Thixotropic Model Research Articles

Non-integer asymptotic scaling of a thixotropic-viscoelastic model in large-amplitude oscillatory shear

We demonstrate that a simple thixotropic-viscoelastic constitutive model has a unique rheological fingerprint that fits data that no other model is known to fit. The key rheological signature is the non-integer power law scaling in asymptotically-nonlinear large-amplitude oscillatory shear (LAOS), sometimes called medium-amplitude oscillatory shear (MAOS). We begin with a minimalist constitutive model that contains only five material parameters, which we show to be the minimum required to capture all fundamental thixotropic and viscoelastic phenomena. We demonstrate that the low amplitude power-law scaling of the asymptotically nonlinear first and third harmonic stresses (scaling as input amplitude squared) is different than that observed in all other known constitutive model predictions (which predict nonlinearities to scale as input amplitude cubed). We then explore the effects of a sixth model parameter n (the most common addition to thixotropic models in the literature), introduced to govern the order of the kinetic rate equation. We show that this parameter gives further variability to this unique signature (with nonlinearities scaling as σ∼γn+1). Finally, we compare these model signatures to the experimental signature of a real thixotropic material (Carbopol microgel suspension in water), demonstrating that models with non-integer amplitude scaling are required to match experimental observations.

Performance of an elasto-viscoplastic model in some benchmark problems

A recent elasto-viscoplastic thixotropic model proposed by (de Souza Mendes in J. Non-Newton. Fluid Mech. 164:66–75, 2009; de Souza Mendes in Soft Matter 7:2471–2483, 2011) is applied to five benchmark problems: the flow in a lid cavity, the flow through an expansion followed by a contraction, the flow over a flat plate, the channel entry flow, and the flow around a cylinder confined between parallel plates. One of the main advantages of this approach is its ability to recover a model for elasto-viscoplastic materials in a smooth fashion, i.e., in the limit where the characteristic thixotropic time tends to zero. These problems are numerically solved using the finite element method, with a four-field GLS-type formulation. While the simplified version is applied to the first three problems, the full model including thixotropy is applied to the channel entry flow and the flow around the cylinder. The elasto-viscoplastic problems analyzed show that, in general, elasticity tends to inhibit yielding and is more concentrated in unyielded regions. The thixotropic effects analyzed show that the delay in the microstructure response of the material significantly alters the problem when compared to the pure elasto-viscoplastic counterpart.

A starting pressure prediction of thixotropic cement slurry: Theory, model and example

Abstract In this study, index model of thixotropic fluid is improved, and further on this basis, a prediction model of starting pressure of thixotropic cement slurry is created. Fann viscosimeter with heating unit will be adopted to measure static shearing force and shearing stress. The thixotropic model will be validated by test. Test of starting pressure estimation proves that starting pressure increases rapidly at the early stage of pump shut-down but slowly against the increasing of shut-down time.

Numerical study of pipeline restart of weakly compressible irreversibly thixotropic waxy crude oils

A 3‐D axisymmetric model is developed to predict pressure wave propagation processes during gelled waxy oil pipeline restart operations. A finite volume method is implemented on a staggered grid. An iterative predictor‐corrector algorithm provides solutions to the combined parabolic‐hyperbolic set of governing equations. A new shear‐history‐dependent thixotropic rheology model is proposed for pressure wave propagation computations. Moderate Reynolds number flows within the laminar regime are computed, demonstrating the impact of inertial effects. The results clearly illustrate the important mechanisms of pipeline restart. The nature of pressure wave propagation is governed by gel strength as well as overall fluid compressibility. Three sequential pressure wave propagation regimes are dominated by inertial, viscous, and gel degradation phenomena, respectively. The viscous and gel degradation regimes are effectively coupled by imposed deformation conditions. For initially homogenous thixotropic gels, strain tends to localize near the pipeline wall, playing a central role in assuring the pipeline restart. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2657–2671, 2015

Effect of hydrophobicity on viscosity of carbonaceous solid–water slurry

Carbonaceous solid–water slurry rheology is greatly affected by the surface properties of the carbonaceous solids used. Slurriability studies showed that, for the same solids loading, viscosities of highly hydrophobic petcoke and bitumen–water slurries were approximately one order of magnitude higher than the viscosity of non-hydrophobic Illinois #6 (bituminous) coal–water slurry. Apart from slurriability, the hydrophobicity of the carbonaceous solids was found to influence the type of additives used to reduce the viscosity. Selected to reduce viscosity, the addition of non-ionic additive Triton X-405 caused a drastic reduction in petcoke and bitumen–water slurry viscosities, whereas anionic additive ammonium lignosulfonate reduced Illinois #6 coal–water mixture viscosity more effectively. Optimum particle-size distribution was also found to be dependent on the surface properties of the solids. Experimentally determined optimum particle-size distributions were observed to deviate from the theoretical predictions. A deviation of 8% was noted in the case of Illinois #6 coal–water slurry, whereas deviations of 30% were observed in the case of hydrophobic bitumen and petcoke–water slurries. Viscosity predictions of semi-empirical models were compared to experimentally measured viscosities. The predicted viscosities did not match the experimental results, especially at higher solids loading. A thixotropic model taking into account particle aggregation was found to predict viscosity more accurately in the case of these hydrophobic carbonaceous solid–water slurries.

A modified elasto-viscoplastic thixotropic model for two commercial gelled waxy crude oils

A severe problem to flow assurance occurs when subsea flowlines become blocked with gelled waxy crudes. To design proper surface pump facilities, it is essential to know the minimum pressure required to restart the flow. Simulating and predicting this minimum pressure require the understanding of several physical phenomena, including compressibility, shrinkage, and rheological behavior. This study aims to characterize and simulate the rheological behavior of two commercial waxy crude oils. Based on its survey of the literature, we select the de Souza Mendes and Thompson (2013) model to fit the oil’s behavior and then conduct, using a rheometer, a considerable number of experiments with the selected oils. To verify the solution of our algorithm, we compared our theoretical solutions with some results of the literature. When comparing the simulation with experiments, the model was unable to predict the data perfectly; hence, we propose a modified version without changing the physical meaning of the equations, to improve its predictions. Once any of the empirical parameters were able to influence the elastic behavior in such a way that the shear stress decreased with time, the structural elastic modulus function was modified, which means that the relation of the structure parameter and the storage modulus was modified. One of the interesting results of the analysis is when relating the storage modulus and a new parameter added in the modification, a value was found to be, regardless of the aging time or the oil used, constant.

Evaluation of Thixotropic Models for Waxy Crudes

Thixotropy is a great rheological behavior of waxy crudes oils and is of great importance for hydraulic characteristics and security of oil pipeline restart. In this paper, through the experiment of four waxy crudes, three kinds of thixotropic rheology characteristics in the conditions that shear stress decays under a constant shear rate, shear stress decays after shear rate steps up and hysteresis loop of shear rate cycle changes are studied . For eight thixotropic models, experimental data are fitted in the method of least-squares and average deviation is taken as a statistical indicator to evaluate the thixotropic models. It shows that the model with the idea of Cheng that completely reversible and totally irreversible structures both exist in waxy oil products and based on Houska model can describe thixotropic behaviors of waxy crudes most well.

A New Approach to Calculate Shutdown and Restart Pressure of Waxy Crude Pipeline

<p>On the basis of Tianyou Liu start-up pressure calculation model, the restart pressure model was divided into three parts. Considering the pressure drop caused by elevation difference along the pipeline, friction pressure drop was solved by pipe regional discretization and Houska thixotropic model was used in the pressure drop caused by thixotropic factor. A new calculation method of waxy crude oil pipeline restart pressure was set up and Qin-Jing Pipeline data were substituted into corresponding analog computation. Calculation results are in conformity with the actual situation and the new calculation method is more widely applicable.</p>

Modeling of human blood rheology in transient shear flows

We offer here an extension of our previous work [Apostolidis and Beris, J. Rheol. 58, 607–633 (2014)] of modeling blood flow rheology in simple shear steady state flows to time-dependent conditions. The basis of our model is a scalar, structural, parameter thixotropic model. More specifically, we show that a modified version of the “Delaware model” [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102, 157–178 (2002)] is capable of predicting the time-dependent shear flow rheology of blood at low and moderate values of shear rate. At steady state, the model reduces to the Casson constitutive model for low and moderate shear rate values consistent to the findings of our previously mentioned work. At high shear rates it reduces to a Newtonian model, correcting our previous model and consistent to data from the literature [Merrill and Pelletier, J. Appl. Physiol. 23, 178–182 (1967)]. Exploiting the existing parameterization developed before for the steady state Casson model and the Merrill and Pelletier steady state data, the transient thixotropic model introduces only three additional parameters. Each one of these parameters has a specific physical meaning: A zero-shear rate maximum strain, and two kinematic parameters governing the relaxation of the structural parameter and the elastic modulus, respectively. The model is able to naturally account for the additional yield strengthening effect attributable to the red blood cell rouleaux structures developed within blood. The proposed model can fit excellently the experimental data of Bureau et al. [Biorheology 17, 191–203 (1980)], on simple triangular steps in shear flow at low shear rates. The predictions of the present model are then validated comparing them against additional experimental data, collected on the same samples, either on triangular steps in shear flow but at higher shear rates or on rectangular step-up and step-down experiments. The model is further validated by comparing its predictions against recent large amplitude oscillatory shear data [P. C. Sousa et al., Biorheology 50, 269–282 (2013)]. In all these comparisons there is good, at least semiquantitative, agreement, with the observed discrepancies only appearing at the higher shear rates, where the isotropic description resulting from the use of a single scalar internal parameter to describe the blood microstructure naturally breaks down.

Numerical modelling of thixotropic and viscoelastoplastic materials in complex flows

This study is concerned with the finite element/finite volume (fe/fv) simulation of thixotropic and viscoelastoplastic material systems through two model approaches: (i) a new micellar thixotropic constitutive model for wormlike micellar systems (that introduces viscoelasticity into the network structure construction/destruction kinetic equation) and (ii) adopting a Bingham–Papanastasiou model. The computational approach is based on a hybrid parent/subcell scheme, which is cast about a semi-implicit incremental pressure correction (ipc) scheme. The appearance of plastic behaviour arises through the micellar polymeric viscosity, by increasing the zero-shear viscosity (low solvent fractions), whilst the Bingham–Papanastasiou introduces plastic features through the solvent viscosity. The characteristics of thixotropic wormlike micellar systems are represented through the class of Bautista–Manero models. Correction is incorporated, based on physical arguments for fluidity, in which absolute values of the dissipation function are adopted in complex flow, thereby accessing low-solvent fractions and high-elasticity levels. Considering elastic and plastic influences separately, solutions are compared and contrasted for contraction–expansion flow, identifying such flow field features as vortex dynamics, stress field structure, yield front patterns and enhanced pressure drop. Particular attention is paid to the influence of enhanced strain hardening that is introduced through stronger thixotropic structural features. Vortex activity decreases as either We is increased at a fixed τ 0 or τ 0 is increased at a fixed We. Exaggerated strain-hardening properties are observed to have a major impact on vortex activity. Patterns and trends in normal stress difference fields reflect those in re-entrant corner vortex patterns. Yield front patterns are significantly influenced with yield stress τ 0 variation and more so than elevation in elasticity. Findings on excess pressure drop (epd) versus increased yield stress (τ 0) follow a linear trend. Consistently, it is evident that any variation that leads to a more solid-like behaviour produces epd enhancement. In addition, relatively more structured fluids display distinctly larger epd values throughout the τ 0 range covered.

Rheological characterization of metal particle suspension and its relationship with spray-dried granule properties

Cemented carbide is usually produced by sintering particles of metal carbides with binders. The non-aqueous suspension of both materials is spray-dried to produce granules having uniform material distribution, resulting in the excellent toughness of final products after sintering. Although the status of particle aggregation in a suspension should have a strong relationship with granule properties, the effect of surfactant on aggregative nature of particles has not been systematically investigated. In the present study, a new instrument was developed to measure apparent viscosity of metal particle suspension without sedimentation in order to investigate particle aggregation from the rheological point of view. Additionally, the particle interaction has been quantitatively evaluated based on Usui's thixotropy model. It is found that the particle interaction was gradually reduced as increasing surfactant concentration, whereas granule properties changed only at higher concentrations. We also found the suspension stability and product functionality are balanced at the critical concentration.

Structural model to study the influence of thermal treatment on the thixotropic behaviour of waste activated sludge

The present study proposed a thixotropic model to examine the variations in the thixotropic behaviour of waste activated sludge after the application of different thermal specific energies (ES). The model is based on the definition of the time dependence of a structural parameter, S, which quantifies the structural level of the internal structure at any time and shear rate, and the instantaneous variations in the alignment and deformation of flocs. The thixotropic behaviour was quantified based on the kinetic coefficients for the breakdown and build-up processes, which appeared to depend on the shear rate. The application of thermal ES significantly reduced the steady state viscosity and the kinetic coefficient for the breakdown process, suggesting that the thixotropy slightly increased. Complementarily, the sludge was further characterised to understand the variations in sludge rheology. The extracellular polymeric substances (EPSs) present in sludge were fractionated and subsequently analysed by gel permeation chromatography, which revealed that thermal treatment solubilised most of the peptides and proteins of low molecular weight but denatured the high molecular weight proteins. On the other hand, the capillary suction time increased at low thermal ES and decreased at high thermal ES. However, the water removed by centrifugation was increased even at low temperatures, despite the increase in the capillary suction time value.

Rotational Rheology of A356 Semi-Solid Alloy at Low Solid Fractions

The main goal of investigations on semi-solid metal processing is to produce complex parts with enhanced mechanical properties. Flow behavior and die filling in semi-solid processing is an intrest area of researchers. A comprehensive understanding of the behavior of the under investigation metallic slurry is the design key of a successful manufacturing process. In this way the material’s transient response is very important for understanding of the rheological properties and also further commercial development of the process. The material used in this research is an Al-Si alloy which is widely used in automotive and aerospace applications. The experiments were conducted using a Searl rheometer which is specially designed for high temperature rheological measurements. For rheological tests of semi-solid alloy in different solid fractions, the isothermal holding and shear rate step change experiments were examined. Using practical rheological results, a single phase thixotropic model has been derived and adopted with measurements. The investigated alloy behavior was obviously thixotropic which is quantified in a theoretic model. Also instantaneous rheopectic behavior was observed for this alloy. The state of the microstructure has been applied through a structural parameter. The presented model for A356 alloy fits well with the experiments.

Synthesis and characterization of a thixotropic coal–water slurry for use as a liquid fuel

Abstract We reported here a novel approach to synthesize a low-viscosity and stable coal–water slurry for use in many practical applications. The slurry was prepared by mixing coal particles with a gelling solution containing water and 1 wt.% of cobalt-intercalated laponite. The coal particle sizes were less than 75 μm and the coal loading was 50% by weight. The slurry prepared this way was able to transform to a high-viscous and unflowable gel holding coal particles uniformly throughout its volume when it was stored at rest. When it was sheared, its gelling network structure was immediately broken down becoming a low-viscous flowable liquid. The transport and thixotropic properties of the prepared slurry were measured and they were described very well by the Bingham model and the thixotropic model proposed by Usui, respectively.

Shear rheology of hydrophobin adsorption layers at oil/water interfaces and data interpretation in terms of a viscoelastic thixotropic model.

Here, we investigate the surface shear rheology of class II HFBII hydrophobin layers at the oil/water interface. Experiments in two different dynamic regimes, at a fixed rate of strain and oscillations, have been carried out with a rotational rheometer. The rheological data obtained in both regimes comply with the same viscoelastic thixotropic model, which is used to determine the surface shear elasticity and viscosity, E(sh) and η(sh). Their values for HFBII at oil/water interfaces are somewhat lower than those at the air/water interface. Moreover, E(sh) and η(sh) depend on the nature of oil, being smaller for hexadecane in comparison with soybean-oil. It is remarkable that E(sh) is independent of the rate of strain in the whole investigated range of shear rates. For oil/water interfaces, E(sh) and η(sh) determined for HFBII layers are considerably greater than for other proteins, like lysozyme and β-casein. It is confirmed that the hydrophobin forms the most rigid surface layers among all investigated proteins not only for the air/water, but also for the oil/water interface. The wide applicability of the used viscoelastic thixotropic model is confirmed by analyzing data for adsorption layers at oil/water interfaces from lysozyme and β-casein - both native and cross-linked by enzyme, as well as for films from asphaltene. This model turns out to be a versatile tool for determining the surface shear elasticity and viscosity, E(sh) and η(sh), from experimental data for the surface storage and loss moduli, G' and G''.

Capillary flow of milk chocolate

The rheological behaviour of three different commercially manufactured chocolates are studied as a model paste system in order to understand their processing characteristics at different temperatures by using parallel-plate and capillary flow. The rheological behaviour is distinctly different at temperatures below and above 30°C. At temperatures below 30°C it behaves as a soft solid. A previously developed phenomenological mathematical model for polytetrafluoroethylene (PTFE) paste flow was used to model its rheology and capillary extrusion. The model takes into account the elastic–plastic (strain hardening) and viscous nature of the material in its non-melt state. The predictive capability of this model is tested against capillary data for a variety of capillary dies having different length-to-diameter ratios (L/D) and contraction angles (2α). At temperatures above 30°C, chocolate behaves as a visco-elasto-plastic liquid. Its behaviour has been determined as a Herschel–Bulkley viscoplastic material with a small degree of thixotropy. The rheological data obtained from parallel plates and bob–cup rheometer were used to formulate a thixotropic model using a structural parameter. The capillary data were found to be well described with the proposed models.

A simple thixotropic–viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS)

Here we demonstrate that a simple thixotropic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS) distinct from other nonlinear mechanisms and separate from viscoelastic time dependence. Our approach is to define the simplest model that produces the essential features of both thixotropy and viscoelasticity, a structure-parameter evolution equation coupled to a three-element fluid (Jeffreys model). In strain-controlled LAOS, the response of the model depends on four dimensionless parameters: two deformation parameters (Deborah and Weissenberg) and two material parameters (the ratio of viscoelastic to thixotropic timescales and the ratio of infinite shear viscosity to aggregate viscosity). We present numerical results for the full nonlinearities across this four-dimensional parameter space. The dimensionality is reduced by considering the asymptotically-nonlinear regime (Weissenberg number expansion). We present the first analytical solution for a thixotropic model in this asymptotically-nonlinear LAOS regime, which produces distinct power function scaling not predicted by other known solutions to nonlinear viscoelastic models. With this separation of thixotropic from viscoelastic timescales, this canonical model predicts that short thixotropic timescales can be experimentally observed with nonlinear oscillatory deformation. This is relevant to recent suggestions in distinguishing thixotropic versus “simple” yield stress fluids with no experimentally observable thixotropy.

A new constitutive model for worm-like micellar systems – Numerical simulation of confined contraction–expansion flows

This hybrid finite element/volume study is concerned with the modelling of worm-like micellar systems, employing a new micellar thixotropic constitutive model with viscoelasticity within network-structure construction–destruction kinetics. The work focuses on steady-state solutions for axisymmetric, rounded-corner, 4:1:4 contraction–expansion flows. This has importance in industrial and healthcare applications such as in enhanced oil-reservoir recovery. Material functions for the micellar models (time-dependent, thixotropic) have been fitted to match two different extensional configurations of the exponential Phan-Thien/Tanner (PTT) model (rubber network-based, non-thixotropic). This covers mild and strong-hardening response, and re solvent fraction, highly-polymeric (β=1/9) and solvent-dominated (β=0.9) fluids. Solution results are described through normalised Excess Pressure Drop (EPD), vortex intensity and stream function, stress (N1 and N2), and f-functional data. EPD predictions with the new micellar models prove to be consistent (at low rates, some rising) with Newtonian results, contrary to the base-reference modified Bautista–Manero (MBM) results. Markedly different vortex intensity trends are found in comparing micellar and EPTT solutions, which correspond with N2−N1 and f data. In order to address the highly-elastic regime for thixotropic materials, a convoluted approach between EPPT and micellar models has been proposed. Here, numerically stable solutions are reported for impressively large We up to 300 and new vortex structures are revealed.

Thixotropism of micron-sized saltwater clay flocs

Results from microcompression testing of micron-sized saltwater individual kaolinite flocs with different ageing times of up to 152 days show that the rearrangement of flaws or weak links towards a more uniform distribution contributes to the thixotropic increase in floc mechanical properties. Evidence of this newly identified thixotropism of clay flocs is provided by the Weibull moduli of floc stiffness and yield shear strength, which are well fitted using the stretched exponential thixotropy model. The Weibull modulus is a good quantitative descriptor of the thixotropic evolution of clay floc microstructure.

A new thixotropic model for waxy crude

Waxy crude oil shows thixotropic behavior below the gelation temperature. The mostly used thixotropic model for waxy crude is the model proposed by Houska. One problem of Houska’s model is that after the stepwise change in shear rate, the predicted shear stress decreases to its equilibrium value more quickly than the measured data. To address this problem, a new viscoplastic thixotropic model is proposed. The evolution of structural parameter is described by a new kinetic equation. In the kinetic equation, a new pre-factor with shear strain as variable is introduced for the buildup and breakdown terms, and the breakdown term is assumed to be dependent on energy dissipation rate rather than on shear rate. The proposed model was validated by the stepwise shear rate test and hysteresis loop test. And the results showed that the new model’s fitting and predictive capability is satisfactory.