A differential model for the rheological properties of concentrated suspensions with weakly viscoelastic matrices

A model for the rheological properties of a concentrated suspension in weakly viscoelastic fluid matrices is proposed. The model is derived according to the Roscoe differential procedure described in 1952. The analytical results produced recently by Greco et al. (J Non-Newton Fluid Mech 147:1–10, 2007) and Housiadas and Tanner (J Non-Newton Fluid Mech 162:88–92, 2009) for dilute suspensions of neutrally buoyant, non-Brownian rigid spheres in weakly viscoelastic matrix fluids are the key results which are used as a base to predict the properties of concentrated suspensions. The results are compared with the few available experimental data from the literature, showing promising trends for the viscometric properties of the suspensions. In particular, one sees the rapidly increasing value of −N₂/N₁ as concentration increases.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Rheological properties and percolation in suspensions of multiwalled carbon nanotubes in polycarbonate

This paper is concerned with several issues related to the rheological behavior of polycarbonate/multiwalled carbon nanotube nanocomposites. The composites were prepared by diluting a masterbatch of 15 wt.% nanotubes using melt-mixing method, and the dispersion was analyzed by SEM, TEM, and AFM techniques. To understand the percolated structure, the nanocomposites were characterized via a set of rheological, electrical, and thermal conductivity measurements. The rheological measurements revealed that the structure and properties were temperature dependent; the percolation threshold was significantly lower at higher temperature suggesting stronger nanotube interactions. The nanotube networks were also sensitive to the steady shear deformation particularly at high temperature. Following preshearing, the elastic modulus decreased markedly suggesting that the nanotubes became more rigid. These results were analyzed using simple models for suspensions of rod-like particles. Finally, the rheological, electrical, and thermal conductivity percolation thresholds were compared. As expected, the rheological threshold was smaller than the thermal and electrical threshold.     

Effect of temperature on rheological properties of suspensions

A parameter, the product of viscosity of the suspension medium and applied shear rate, is introduced to describe the effect of temperature on the rheological properties of suspensions, considering the mechanism of agglomeration in suspensions. It is found that, by plotting rheograms of the shear stress versus this parameter, a single master curve can be obtained independently of temperature. The dependence of viscosity on temperature and the flow of suspensions are shown to be well described.     

Nonlinear rheology of concentrated spherical silica suspensions: 3. Concentration dependence

Nonlinear rheology was examined for concentrated suspensions of spherical silica particles (with radius of 40 nm) in viscous media, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture and pure ethylene glycol. The particles were randomly and isotropically dispersed in the media in the quiescent state, and their effective volume fraction φ_eff ranged from 0.36 to 0.59. For small strains, the particles exhibited linear relaxation of the Brownian stress σ_B due to their diffusion. For large step strains γ, the nonlinear relaxation modulus G(t,γ) exhibited strong damping and obeyed the time-strain separability. This damping was related to γ-insensitivity of strain-induced anisotropy in the particle distribution that resulted in decreases of σ_B/γ. The damping became stronger for larger φ_eff. This φ_eff dependence was related to a hard-core volume effect, i.e., strain-induced collision of the particles that is enhanced for larger φ_eff. Under steady/transient shear flow, the particles exhibited thinning and thickening at low and high γ˙, respectively. The thinning behavior was well described by a BKZ constitutive equation using the G(t,γ) data and attributable to decreases of a Brownian contribution, σ_B/γ˙. The thickening behavior, not described by this equation, was related to dynamic clustering of the particles and corresponding enhancement of the hydrodynamic stress at high γ˙. In this thickening regime, the viscosity growth η₊ after start-up of flow was scaled with a strain γ˙t. Specifically, critical strains γ_d and γ_s for the onset of thickening and achievement of the steadily thickened state were independent of γ˙ but decreased with increasing φ_eff. This φ_eff dependence was again related to the hard-core volume effect, flow-induced collision of the particles enhanced for larger φ_eff. Received: 26 June 1998 Accepted: 9 December 1998     

Effect of poly(ethylene oxide) on the rheological behavior of silica suspensions

The steady-shear viscosity, dynamic viscoelasticity, and sedimentation behavior were measured for silica suspensions dispersed in aqueous solutions of poly(ethylene oxide) (PEO). For suspensions prepared with polymer solutions in which the transient network is developed by entanglements, the viscosity at a given shear rate decreases, shows a minimum, and then increases with increasing particle concentration. Because the suspensions are sterically stabilized under the conditions where the particle surfaces are fully covered with by a thick layer of adsorbed polymer, the viscosity decrease can be attributed to the reduction of network density in solution. But under the low coverage conditions, the particles are flocculated by bridging and this leads to a viscosity increase with shear-thinning profiles. The polymer chains with high molecular weights form flexible bridges between particles. The stress-dependent curve of storage modulus measured by a stress amplitude sweep shows an increase prior to a drastic drop due to structural breakdown. The increase in elastic responses may arise from the restoring forces of extended bridges with high deformability. The effect of PEO on the rheological behavior of silica suspensions can be explained by a combination of concentration reduction of polymer in solution and flocculation by bridging.     

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.     

Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions

The overall objective is to present a procedure based on a Couette analogy to quantitatively analyse torque/rotor speed data and extract viscosity/shear-rate curves using a non-conventional geometry. Diphasic flows of energetic concentrated suspensions of melt-cast insensitive explosives exhibit particular rheological properties. The characterization of these complex fluids may be a challenging task when conventional rheometers are used. Placing these dense suspensions in a classic cylindrical geometry may lead to a partial destruction of the internal fluid structure. To prevent that, a “RheoXF” a mixer-type rheometer has been developed: it consists of a mixing device with quite a complex geometry rotating in a cylindrical tank. To evaluate the rheological constants (virtual radius, virtual shear rate and stress constants) of thus mixing rheometer, we used five Newtonian fluids. After this calibration, the rheological characterizations were carried out on five formulations. The unique parameter which changes in these formulations is the batch's origin of a secondary explosive: the 3-nitro-1,2,4-triazole-5-one. These energetic particles differ by their morphology, maximum packing density and may be by their process synthesis. After having determined pseudoplastic parameters, a correlation has been made with the evolution of maximum packing density values calculated with De Larrard model.     

Dynamic rheological properties of a fumed silica grease

The thermo-rheological characteristics of a fumed silica lubricating grease in linear and nonlinear oscillatory experiments have been investigated. The material rheological behavior represents a soft solid being thermo-rheologically complex. There is an abnormal temperature dependency in the range of ??10 to 10 °C which is related to the phase transition of the base oil. The dynamic moduli data in linear viscoelastic envelop (LVE) have been modeled using mode-coupling theory (MCT) in the whole temperature range. Two main relaxation mechanisms can be identified through linear and nonlinear viscoelastic properties related to interaction of the primary particle and its neighbor particles as well as a slow relaxation process which represents the escape of this particle from its “cage”. Finally, it is demonstrated that the dominant yielding process in large amplitude oscillatory experiments can be explained based on either particle cage rupture (consistent with MCT framework) or particle “hopping” out of its cage proposed in soft glassy rheology (SGR) model. It will be discussed that the governing mechanism depends on the applied frequency.     

Rheological properties of concentrated latex suspensions of poly(styrene-butadiene)

Concentrated suspensions of charged latex particles of poly(styrene-butadiene) have been used as model systems to investigate the influence of surface charges on the rheology of colloidal suspensions. The suspensions were found to behave as elastic solids at small strains and to require a finite stress to flow. This was related to an ordered structure of the suspensions at rest, resulting from electrostatic and van der Waals forces. Important shear-thinning effects were observed as a consequence of structure rearrangements under shear. At a fixed shear rate, the steady-shear viscosity as a function of the ionic strength exhibits a minimum. Under oscillatory shear flow, the behavior of the concentrated suspensions was found to be non-linear above a very small strain amplitude. The non-linear output signal from dynamic experiments was analyzed using a fast Fourier transform algorithm. A maximum in the third harmonic intensity as a function of the strain amplitude was observed and the intensity of higher harmonics decreased with increasing ionic strength. The behavior of the suspensions could be adequately described using the structural model of Yziquel et al. (Yziquel F, Carreau PJ, Moan M, Tanguy PA (1999) Rheological modeling of concentrated colloidal suspensions. J Non-Newtonian Fluid Mech 86:133–155).     

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.

     

Lithium-storage properties of SiO2 nanotubes@C using carbon nanotubes as templates

Silica-based anode material is the most concerned material at present, which has the advantages of good cycle stability, high theoretical specific capacity and abundant reserves. However, silica suffers from inherent low conductivity, severe volume expansion effect and low initial coulombic efficiency, which limits its application in lithium-ion batteries. Nanotubes structure can mitigate the volume expansion during lithiation/delithiation. In this article, silica nanotubes (SNTs) were prepared using carbon nanotubes (CNTs) as a template, and then the uniform carbon layer was coated on their surface by carbonization of citric acid. The hollow structure of nanotubes provides more sites for the insertion of Li⁺ during lithiation and additional channels for Li⁺ migration in the cycles, which improves the electrochemical performance. Conductivity can be enhanced by coating carbon layer. The specific capacity of the composite material is about 650 mAh g⁻¹ at 0.1 A g⁻¹ after 100 cycles. With a specific capacity of 400 mAh g⁻¹ even at 1 A g⁻¹ after 100 cycles. The silica-based material is a competitive anode material for lithium-ion batteries.     

Free-surface flow of concentrated suspensions

Free-surface flows of concentrated suspensions exhibit many interesting phenomena such as particle segregation and surface corrugation. In this work the flow structures associated with free-surface has been studied experimentally. The free-surface velocity for neutrally buoyant suspension of uniform spheres in a gravity driven inclined channel flow was determined by particle imaging velocimetry (PIV) technique. Experiments were carried out for concentrated suspensions with particle fractions ? ranging from 0.40 to 0.50. The measured velocities show blunted profile in the channel. The blunting of the velocity profile increases with the particle concentration. The rms velocity fluctuations measured at the free-surface progressively increase with particle fraction ? and are linear in shear rate γ. The surface roughness were characterized by analyzing the power spectral density of the refracted light from the free-surface. The characteristics observed are in support of earlier findings.     

Linear and non-linear rheological behaviour of cement and silica suspensions. Effect of polymer addition

Oil well cement pastes and model silica suspensions demonstrate similar rheology: in oscillatory shear, beyond a critical stress, a sharp transition is ob- served between gel and liquid behaviour. In creep tests, an apparent yield stress and shear-thinning are followed by the appearance of shear thickening. The minimum viscosity measured in steady shear is close in value to the complex viscosity obtained from oscillatory measurements. The observations can be explained by the formation of liquid trapping aggregates whose compactness may be estimated by fitting the Tsenoglou model, and whose cohesion is reflected in the rigidity of the gel and in the critical strain (or stress) of gel dissolution. Substituting cement or silica particles by polymer redispersible powder causes a decrease of the storage modulus in the gel state and a lower viscosity, while leaving the general features of the flow curve unchanged. Decrease in material rigidity may be due to a weaker inter-particle attraction generated by the polymer presence. The decrease in viscosity is explained by a lessening of water entrapped within the aggregates, which now contain polymer particles which are less hydrophilic than either cement or silica.     

Heat conductivity of concentrated suspensions

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 94–97, November–December, 1990.     

Effects of temperature change on the rheological property of modified multiwall carbon nanotubes

Applied Mathematics and Mechanics - Solvent-free nanofluids hold promise for many technologically significant applications. The liquid-like behavior, a typical rheological property of solvent-free...     

Predicting the elastic properties of single-walled carbon nanotubes

Advances in the prediction of the mechanical properties of single-walled carbon nanotubes (SWNTs) are reviewed in this paper. Based on the classical Cauchy-Born rule, a new computational method for the prediction of Young's modulus of SWNTs is investigated. Compared with the existing approaches, the developed method circumvents the difficulties of high computational efforts by taking into consideration of the microstructure of nanotube and the atomic potential of hydrocarbons. Numerical results of Young's modulus and its variation with respect to the deformation gradient tensor are given and discussed. The results obtained are in good agreement with those obtained by laboratory experiments and other numerical methods.     

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.     

Viscosity of concentrated noncolloidal bidisperse suspensions

At the same solid volume fraction (Φ) the relative viscosity (η _r ) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension. In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method. In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction Φ _m which depends upon both the diameter ratio (λ) of large to small particles and the volume fraction of large particles (ξ=Φ _l /Φ). This model shows that at high solid volume fraction, Φ > 0.40, both λ and ξ significantly influence η _r . For example, at Φ=0.5, it predicts that for monodisperse suspensions η _r =70, while for bidisperse suspensions (λ=2 and ξ=0.7) η _r =40. Comparison shows that, at high solid volume fraction (0.4–0.5), the relative viscosity predicted by this model is in good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than that predicted by the work of others. Received: 27 February 2001 Accepted: 25 April 2001