Analysis of rheological properties of fiber suspensions in a Newtonian fluid by direct fiber simulation. Part 3: Behavior in uniaxial extensional flows

The present work presents a predictive direct fiber simulation of fiber suspensions under uniaxial extensional flows by Stokesian dynamics, considering both near- and farfield hydrodynamic intrafiber interactions and lubrication approximation for interfibers. Initially, code validation is performed and simulation predictions compared with experimental data. Afterwards, the orientation tensor under flow is discussed as a function of volume fraction, aspect ratio and flexibility. Based on the results, a general constitutive equation with a proposed parameter is proposed and verified by comparing experimental data of high volume fraction and high aspect ratio systems.     

Simulation of the rheological properties of suspensions of oblate spheroidal particles in a Newtonian fluid

A simulation algorithm was developed to predict the rheological properties of oblate spheroidal suspensions. The motion of each particle is described by Jeffery’s solution, which is then modified by the interactions between the particles. The interactions are considered to be short range and are described by results from lubrication theory and by approximating locally the spheroid surface by an equivalent spherical surface. The simulation is first tested on a sphere suspension, results are compared with known experimental and numerical data, and good agreement is found. Results are then presented for suspensions of oblate spheroids of two mean aspect ratios of 0.3 and 0.2. Results for the relative viscosity η _r, normal stress differences N ₁ and N ₂ are reported and compared with the few available results on oblate particle suspensions in a hydrodynamic regime. Evolution of the orientation of the particles is also observed, and a clear alignment with the flow is found to occur after a transient period. A change of sign of N ₁ from negative to positive as the particle concentration is increased is observed. This phenomenon is more significant as the particle aspect ratio increases. It is believed to arise from a change in the suspension microstructure as the particle alignment increases.     

Numerical analysis of complex flow of fibre suspensions in a viscoelastic fluid

Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids. Though short fibre composites are mostly made of polymers, lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid. This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them. Some numerical results of flow past a sphere in a tube are also presented. This paper is supported by the University of Melbourne, the National Natural Science Foundation of China and Zhejiang Province.     

Stokesian Dynamics simulation of the role of hydrodynamic interactions on the behavior of a single particle suspending in a Newtonian fluid. Part 2. 2D flexible and rigid rings

In this work, a Stokesian Dynamics simulation, which considers deformation due to induced flows, was performed in order to analyze the behavior of a ring-shaped particle in a Newtonian fluid under shear as well as corresponding rheological properties in the absence of Brownian motion. The following results are obtained: (1) the tumbling orbit is kept when ring is rigid, whereas the normal direction of the ring is the independent of the initial state after a large strain when the ring is flexible. (2) When the ring is flexible, there are two states under shear: a stable state, showing a constant tilt angle, and an unstable state, showing a tumbling motion. (3) When the ring is semi-flexible, in steady-state, i.e., after a large strain, a bi-axial nematic phase is predicted when the system is dilute.     

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.     

Numerical simulation of sedimentation of rectangular particle in Newtonian fluid

The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian–Eulerian domain method. The numerical procedure was validated by comparison of the simulation results with existing numerical work. Moreover, good agreement was obtained between the simulation results and experimental measurements performed in the current study. The equilibrium position, stable orientation and drag coefficient of a rectangular particle for different particle Reynolds numbers (Re_p) were studied. The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid. When Re_p is smaller than the critical value, the particle falls with its long side parallel to gravity; otherwise the particle falls with its long side perpendicular to gravity. The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio. The distributions of pressure and shear stress on rectangular particle surface were analyzed. Moreover, the drag coefficient of the rectangular particle decreases as Re_p or the blockage ratio increases; however, it appears to be independent of aspect ratio.     

Some rheological properties of dilute suspensions of polyoxymethylene crystals in p-xylene

Summary Dilute suspensions of polyoxymethylene crystals inp-xylene have been shown to behave as Bingham Plastic Fluids. The crystals are very thin hexagonal platelets and low concentrations are sufficient to provide a continuous high-voidage matrix which requires the application of a finite stress before deformation occurs. The behaviour of the system has been characterised with respect to changes in shear rate, temperature and concentration of suspended polymer.

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Zusammenfassung Es wurde gezeigt, daß sich verdünnte Lösungen von Polyoxymethylen-Kristallen in p-Xylol wie eine Bingham-Flüssigkeit verhalten. Die Kristalle sind sehr dünne hexagonale Plättchen. Niedrige Konzentrationen sind für eine beständige Matrix, die das Aufbringen einer endlichen Spannung erfordert, bevor eine Deformation auftritt, ausreichend. Das Verhalten dieses Systems wurde unter Berücksichtigung von Änderungen der Schergeschwindigkeit, der Temperatur und der Konzentration des suspendierten Polymers charakterisiert.

     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

Stokesian dynamics simulation of the role of hydrodynamic interactions on the behavior of a single particle suspending in a Newtonian fluid. Part 1. 1D flexible and rigid fibers

As seen in textbooks of polymer physics, a linear polymer chain can be modeled as a filament of connected beads. This concept can also be adapted to fibers and, for example, flexible fibers can be modeled by considering a stretch force, bending and torsion torques with a non-slip condition between adjacent beads, following the particle simulation method. In predicting fiber motions and their relating rheological properties, the importance of hydrodynamic interactions should be analyzed, so in this work we study the effect of hydrodynamic interactions on the behavior of a single flexible fiber under shear using Stokesian dynamics simulation with a 11N × 11N mobility matrix, where N is the aspect ratio of the fiber. Our results indicate that hydrodynamic interaction becomes significant when the fiber is highly flexible.     

A comparative study of ECNC and CNC suspensions: effect of salt on rheological properties

This paper addresses the effect of monovalent (Na⁺) and divalent (Ca²⁺) ions on the shear viscosity and viscoelastic properties of two different aqueous suspensions of nanoparticles, cellulose nanocrystals (CNCs), and electrosterically stabilized nanocrystals of cellulose (ECNCs). ECNC is similar as CNC, but with carboxylated cellulose chains protruding from both endcaps. The different suspensions were studied in the semi-dilute regime, which corresponded to concentrations ranging from 0.5 to 8 wt% for CNCs and from 0.6 to 9 wt% for ECNCs. As the charges on CNCs are presumably distributed all along the crystal domains and the CNC have a twist in their backbone structure, their suspensions shifted to a cholesteric state as the volume fraction increased while ECNC suspensions did not. This is because the charges on ECNCs are mainly distributed at the endcaps of the particles and the protruding chains expel each other. On the one hand, it was demonstrated that at moderate ionic strength (I = 20 mM), CNC suspensions formed gels even at really low concentrations due to agglomeration. Calcium chloride (CaCl₂) had a greater effect than sodium chloride (NaCl) on both shear and viscoelastic properties due to stronger network formation. On the other hand, ECNCs could withstand much higher ionic strengths than CNCs. NaCl had no effect other than making the ECNC particles precipitate above a concentration of 200 mM, while CaCl₂ made ECNC suspensions turn into gels due to a bridging effect with their carboxylic acid groups at a concentration of [Ca2+] ≈ [COOH]/2.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

The main purpose of this study was to examine the viscous and elastic properties and capillary flow of fiber suspensions in Newtonian fluids as well as in polymer solutions. The fillers used were glass, carbon, nylon and vinylon fibers. Glycerin was used as a Newtonian suspending medium and HEC and Separan solutions as viscoelastic suspending media. The viscosity and the first normal-stress difference were measured using a coaxial cylindrical rotating viscometer and a parallel-plate rheogoniometer respectively. The influence of the concentration, aspect ratio, diameter and flexibility of the fibers on the viscous and elastic properties of the fiber suspensions was investigated. Empirical equations were obtained for the relative viscosity and first normal-stress difference for the fiber suspensions in glycerin. The capillary flow of these suspensions is discussed in part II.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

The rheological behaviour of Ca(OH)2 suspensions in water

The rheological characteristics of Ca(OH)₂ suspensions are investigated in order to check the elastic floc model for energy dissipation during flow. It is found that the energy, required to overcome the viscous drag experienced by particles moving within flocs, can account for the total energy dissipation.     

Numerical simulation of the motion of neutrally buoyant particles in the plane Poiseuille flow of a Newtonian fluid

In this note we discuss the generalization of a Lagrange multiplier based fictitious domain method to the simulation of migration of neutrally buoyant particles in plane Poiseuille flow of a Newtonian fluid. The migration away from the center of the channel is believed to be an effect of the curvature of the velocity profile. We found this effect is not weakened by the presence of many particles, but instead by the collisions among the particles. Experiments and simulations show that the particles concentrate in the central region where the shear rate is low.     

The indentation of a Newtonian fluid in a finite cylindrical container by a right circular cylinder

The indentation of the free surface of a Newtonian fluid in a finite cylindrical container by a right circular cylinder is considered. It is assumed that weight and inertia effects are negligible compared to viscous effects. A finite difference technique is used to obtain approximate values for initial velocities, pressures, and stresses at any point in the fluid as well as an estimate of the force required to indent the fluid with a given velocity. The solution obtained forms the basis for a primary indenter viscometer for very viscous fluids which have viscosities in the range of 10⁴–10¹⁰ poises.     

Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects

A detailed analysis is carried out of the flow of a Newtonian fluid in the annular region between two infinitely long circular cylinders with parallel axes, resulting from the uniform rotation of one, or both, of the cylinders about their axes. No restriction is placed on the geometry of the system and results are obtained both with the neglect of inertial effects and for the linearized inertial approximation. In both cases, the resultant of the forces exerted by the fluid on the cylinders and the distribution of their normal and tangential components over the cylinders are calculated, and the stream-line patterns are analyzed in some detail. A number of conditions, under which stagnation points, separation points and eddies can exist, are established.     

The translation of a Newtonian droplet in a 4-constant Oldroyd fluid

The viscoelastic correction to the Hadamard—Rybczynski terminal velocity was calculated for the retarded motion translation of a finite viscosity Newtonian droplets in a 4-constant Oldroyd fluid. The droplet translational velocity can be enhanced or hindered relative to the Hadamard—Rybczinski value depending upon the degree of shear thinning, and elongational and memory effects in the viscoelastic fluid. Specifically, it is found that for a large droplet viscosity, for which surface mobility is negligible, shear thinning and fluid memory enhance translational motion. At the other extreme, when the droplet surface is very mobile (i.e. for gas bubbles) the translational velocity can be enhanced or hindered relative to the Hadamard—Rybczynski value depending on the relative influence of the memory and the elongational properties of the viscoelastic phase.     

Newtonian and Power-Law fluid flow in a T-junction of rectangular ducts

The aim of the present study is the numerical investigation of the shear-thinning and shear-thickening effects of flow in a T-junction of rectangular ducts. The employed CFD code incorporates the SIMPLE scheme in conjunction with the finite volume method with collocated arrangement of variables. The code enables multi-block computations in domains with multiple apertures, thus coping with the two-block, two-outlet layout of the current 3D computational domain. The shear-thinning and shear-thickening behaviours of the flow are covered by changing the index n of the Power-Law model within a range from 0.20 to 1.25, and the subsequent effects are investigated by means of different flow parameters namely the Reynolds (Re) number and the boundary conditions at the outlets. Results exhibit the extent of the effect of the Re number on the velocity profiles at different positions in the domain for both Newtonian and non-Newtonian cases. Similarly, the trend of the effect of shear-thinning and shear-thickening behaviours on the flow rate ratio between inlet and outlets, in the case of equal pressure imposed on outlets, is shown.