic model yield stress fluids.     

Separating forces in blade coating of viscous and viscoelastic liquids

Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A single simple geometry, a blade over a rotating roll, is considered. A perturbation solution to the Navier-Stokes equations yields a lubrication theory with first order corrections for curvature and inertia. A numerical solutions by the Finite Element Method (FEM) is compared to the analytical solutions. For Newtonian fluids, agreement between these mathematical models, and data on blade loading, is quite good.The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power law model. The zeroth-order (lubrication) equations are solved by the method of Steidler and Horowitz, and predictions for coating thickness and blade loading agree quite well with those obtained from a FEM solution of the full equations of motion for a power law fluid. Data on blade loading, obtained using a strongly elastic polymer solution, are compared to these mathematical models, and discrepancies are noted.     

The dynamics and dissolution of gas bubbles in a viscoelastic fluid

This paper reports an experimental study of the motion of dissolving and non-dissolving gas bubbles in a quiescent viscoelastic fluid. The objective of the investigation was to determine the influence of the abrupt transition in bubble velocity, which had been observed at a critical radius of approx. on the rate of mass transfer. Thus, a range of bubble sizes from an equivalent (spherical) radius of 0.2–0.4 cm was employed using CO₂ gas, and five different fluids, including one Newtonion glycerine/water solution and four viscoelastic solutions of Separan AP30 in water (0.1, 0.5, 1% by weight) and in a water/glycerine mixture.The experimental data on bubble velocity shows that the discontinuous increase with bubble volume observed previously for air bubbles in viscoelastic fluids, does not occur for dissolving CO₂ bubbles—presumably due to the continuous decrease in bubble volume. Instead, a very steep but definitely continuous transition is found. Mass transfer rates are found to be significantly enhanced by viscoelasticity, and comparison with available theoretical results shows that the increase is greater than expected for purely viscous, power-law fluids. We conclude that a fully viscoelastic constitutive model would be necessary for a successful analysis of the dissolution of a gas bubble which is translating through a (high molecular weight) polymer solution.     

Linear viscoelastic analysis using frequency-domain algorithm on oscillating circular shear flows for bubble suspensions

To achieve a stable evaluation of the linear viscoelasticity of bubble suspensions, which have difficulties for conventional rheometers from spatial distributions of rheological properties with bubble deformations, we proposed a novel rheometry based on spatio-temporal velocity data obtained by ultrasonic velocity profiling (UVP). A frequency-domain algorithm was adopted to overcome a critical influence of measurement noise on the rheological assessment, which is inferred from error propagation characteristics through the equations of motion in discretized form. Applicability and advantage of the present rheometry with the frequency-domain algorithm were verified by two kinds of fluids: high viscous oil as a Newtonian fluid and polyacrylamide aqueous solution as a shear thinning, viscoelastic fluid. The rheometry was finally adopted for bubble suspensions subject to high oscillatory shear, and it could validly extract elasticity-originated momentum transfer as a function of space.     

Modeling and simulation of three‐dimensional extrusion swelling of viscoelastic fluids with PTT,Giesekus and FENE‐P constitutive models

The investigation of the extrusion swelling mechanism of viscoelastic fluids has both scientific and industrial interest. However, it has been traditionally difficult to afford theoretical and experimental researches to this problem. The numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three‐dimensional extrusion swelling of viscoelastic fluids flowing through out of a circular die. The rheological responses of viscoelastic fluids are described by using three kinds of differential constitutive models including the Phan‐Thien Tanner model, the Giesekus model, and the finite extensible nonlinear elastic dumbbell with a Peterlin closure approximation model. A streamface‐streamline method is introduced to adjust the swelling free surface. The calculation stability is improved by using the discrete elastic‐viscous split stress algorithm with the inconsistent streamline‐upwind scheme. The essential flow characteristics of viscoelastic fluids are predicted by using the proposed numerical method, and the mechanism of swelling phenomenon is further discussed.Copyright © 2013 John Wiley & Sons, Ltd.     

Flow of a mixture of a viscous fluid and a granular solid in an orthogonal rheometer

In this paper, we study the flow of a linearly viscous fluid and a granular solid, consisting of many particles, situated between two parallel plates rotating about different axes. Flow in orthogonal rheometers has been studied for many viscoelastic fluids so that their rheological properties can be measured. The mixture is modeled using the theory of interacting continua, and constitutive relations for the fluid phase, the granular phase, and the interaction forces are provided. For a very special case, an analytical solution to the equations of motion is also provided.     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.