Transient Shear Flow Research Articles

Transient shear flow of model lithium lubricating greases

This paper deals with the analysis of the transient shear flow behavior of lithium lubricating greases differing in soap concentration and base oil viscosity. The shear-induced evolution of grease microstructure has been studied by means of stress-growth experiments. With this aim, different lubricating grease formulations were manufactured by modifying the concentration of lithium 12-hydroxystearate and the viscosity of the base oil, according to a RSM statistical design. Moreover, atomic force microscopy (AFM) observations were carried out. The transient stress response can be successfully described by the generalized Leider-Bird model based on two exponential terms. Different rheological parameters, related to both the elastic response and the structural breakdown of greases, have been analysed. In this sense, it has been found that the elastic properties of lithium lubricating greases were highly influenced by soap concentration and oil viscosity. The stress overshoot, τ max , depends linearly on both variables in the whole shear rate range studied, although the effect of base oil viscosity on this parameter is opposite at low and high shear rates. Special attention has been given to the first part of the stress-growth curve. In this sense, it can be deduced that the “yielding” energy density not only depends on grease composition, but also on shear rate. Moreover, an interesting asymptotic tendency has been found for both the “yielding” energy density and the stress overshoot by increasing shear rate. The asymptotic values of these parameters have been correlated to the friction coefficient obtained in a ball-disc tribometer.

A mesoscopic tube model of polymer/layered silicate nanocomposites

Rheology of isothermal suspensions of completely exfoliated silicate lamellae in polymer melts is investigated. In order to express more faithfully the physics involved in low shear rates and low frequencies, we model the polymer molecules composing the melt as chains whose motion is confined to a tube formed by surrounding chains and lamellae. In the absence of lamellae, the model reduces to the mesoscopic model of reptating chains developed in Eslami and Grmela (Rheol Acta, 2008). If the chains are seen only as FENE-P dumbbells, the model reduces to the model developed in Eslami et al. (J Rheol 51:1189–1222, 2007). Responses to oscillatory, transient, and steady shear flows are calculated and compared with available experimental data. Particular attention is payed to the region of low shear rate and low frequency.

Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow

The deformation and orientation of droplets during transient shear flow is studied in a counterrotating device using microscopy. The effect of the degree of confinement and viscosity ratio is systematically investigated. The system consists of polydimethylsiloxane droplets of varying sizes and viscosities dispersed in a polyisobutylene matrix. The observations are compared with the predictions of an adapted version of the Maffettone and Minale model [Maffettone, and Minale, J. Non-Newtonian Fluid Mech. 78, 227–241 (1998)] which includes confinement effects [Minale, Rheol. Acta 47, 667–675 (2008)]. For flow start-up at low capillary numbers, the deformation of confined droplets and their orientation towards the flow direction are increased with respect to the unconfined situation for all viscosity ratios under investigation. The confined model results for start-up and the experimental data at low capillary numbers are in good agreement both showing similar monotonous transients. At high degrees of confinem...

Rheometric investigation on the temporal shear thickening of dilute micellar solutions of C14‐, C16‐, and C18TAB∕NaSal

The rheological behavior and especially the rheopexy phenomena of dilute self-assembled solutions in the presence of a counterion are examined in stationary and transient shear flows. In the first part, a continuous and gradually increasing strain is applied on the same sample. We study the effect of the initial shear rate, the temporal variation of the viscosity, and the hysterisis between charge and discharge curves. The results show that the properties of shear thickening are independent of the initial shear rate. In the second part, fresh samples are successively subjected to increasing shear strains; this method allows us to follow the evolution of the rheological characteristics during long measuring durations and gives us a distinct picture of the behavior per shear rate. In both cases, we confirm that the chain length has a strong influence on the emergence and amplitude of the shear thickening. It was also found by studying the start-up flow behavior that the structure at equilibrium is composed of bigger structures for longer chain lengths. The maximum of the viscosity in the shear thickening transition occurs in a range of lower shear rates when enough time is given to the system to undertake the formation of the shear induced structure. Considering this result, we introduce the concept of “temporal shear thickening transition.”

Numerical solution of the Fokker–Planck equation for fiber suspensions: Application to the Folgar–Tucker–Lipscomb model

The probability distribution function for fiber orientation under flow (Fokker–Planck equation) is numerically solved using a finite volume method. Different time and spatial schemes have been tested to reduce considerably the computational time and to cover a wide range of the Peclet ( Pe) number. For Pe ≤ 10 3, the results are compared with data available in the literature and for Pe ≥ 10 3, the numerical schemes are assessed using an analytical solution. Excellent agreement was observed and the method allowed us to describe the evolution of the fourth-order orientation tensor components of fibers in transient simple shear (forward and reverse) flows, and compare with the predictions of an orthotropic closure approximation. In addition, the Folgar–Tucker–Lipscomb (FTL) model was used with no closure approximation to predict the rheological behavior of a short fiber-filled polypropylene in simple shear flow. The accuracy of commonly used closure approximations is discussed, and key aspects of the FTL model that still need to be improved are highlighted in the scope of this work.

Power law gels at finite strains: The nonlinear rheology of gluten gels

Many complex fluids exhibit power-law responses in their relaxation modulus; examples include foods, soft solids, fractal gels, and other polydisperse systems. In the present study we investigate the rheological characteristics of such materials beyond the linear regime using a gluten-water gel as a prototypical system. The material functions of gluten dough under finite strains can be described by combining the linear viscoelastic response of a critical gel [Chambon, and Winter, J. Rheol. 31, 683–697 (1987)] with a Lodge rubberlike network to develop a frame invariant constitutive equation [Winter and Mours, Adv. Polym. Sci. 134, 165–233 (1997)]. This generalized gel equation is a simple but accurate description of the material functions in the linear regime and also at large strains, using only two parameters. We compare the model predictions with experimental measurements in transient shear and elongational flows of gluten gels over a wide range of deformation rates. An essential feature of both the ex...

Rheology modification in mixed shape colloidal dispersions. Part II: mixtures.

We report the results of a comprehensive study of the rheological properties of a series of mixed colloid systems where the shape of one of the components has been varied systematically. Specifically we have measured the oscillatory, transient (creep) and continuous steady shear flow behaviour of a 2.5 wt% dispersion in water of a well-characterised hectorite clay modified by the addition of a series of aluminasol colloidal particles whose shape varies systematically from rod (boehmite) to platelet (gibbsite) to sphere (alumina-coated silica), all having essentially the same smallest dimension, which is similar to that of the hectorite. The particle characterisation and rheological properties of the pure components have recently been reported in Part I of this series (Soft Matter, 2007, 3, 1145). The mixtures show the same general behaviour as the pure systems, displaying a complex 'yield space' transition from an elastoviscous gel at low applied stresses to a viscous, weakly elastic, shear-thinning liquid at high stresses. The unifying theme of this work is that the addition of 0.25 wt% of the minor component in all cases results in dramatic enhancements to the dispersion rheological properties. At the same time the magnitude of this effect depends on the shape of the particles. Shear moduli, low stress viscosities and effective yield stresses all increase in the additive order rods < platelets < spheres, with enhancements for the latter being up to a factor of 500 and typically 20. At the same time the critical failure strains for the gels decreased in the same order - the strongest gels are also the most fragile in this sense. The physicochemical factors underlying this behaviour are discussed and a simple qualitative model described. While no complete explanation or model can be proposed at this stage, the study provides a quantitative model-system baseline for mixed colloidal dispersions already used for industrial applications (e.g. oilwell-drilling fluids) and suggests ways in which such fluids may be optimised and controlled.

Experimental and Theoretical Study on Shear Flow Behavior of Polypropylene/Layered Silicate Nanocomposites

Polypropylene/layered silicate nanocomposites containing maleic anhydride grafted polypropylene were prepared by melt compounding and their rheological behavior was investigated in shear flow. Transient and steady shear flows were simulated numerically by using the K-BKZ integral constitutive equation along with experimentally determined damping functions under dynamic oscillatory and step strain shear flows. Nonlinear shear responses were predicted with the K-BKZ constitutive equation using two different damping functions such as the Wagner and PSM models. It was observed that PP-g-MAH compatibilized PP/layered silicate nanocomposites have stronger and earlier shear thinning and higher steady shear viscosity than pure PP resin or uncompatibilized nanocomposites at low shear rate regions. Strong damping behavior of the PP/layered silicate nanocomposite was predicted under large step shear strain and considered as a result of the strain-induced orientation of the organoclay in the shear flow. Steady shear viscosity of the pure PP and uncompatibilized nanocomposite predicted by the K-BKZ model was in good agreement with the experimental results at all shear rate regions. However, the model was inadequate to predict the steady shear viscosity of PP-g-MAH compatibilized nanocomposites quantitatively because the K-BKZ model overestimates strain-softening damping behavior for PP/layered silicate nanocomposites.

A mesoscopic rheological model of polymer/layered silicate nanocomposites

A mesoscopic rheological model is proposed for polymer/layered silicate nanocomposites. The conformation tensors c and a are chosen to characterize states of macromolecules and silicate layers (plates), respectively. In the absence of the plates, the model reduces to the well known FENE-P model. The predictions of the model are shown to agree with thermodynamics. Other predictions of the model, obtained by solving numerically its governing equations, are responses of the suspension to transient (start-up and relaxation) and steady shear flows. The results show that the model predictions cover a wide range of the rheological behavior generally observed for polymer/layered silicate nanocomposites.

A thermodynamically consistent model for the thixotropic behavior of concentrated star polymer suspensions

Concentrated multiarm star polymer solutions are used in this work as prototype, well defined, systems that clearly exhibit viscoplasticity and thixotropy. A thermodynamically consistent approach is used here to develop a continuum rheological model for these systems that is novel for thixotropic systems and has considerable advantages over previously postulated models: The basic rheological model is constructed from the beginning in a materially objective and flow type-independent form, in contrast to previous continuum models for thixotropy that typically are suitable only for shear flows. It is also consistent with non-equilibrium thermodynamics. The model is based on a Johnson–Segalman viscoelastic constitutive equation with a variable non-affine parameter. The non-affine parameter is considered representative of the structure and the aggregations between the particles in the system: as the deformation rate increases, those aggregations are assumed to be destroyed more and more, thus leading to discontinuities in the uniform viscoelastic deformation of the constituent multiarm polymer particles. This is described phenomenologically in the proposed model by a consistent increase in the non-affine parameter value from zero, which was taken to represent the virgin structure (where the deformation was assumed to be perfectly affine), to a maximum value at high rates, representing a concentrated suspension of viscoelastic particles. Simultaneously to those changes in the non-affine parameter, which are described by an empirical kinetic equation, the characteristic relaxation time of the system is also assumed to change dramatically: from infinity, at static equilibrium, to a minimum value characterizing the residual viscoelasticity of the fully broken-down medium. This behavior is modeled by assuming the relaxation time to be inversely proportional to the non-affine parameter. In addition to this viscoelastic contribution to the stress, a purely viscous contribution is considered modeled by a standard power law expression of the rate of strain. The model has been applied to transient and steady simple shear flows. The results show good semi-quantitative agreement with the experiments performed with the model multiarm star polymers.

On the predictive/fitting capabilities of the advanced differential constitutive equations for linear polyethylene melts

This contribution examines the capabilities of three differential constitutive models (XPP, PTT-XPP, and modified Leonov) in predicting rheological properties of two virtually linear polyethylene materials (HDPE Tipelin FS 450-26, mLLDPE Exact 0201) with specific attention to both steady as well as transient shear and uniaxial elongational flow situations. For each situation the (dis)advantages of the individual models are discussed and both, qualitative and quantitative model efficiency evaluation has been carried out.

Effect of reactive compatibilization on droplet coalescence in shear flow

The evolution of the morphology of blends of polyethylene and polyamide with a droplet–matrix morphology, generated by transient shear flows, has been determined using a method based on quenching following deformation of the samples kept between the parallel plates of a rheometer. Droplet size evolution and transient viscosity of blends compatibilized with different amounts of polyethylene-graft-maleic anhydride were measured as a function of the total strain. The effects of applied shear rates and concentration of the reactive compatibilizer were investigated. The results indicate that initially the droplet size was governed by coalescence, whereas, when the droplet size became comparable to the break-up limit, no further significant increase was observed at large strain values. A significant coalescence inhibition was only observed when a relatively high amount of compatibilizer was used. This corresponded to an important interfacial coverage of the interface by the grafted copolymer chains. In that situation, the intensity of the coalescence became independent of the applied shear rate. On the contrary, the coalescence was favoured by the absence of compatibilizer or the use of a low compatibilizer concentration and increased with increasing shear rate. The rather “complex” effect of the compatibilizer addition on coalescence phenomena has been analyzed in terms of blend microstructure changes induced by the compatibilizer addition in relation to droplet collision frequency. Predictions of the droplet size evolution and viscosity under transient shear flows using a modified version of Lee and Park model is shown to describe the coalescence and break-up phenomena under large deformation shear flow. The predictions of the droplet size evolution are greatly improved when an additional parameter for non-affine deformation (slip parameter), is introduced in the model. On the other hand, the predictions are much less satisfactory for the transient viscosity data.

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.

Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow

Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the e...

Revisitation of PTT model

Nearly 30 years ago the PTT constitutive equation for molten polymers and solutions was published, and since then it has been widely used. In the intervening time much progress has been made in polymer science and mechanics, especially via network and tube theories. It is natural to unite these points of view in a revisitation of PTT-type models. We show that a new improved form of the PTT model, called the PTT-X model, can closely describe, in particular, the rheological behaviour of low-density polyethylene in (steady and transient) shear and elongational flow and in recoil from an elongational stretch. The results of an attempt to reduce the number of parameters are also described and we place the new model within the context of general network theory and tube theory.

Influence of shear and orthogonal vibration on semisolid aluminum flow properties

Understanding flow properties and flow effects of liquid and semisolid aluminum became a key solution for know-how of the casting processes. It is essential to find and study a new solution of interactive and efficient structure control of processed aluminum suspension. This task was solved by an adaptation of an electromagnetic actuator and high-resolution tempering unit to a conventional rotational rheometer. Initially, the research reveals a precise detection of transition temperatures in steady and transient shear flow. It was found that superposition of mechanical vibration orthogonal to the shear flow radically decreases shear viscosity of semisolid slurry. However, liquid state rheological properties show structural behavior, but stayed insensitive to mechanical oscillations. Analysis of boundary conditions before fundamental experiment shows that no considerable side effects were present during the experiment under vibration. The study reveals transition of strongly shear-thinning concentrated aluminum suspension to almost Newtonian fluid under vibration in shear flow. It is recommended to relate such phenomenon to non-equilibrium between structure formation and structure break-up under vibration and hydrodynamic forces of shear flow. The results illustrate how sensitive the structure of slurry is to vibration in general and in particular during the solidification phase. The revealed results provide a solid basis for further fundamental investigations.

Rheological Properties of Shear-Induced Structure in CTAB/NaSal Aqueous Solution-Viscosity and Elasticity Change under Start-up Flows-

Start-up shear flow was applied to CTAB/NaSal aqueous solutions which form wormlike micelles, and transient behaviors of viscosity and first normal stress difference were observed. In the transient shear flow, the shear-induced structure, SIS, was generated and strongly affected the flow properties. The maximum value of viscosity in the transient flow suddenly increased once the SIS appeared up to 40 times as high as the complex viscosity measured under oscillatory shear flow. The coefficient of first normal stress difference also increased by the appearance of SIS. Thus, SIS showed not only high viscosity but also strong elasticity. At low shear rates, the strain value at the viscosity maximum was smaller than that at the first normal stress difference maximum. With increasing shear rates, this difference in the two strains became smaller and dimmish when the flow instability was observed. Weissenberg number, a ratio of the first normal stress difference to the shear stress, was evaluated as a function of strain, which showed a sudden increase just before the flow-instability. These findings are influenced by the geometry used to generate shear flows. In the concentric cylindrical geometries, SIS was observed at shear rates lower than in the cone-plate and the parallel plate geometries.

Stress overshoots of organoclay nanocomposites in transient shear flow

Forward and reverse stress growth experiments have been conducted on polypropylene/organoclay nanocomposites containing the same clay loading but characterized by different microstructures. Stress overshoots have been observed for the initial start-up experiments and for the following reverse start-up experiments after a certain rest time. The amplitude of these overshoots increased with the applied shear rate and rest time, but the overshoots occurred at the same strain of about 1.7. The overshoots are related to the structure of the nanocomposites, in particular the magnitude of the overshoots increased with the degree of the clay exfoliation in the matrix. Two models, initially developed for colloidal suspensions and fiber suspensions, have been used to describe the observed phenomena. The overshoots are fairly well predicted by the first (structure network) model and explained by the competing effects of the structure breakdown under flow and reorganization during rest time. However, the model predicts that the shear stress following the overshoot decreases and reaches steady-state too rapidly. The second model developed for ellipsoid suspensions describes quite well the stress overshoots for the initial forward flow, but no effect of rest time is predicted. A modified version has been proposed by adding a molecular diffusivity contribution in the Folgar–Tucker equation. The effect of the particle disorientation is qualitatively predicted, but the kinetics is too slow compared to that deduced from experiments.

The effect of shear flow on reaction of melt poly(ethylene-α-octene) elastomer with dicumyl peroxide

The reaction of melt poly(ethylene-α-octene) (POE) initiated by dicumyl peroxide (DCP) was studied at elevated temperature in both oscillatory and transient shear flow fields. In oscillatory shear flow, the storage modulus evolution was monitored by parallel plate rheometer with certain oscillatory frequencies and different strains, which were chosen to represent different flow fields. Our results indicated that at low frequencies (0.1 and 0.4 Hz) the dominant reaction was coupling with small strain amplitudes within the linear viscoelastic regime. However, the degradation, which was caused by β-scission of tertiary carbon macromolecular radicals, also occurred when large strains were applied, which were out of the linear viscoelastic regime. The threshold strain of degradation was only 8% at 1.5 Hz, still within the linear viscoelastic regime. The mechanisms of how the frequency and strain affected the degradation were different. On the other hand, in transient shear flow the degradation could hardly take place when the shear rate was lower than the critical value of 0.0025 s −1. Moreover, the larger the shear rate, the more distinct was the degradation.

Dough processing in a Couette-type device with varying eccentricity: Effect on glutenin macro-polymer properties and dough micro-structure

Dough mixing involves a combination of different deformation flows, e.g. shear and elongation. The complicated nature of mixing process makes it difficult to understand dough processing at a mechanistic level. A new Couette device allowed the effects of shear flow on the physical properties of glutenin macro-polymer (GMP) and micro-structure formation of the dough to be studied. Steady shear deformation using concentric Couette-type flow did not decrease GMP content or size of glutenin particles. Confocal scanning laser microscopy revealed the formation of interconnected gluten domains indicating the development of a gluten network. In an eccentric Couette configuration the results depended on the degree of eccentricity. A higher degree of eccentricity and a longer processing time led to considerable reduction in GMP content and size of glutenin particles. The micro-structural change in the narrow gap regions of the eccentric cell occurred early in processing, leading to a break up of large protein domains, and a microscopically more homogeneous dough. Transient high shear flow led to elongation and break up of the macroscopic gluten network. In low shear regions of the eccentric cell (wider gap settings), reformation or aggregation of protein domains was observed. Thus, the gluten aggregation–break up mechanisms are strongly influenced by the local flow profile in a conventional mixer. The impact of different types of shear flow must be taken into account in the design of dough mixers.