Rheological studies and optimization of Herschel-Bulkley flow parameters of viscous karaya polymer suspensions using GA and PSO algorithms

Rheological characteristics of gum karaya suspensions which is proposed as a fracturing fluid were investigated with the main objective to determine the yield stress and other rheological parameters using various models. The flow hysteresis confirms the thixotropic behavior of fluid with increased structural breakdown at higher concentration and temperature. An empirical model developed for the studied samples accurately predicts the temperature and polymer concentration sensitivity of the apparent viscosity. The Herschel-Bulkley model showed the best fit to the experimental data; however, the yield stress obtained from some of the samples using nonlinear regression (NL) method reported physically insignificant, negative values. The proposed optimization technique, i.e., “Particle Swarm Optimization” offered the most realistic results with faster convergence over genetic algorithm making it a better choice. The oscillatory study provided more reliable yield stress values and revealed the thermogelation behavior of polymer suspensions making it suitable for high-temperature fracturing application.     

Rheological characterization of a solder paste for surface mount applications

Solder pastes used in surface mount soldering techniques (SMT) are very complex suspensions containing high volumes of metallic powder in a carrier fluid. The rheological complexity results largely from the carrier fluid itself, which is a suspension of colloidal particles. In this work, we have characterized the rheological properties of a typical carrier fluid and its solder paste containing 64 vol.% metallic powder. A six-blade vane geometry was used to avoid wall slip and sample fracture. All measurements were carried out following pre-shearing and rest time in order to obtain reproducible results. Steady shear experiments showed that the solder paste was highly shear-thinning and thixotropic. In oscillatory shear, the linear viscoelastic domain was found to be very narrow for both the suspending fluid and the paste. Frequency sweep tests in the linear domain revealed a gel-like structure with a nearly constant G′ for the suspending fluid and a slightly increasing G′ for the solder paste. From creep experiments, a yield stress of about 40 Pa was determined for the suspending fluid at temperatures between 25 and 40°C, and of 100 Pa at 4°C. A much larger yield stress, 480 Pa, was determined for the solder paste at 25°C.     

On the behavior of fine mud suspensions

Flows of natural mud-water mixtures are of great interest for industrial and civil engineering. But there is still no general agreement about the methods for determining the main rheological characteristics of these systems. We propose here an accurate rheological study of some natural mud-water mixtures. We first discuss the possible effects of changing various parameters such as temperature, pH, electrolyte concentration, solid concentration, clay type. The behavior of these muds appears to be very sensitive to most of these parameters and to be hardly predictable from a knowledge of their components. Then, we show that a Herschel-Bulkley model fits very well steady flow experimental data for a very large range of shear rates. We also suggest physical explanations of this model in agreement with our observations of behavior changes when some parameters change. The yield stress value of this model provides a good estimation of real yield stress which is a key parameter for mixture behavior. These considerations are very useful to characterize, predict, and compare various mud flows.     

Comparative yield stress determination for pure and interstratified smectite clays

Different experimental devices and operative procedures were used to obtain the main properties of suspensions of two purified clays, a pure smectite and an interstratified illite-smectite natural clay, at different concentrations. The yield stress values derived from flow and creep tests were found to be very consistent, while those derived from dynamic tests were observed to be much more sensitive to experimental conditions. Qualitatively, the two clays exhibit the same rheological behaviour, which can be modelled using the Herschel-Bulkley model; their yield stress increases with clay concentration and they present a thixotropic character for low concentrations, with an inversion of the curves when the clay concentration increases. However, significant differences were observed when considering numerical values. For the same clay concentration in the suspension, the yield stress of the pure smectite is distinctly higher than that of the interstratified one. The rheological properties of the pure smectite clay can be related to the swelling properties and the organisation of the minerals in water, leading to three-dimensional strong but deformable structures. On the other hand, the presence of a small percentage of illite in the natural clay gives it a brittle behaviour which collapses more easily under stress.     

Transient phenomena in thixotropic systems

A nonlinear rheological model which accounts for the time-dependent elastic, viscous and yielding phenomena is developed in order to describe the flow behavior of thixotropic materials which exhibit yield stress. A key feature of the formulation is a smooth transition from an ‘elastically’ dominated response to a ‘viscous’ response without a discontinuity in the stress–strain curve. The model is phenomenological and is based on the kinetic processes responsible for structural changes within the thixotropic material. As such, it can predict thixotropic effects, such as stress overshoot during start-up of a steady shear flow and stress relaxation after cessation of flow. Thus this model extends a previously proposed viscoplastic model [J. Rheol. 34 (1991) 647] to include thixotropy.An analysis and comparison to experimental data involving oscillatory shear flow are provided to evaluate the accuracy of the model and to estimate the model parameters in a prototype concentrated suspension. The experiments were conducted using a series of concentrated suspensions of silicon particles and silicon carbide whiskers in polyethylene. The data obtained with this experimental system indicated much better agreement between the theory and experiments that obtained in earlier work.     

Rheology of cocoa-pod husk aqueous system. Part-I: steady state flow behavior

A fundamental rheological data describing the flow behavior of an aqueous system prepared from an agricultural harvest residue, cocoa-pod husk in fixed chemical environment, has been presented. Shear stress and viscosity data were obtained and analyzed at different solid concentrations in order to investigate basic particle interactions and how far the aqueous system conforms to relevant standard rheological models. The resulting suspension is a complex non-Newtonian thixotropic viscoelastic system, highly flocculating, weakly gel-like and conforming reasonably with the Power-Law, Herschel-Bulkley, Cross, and Carreau models. The result is consistent with that of a flocculated system indicating that this agricultural waste could serve as a filler material in conventional organic-based matrix materials for affordable composite fabrication for panels.     

Understanding thixotropic and antithixotropic behavior of viscoelastic micellar solutions and liquid crystalline dispersions. I. The model

A simple model consisting of the Upper Convected Maxwell constitutive equation and a kinetic equation for destruction and construction of structure, first proposed by Fredrickson in 1970, is used here to reproduce the complex rheological behavior of viscoelastic systems that also exhibit thixotropy and rheopexy under shear flow. The model requires five parameters that have physical significance and that can be estimated from rheological measurements. Several steady and unsteady flow situations were analyzed with the model. The model predicts creep behavior, stress relaxation and the presence of thixotropic loops when the sample is subjected to transient stress cycles. Such behavior has been observed with surfactant-based solutions and dispersions. The role of the characteristic time for structure built up, λ, in the extent and shape of the thixotropic loops is demonstrated.     

Flow properties of oven-curing high solids white enamels

For the characterization of the rheological behaviour of a white, high solids, oven-curing enamel for household equipment with regard to its industrial application, attention was focused on the flow aspects involved in laying down process and film formation phenomena, i.e. viscosity at very high and very low shear rate, structural build-up in rest conditions, presence and magnitude of elastic components. Hence, investigations were aimed at (1) the determination of the equilibrium flow curve; the application of the Shangraw-Grim-Mattocks model led to the evaluation of parameters to describe infinite shear-rate viscosity and yield stress; (2) obtaining information about particle aggregation state in shear conditions. Quemada model gave indication that, even at very high shear, particle aggregates are stable; (3) the determination of time-dependent behaviour: elastic components were found to be almost negligible; the Trapeznikov-Fedotova procedure allowed thixotropic build-up in rest conditions to be evaluated, as concerns both amount and kinetics. Remarkable flow features found were: differences in the temperature dependence of viscosity at low shear rate and of yield value for enamels formulated with different pigment volume concentrations and the strong effect of the pigment volume concentration on the initial rate of thixotropic build-up in rest conditions.     

Composite viscoelasticity in glassy,transitional and molten states

As part of a study of viscous and elastic behaviors, over a range of temperatures from below the glass transition up to the hot melt, we here report steady-shear viscosities at 0.007 to 13 s^?1 and at 160 to 220 °C of polystyrene containing 0 to 60% by mass of 0.18-micron diameter titanium dioxide particles. The materials were shearthinning without a yield stress, with a constant activation energy at constant stress, but having a shear-dependent activation energy at constant shear rate — proportional to the volume fraction of the polymer matrix. Superposition of the flow curves at different temperatures for the unfilled and filled systems was possible. All the data were represented by one equation with four parameters: 1) a shear stress coefficient (units Pa · s²); 2) a characteristic stress level for non-Newtonian behavior, independent of temperature and composition; 3) an activation energy at constant stress; and 4) an Einstein coefficient (or intrinsic viscosity of the filler). Other equations also fitted the data, but the others diverged widely when extrapolated.     

Correlation between thermal and rheological studies to characterize the behavior of bitumen

The objective of this work is a comprehensive thermo-rheological study of pure bitumen. The bitumen is a complex material consisting of asphaltenes dispersed in a maltene matrix. As a consequence, its flow behavior is characterized by the presence of a yield stress, which depends on temperature below 50°C. Applying the Cox–Merz rule, a master curve of viscosity can be obtained over a wide range of shear rates for temperatures above 50°C. It can be accurately modeled by a Carreau–Yasuda law with a yield stress. This specific rheological behavior can be explained by the changes induced by the temperature on the microstructure, evidenced by modulated differential scanning calorimetry measurements.     

Rheological behaviour of a filled wax system

The temperature dependent rheological behaviour of a pigment filled wax system is investigated in a cone-and-plate viscometer over a range of shear rates from 60 to 10 000 s^–1. A strong influence of water adsorbed by the pigment on rheological properties of the filled system can be found. The increase of the yield stress and the viscosity at low shear rates can be related to a build-up of pigment structures due to growing water content. The flow behaviour can be described by the Casson equation as well as by the Herschel-Bulkley equation.Both formulations are compared and discussed. The Casson model is evaluated more closely by the calculation of characteristic structural parameters of the suspension which are critically discussed.Dedicated to Prof. Dr. Joachim Meissner on the occasion of his retirement from the chair of polymer physics at the Eidgenössische Technische Hochschule (ETH), Zürich.     

Evaluating rheological models for human blood using steady state,transient, and oscillatory shear predictions

The rheological characterization of human blood, through modeling and analysis of steady state, transient, and oscillatory shear flows, has made tremendous progress recently. Due to the aggregation of red blood cells at low shear rates, many recent models for blood rheology include a structural, thixotropic component with one of the most recent attempts unifying this approach with a viscoelastic formulation. We will show how these models, along with proposed modifications to another recent structural, kinetic thixotropy model, can improve modeling predictions. Results are compared to the Maxwell-like Bautista-Manero-Puig model, the Oldroyd-8 inspired viscoelastic Anand-Kwack-Masud model, a viscoelastic-thixotropic model from Blackwell and Ewoldt, and the Herschel-Bulkley model. We explore the weaknesses of the legacy blood models and then demonstrate the efficacy of the newly improved models for modeling human blood steady state and transient shear rheology to predict oscillatory shear flow.     

Mapping thixo-elasto-visco-plastic behavior

A century ago, and more than a decade before the term rheology was formally coined, Bingham introduced the concept of plastic flow above a critical stress to describe steady flow curves observed in English china clay dispersions. However, in many complex fluids and soft solids, the manifestation of a yield stress is also accompanied by other complex rheological phenomena such as thixotropy and viscoelastic transient responses, both above and below the critical stress. In this perspective article, we discuss efforts to map out the different limiting forms of the general rheological response of such materials by considering higher dimensional extensions of the familiar Pipkin map. Based on transient and nonlinear concepts, the maps first help organize the conditions of canonical flow protocols. These conditions can then be normalized with relevant material properties to form dimensionless groups that define a 3D state space to represent the spectrum of thixotropic elastoviscoplastic (TEVP) material responses.     

Application of the Casson model to thixotropic waxy crude oil

The rheological behavior of a waxy crude oil was investigated using a coaxial cylinder viscometer. Experimental flow curves were fitted with the Casson equation. The Casson model was modified to interpret the hysteresis between upward and downward curves obtained in a series of consecutive runs. At the same shear rate, the mean axial ratio of the flow unit related to a down-curve (↓) is smaller than that related to an equilibrium up-curve (↑). This results in a decrease of the Casson yield stress τ_c↓ with respect to τ_c↑. A certain ξ coefficient describing departure from the equilibrium mean axial ratio was introduced into the model. Values of ξ calculated from the Casson yield stresses agreed satisfactorily with the theoretically predicted ones. Deviations from the Casson model at low shear rates were also explained. Received: 28 July 1998 Accepted: 18 February 1999     

A structural model for thixotropy of colloidal dispersions

The present study proposes a structural model to describe the thixotropic behavior of colloidal dispersions. This model uses structural viscosity and elasticity as internal parameters, and predicts the evolution of shear stress when shear rate varies over time. Viscosity represents the structural level of colloidal aggregates and is dependent upon their alignment. Changes in alignment are linked to changes in shear rate, are regarded as instantaneous and are not believed to cause thixotropic behavior. Only changes in the structural level or structural viscosity and in the elastic deformation of colloidal aggregates cause measurable thixotropic behavior. Variations in structural viscosity over time, and at a fixed shear rate, follow a first-order kinetic equation based on two characteristic thixotropic times. This model incorporates several parameters, which are fitted independently by the appropriate rheological tests, in order to avoid any mathematical coupling. This model has been tested in 3 wt% Laponite aqueous dispersions using different ionic strengths.     

Contemporary modeling and analysis of steady state and transient human blood rheology

The rheological characterization of a human blood, through modeling and analysis of transient flows and large-amplitude oscillatory shear (LAOS) flow, has made tremendous progress recently. We show how various components, and modifications of two recent scalar, structural kinetic, thixotropic models, can offer several modeling and prediction improvements, and compare our results to the Maxwell-like Bautista-Manero-Puig (BMP) model, and a recent transient model based on the Herschel-Bulkley. We explore the weakness of the legacy blood models, and then, we apply this newly improved model to recently published data from the literature in order to demonstrate its efficacy in modeling steady state, transient, and oscillatory shear flow. Following this effort, we demonstrate a novel approach using the sequence of physical phenomena (SPP) to facilitate interpretation, characterization, mapping, and “fingerprinting” of transient blood data from the literature. We compare the SPP approach to other LAOS analysis techniques in the literature and show how our approach can function as a mechanical-property diagnostic blood analysis tool. The goal of this work is a deeper understanding of the microstructural basis and validity of structural thixotropic blood models, and transient flow analysis techniques and procedures.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

An experimental investigation of the shear behaviour of polyethylenes with different structures

Rheological properties in shear flow are presented for four different polyethylene samples: a high density, a linear low density and two low density polyethylenes manufactured using different techniques. Tests have been performed with the aid of capillary types of instrument equipped with capillaries of various lengths at three different temperatures. End correction factors have been determined and true flow curves obtained. Swelling ratios for both unannealed and annealed samples have been determined as well as the shear rate and shear stress at which irregularities begin. In some cases generalized plots have been prepared and in all cases the rheological response is discussed in terms of molecular characteristics, in particular the average molecular weight, molecular weight distribution and degree of branching.     

Rheological behavior of sewage sludge and strain-induced dewatering

In order to study the strain-induced water release in sewage sludge and its connection with rheological behavior, two types of rheological tests have been carried out. The rheology of sewage sludge samples stemming from a urban sewer was first characterized using a Couette cell system. In particular, the yielding behavior and the elastic modulus of the sludge has been considered under shear flow conditions. In these pure shear tests the reproducibility of the measurements was rather poor, limiting this study to low strains. Consequently, a second type of rheological tests, namely the squeeze test, which is more appropriate for these paste-like materials, has been considered. The rheological behavior along with the dewatering efficiency have been studied under the squeeze flow conditions. Surprisingly, it was found that, under certain conditions, the strain-induced water release mechanism became more effective when decreasing the squeeze speed. This was interpreted in terms of a competition between the paste flow and the water filtration through the porous media made up by the flocs.     

Temperature imaging of turbulent dilute spray flames using two-line atomic fluorescence

To study the behavior of thixotropic yield stress fluids, information at the local scale is required in order to determine precisely the yield point value, and the shear rate and stresses can be obtained all over the flow. This study focuses on the flow in a large shear cell of a Laponite suspension. In order to be able to construct a local rheogram for this suspension, two different methods issued from fluid mechanics and solid mechanics are used. Local velocities are determined with a PIV technique, and local stresses are determined with the photoelasticimetry technique.