Herschel-Bulkley Research Articles

Rheological Properties of Some Fruit Spreads

Rheological properties of three Smooth homogenized spreads were evaluated at different shear rates (2.29 – 34.35 s-1) using Brookfield rotational viscometer (DVIII Ultra). The spreads were prepared from purees of three fresh fruits, (Guava, Banana and Strawberry). To 100 g of puree; 1 g citric acid, 2 g sugar, 10 g water and 1g of a thickening agent were added and the mixture was homogenized. Xanthan, guar and carboxy methyl cellulose (CMC) gums were used for making three guava spreads, whereas xanthan only was used for making banana and strawberry spreads. Different rheological models were fitted to the data. The effect of temperature on rheological properties of guava, banana and strawberry spreads was studied. All fruit spreads, exhibited non-Newtonian pseudoplastic behavior. Herschel-bulkley (HB) model was the best fit (i.e. highest R2) for data of guava and strawberry spreads followed by Casson and Power law models. Bingham model showed higher values for yield stress of all spreads than those of HB model, whereas those of Cassons’ were the least. Guava spread containing xanthan was more viscous than those containing guar or CMC. In general, spread viscosity decreased as temperature was increased. Heat penetration tests conducted on xanthan-containing spreads packed into flexible PA/PE pouches suggested possible use of such pouches for packaging fruit spreads. Xanthan-containing spreads when subjected to sensory evaluation gained satisfactory scores or butter which indicated panelists’ appreciation for the new products.

Coupled effects of silica fume and time after water addition on rheology of fresh concrete

The fresh-state behaviour of plain and silica fume (SF) modified concrete was measured using a wide-gap viscometer, and classical workability (slump flow and J-ring slump flow) was measured. The Herschel–Bulkley (HB) model was used to describe the rheology of fresh concrete and the HB parameters (including yield stress, consistency coefficient, flow index and apparent plastic viscosity) under the coupled effect of SF and time after water addition were derived. According to the experimental results, shear thickening behaviour is found to be strongly influenced by SF content and the time after water addition. In general, the flow index declined with SF and water addition time. A simplified model is constructed to forecast the value of the flow index for the coupled effects of SF content and water addition time.

Simplified Explicit Flow Equations for Herschel-Bulkley Fluids in Couette-Poiseuille Flow—For Real-Time Surge and Swab Modeling in Drilling

SummarySimplified flow equations are developed for Herschel-Bulkley (HB) fluids in laminar Couette-Poiseuille (CP) flow. Such flow problems are encountered in drilling when the drillstring is moved longitudinally (surge and swab operations). The new equations give the frictional-pressure gradient explicitly as a function of the bulk-flow rate. This makes them very well-suited for applications in fast, robust dynamic models for real-time applications. Incorporating these equations in a dynamic model based on ordinary differential equations (ODEs) enables coupling with system identification and control-system theory. This is a great advantage in drilling applications where there are many uncertain parameters and few measurements. Thorough analysis of relevant analytical solutions is performed to replace the most complex (implicit) parts of the solution with simpler approximations. The accuracy of the new equations, in comparison with numerical simulations and available analytical solutions, is shown to be acceptable for most practical applications.

Non-locality and viscous drag effects on the shear localisation in soft-glassy materials

Abstract We study the Couette flow of a quasi-2d soft-glassy material in a Hele–Shaw geometry. The material is chosen to be above the jamming point, where a yield stress σY emerges, below which the material deforms elastically and above which it flows like a complex fluid according to a Herschel–Bulkley (HB) rheology. Simultaneously, the effect of the confining plates is modelled as an effective linear friction law, while the walls aside the Hele–Shaw cell are sufficiently close to each other to allow visible cooperativity effects in the velocity profiles (Goyon et al., 2008). The effects of cooperativity are parametrized with a steady-state diffusion–relaxation equation for the fluidity field f = γ ˙ / σ , defined as the ratio between shear rate γ ˙ and shear stress σ. For particular rheological flow-curves (Bingham fluids), the problem is tackled analytically: we explore the two regimes σ ≫ σY and σ ≈ σY and quantify the effect of the extra localisation induced by the wall friction. Other rheo-thinning fluids are explored with the help of numerical simulations based on lattice Boltzmann models, revealing a robustness of the analytical findings. Synergies and comparisons with other existing works in the literature (Barry et al., 2011) are also discussed.

Optimization of Soy-Butter from Sprouted Soybean and its Quality Parameters

The time and temperature of roasting of sprouted soybean was optimized using response surface method. The effect of roasting on sprouted whole kernel of soybean indicated that roasting time and temperature individually, as well as in combination, had a significant effect on hardness of roasted kernels. Sprouted soybean kernels were roasted at optimized temperature (127C) and time (37 min) and subsequently made into soy-butter (SB) and compared with reference soy-butter (RSB) on the basis of nutrient content, particle size, color, sensory quality and rheology. SB contained 38 g/100 g protein and 34 g/100 g fat. There was significant difference (P < 0.05) between RSB and SB in L* values. Sprouting improved flavor scores and SB showed higher organoleptic acceptability compared with RSB on a 9-point hedonic scale. Rheology showed that SB behaved like viscoelastic shear thinning material; like Bingham plastic at lower shear rates and Herschel-Bulkley (HB) fluid at higher shear rates. Practical Applications Soybean is an important crop due to its high protein content but soy products are not very popular due to problems of trypsin inhibitor, off-flavors, etc. Sprouting is a process known to improve the nutritional and functional quality while reducing the content of trypsin inhibitors and off-flavors of the bean and consequently of the product. SB, a comparatively new product of soybean, offers all positive attributes of soybeans, sprouting and sensory qualities of vegetable butters. A new process for manufacture of SB has been proposed in this paper. The nutrient quality, particle size and rheology have been studied. The process is simple and does not require any expensive or specialized equipment for commercial manufacture. Quality attributes of the product have been modeled so that effect of any change in process on the quality of product can be predicted or the manufacture process can be modified to achieve certain quality attribute.

Rheological properties of soft-glassy flows from hydro-kinetic simulations

Based on numerical simulations of a lattice kinetic model for soft-glassy materials, we characterize the global rheology of a dense emulsion-like system, under three representative load conditions: Couette flow, time-oscillating Strain and Kolmogorov flow. It is found that in all cases the rheology is described by a Herschel-Bulkley (HB) relation, , with the yield stress largely independent of the loading scenario. A proper rescaling of the HB parameters permits to describe heterogeneous flows with space-dependent stresses, based on the notion of cooperativity, as recently proposed to characterize the degree of non-locality of stress relaxation phenomena in soft-glassy materials.

An Explicit and Continuously Differentiable Flow Equation for Non-Newtonian Fluids in Pipes

Summary A simple model approximates Herschel-Bulkley (HB) non-Newtonian fluids in laminar flow in pipes. It is continuously differentiable and explicit in the frictional pressure gradient. Such properties are needed for control, real-time optimization, and prediction in drilling operations. The accuracy of the new model is evaluated by comparing it with a numerical implementation of the implicit HB model and some representative approximations used in the literature. Very little loss in accuracy is experienced compared with the implicit solution.

Wall slip and flow of concentrated hard-sphere colloidal suspensions

We present a comprehensive study of the slip and flow of concentrated colloidal suspensions using cone-plate rheometry and simultaneous confocal imaging. In the colloidal glass regime, for smooth, nonstick walls, the solid nature of the suspension causes a transition in the rheology from Herschel–Bulkley (HB) bulk flow behavior at large stress to a Bingham-like slip behavior at low stress, which is suppressed for sufficient colloid-wall attraction or colloid-scale wall roughness. Visualization shows how the slip-shear transition depends on gap size and the boundary conditions at both walls and that partial slip persist well above the yield stress. A phenomenological model, incorporating the Bingham slip law and HB bulk flow, fully accounts for the behavior. Microscopically, the Bingham law is related to a thin (subcolloidal) lubrication layer at the wall, giving rise to a characteristic dependence of slip parameters on particle size and concentration. We relate this to the suspension’s osmotic pressure and yield stress and also analyze the influence of van der Waals interaction. For the largest concentrations, we observe nonuniform flow around the yield stress, in line with recent work on bulk shear banding of concentrated pastes. We also describe residual slip in concentrated liquid suspensions, where the vanishing yield stress causes coexistence of (weak) slip and bulk shear flow for all measured rates.

Optimal determination of rheological parameters for herschel-bulkley drilling fluids using genetic algorithms (GAs)

The rheological properties of a drilling fluid directly affect flow characteristics and hydraulic performance. Drilling fluids containing bentonite mixtures exhibit non-Newtonian rheological behavior which can be described with a high degree of accuracy by the three-parameter Herschel-Bulkley (HB) model. To determine the HB parameters, standard statistical techniques, such as the non-linear regression (NL) method are routinely used. However, sometimes they provide non physically acceptable solutions which could produce wrong values of the significant hydraulic parameters which affect drilling operations. To obtain more accurate results, the Golden Section (GS) method was subsequently developed by Kelessidis et al. (2006). In this work a different technique was developed using the Genetic Algorithms (GAs) to provide an easy-to-use tool in order to determine the three parameters of the Herschel-Bulkley model more accurately. To evaluate the accuracy of the GAs method, experimental viscometric data sets of drilling fluids were taken from the literature and the results were compared with the ones obtained by using the NL and GS techniques. The results show that the GAs and the GS methods provide similar results with very high correlation coefficients and small sum of square errors for most of the samples exhibiting negative yield stress values by the NL technique, while giving similar to the NL technique for the samples that were predicted with positive yield stress. However, in some cases, the GAs method gives better and more realistic results than the GS method.

Effect of Reagents on the Rheological Behavior of an Iron Ore Concentrate Slurry

The influence of dosages of flocculants, dispersants and coagulants on the rheological behavior and state of aggregation and dispersion of an iron ore concentrate slurry was evaluated by determining the degree of dispersion using a settling tube, together with the analysis of flow curves obtained in a concentric cylinder rheo meter. These curves were fitted according to models of Herschel-Bu lkley and Bingham. The objective was to select reagents that promote a higher slurry thermodynamic stability, at pH 10 (p H used at SAMARCO's regrinding circuit). These reagents would be evaluated later as grinding aids. None of the evaluated twenty reagents caused significant increases in the slurry's degree of dispersion. Of the twenty selected reagents, six reduced the fluid consistency index (k coefficient) and apparent viscosity, at the dosage 300 g/t: three polyacrylic acids, silicone acrylate copolymer, citric acid and sodium hexametaphosphate.

Rheological, Textural, Microstructural, and Sensory Properties of Sorbitol-Substituted Mango Jam

Production of low-calorie mango jam was investigated by substituting sucrose with sorbitol. Quality of sorbitol jam was evaluated with respect to rheological, textural, microstructural, color, and sensory attributes. Principal component analysis revealed that sucrose- and sorbitol concentration, hardness, and work of shear were the most relevant parameters in sorbitol jam manufacturing. Sorbitol-substituted mango jam behaved as pseudoplastic fluid exhibiting yield stress. The Herschel–Bulkley (HB) model described adequately the steady-state rheological behavior of jam. Temperature dependence of the consistency index followed Arrhenius relationship. Yield stress of the jam increased with total soluble solids (TSS) content during gelation process and decreased with increasing temperature. Time-dependent structural breakdown characteristics of mango jam followed Hahn model. Hardness of mango jam decreased with increasing sorbitol concentration because of weaker junction zones of pectin molecules. Lightness (L*) and yellowness (b*) decreased, but redness (a*) increased with TSS in mango jam for selected sorbitol levels. The mango jam manufactured at sorbitol level = 70 with 75% sorbitol substitution received the highest overall acceptability score. Microstructure of sorbitol jam was found to be composed of network regions with large pores as well as dense, compact regions with small pores.

From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton {\it et al., Rheol Acta}, 2008, {\bf 47}, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress $\sigma$ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration $\tau_f$ of this fluidization process scales as $\tau_f \propto 1/(\sigma - \sigma_c)^{\beta}$, where $\sigma_c$ stands for the yield stress of the microgel, and $\beta$ is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux {\it et al., Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the {\it steady-state} HB exponent appears as the ratio of the two fluidization exponents extracted separately from the {\it transient} fluidization processes respectively under controlled shear rate and under controlled shear stress.

Fractal analysis of Herschel–Bulkley fluid flow in porous media

The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media.

Rheological, textural, micro-structural and sensory properties of mango jam

Mango jam behaved as pseudoplastic fluid exhibiting yield stress. The Herschel–Bulkley (HB) model described adequately the steady-state rheological behavior of jam. Temperature dependence of the consistency index followed Arrhenius relationship. Time dependent structural breakdown characteristics of mango jam followed Hahn model. Hardness of mango jam increased with pectin concentration and acidity. Hardness increased up to 60% sugar concentration but decreased with further increase in sugar concentration at all pH and pectin levels. Stickiness, work of shear, and adhesion did not show any systematic trend with pH, pectin, and sugar concentration. The overall acceptability was rated highest for mango jam prepared with 65% sugar, 1% pectin at pH 3.4. Principal component analysis (PCA) revealed that hardness and work of shear are the most relevant among all the characteristics (physicochemical, sensory, textural, rheological, and compositional) studied for mango jam. Microstructure of mango jam was found to be composed of network regions with large pores as well as dense, compact regions with small pores.

Rheological behavior of blueberry

The physical and physicochemical characteristics of blueberry (Vaccinium myrtillus) fruits produced in Brazil were analyzed. Rheological properties were measured at 5, 25, 45 and 65 °C, on a stress controlled rheometer equipped with grooved a stainless-steel parallel-plate in a shear rate range of 0-300 s-1, with the objective of determining the influence of temperature on the rheological properties. The pseudoplastic behavior with yield stress was well described by the Ostwald-de-Waele (Power Law), Herschel-Bulkley (HB) and Mizhari Berk models. The yield stress and behavior index decreased with the increase in the temperatures for 5, 25, and 45 °C whereas for the temperature of 65 °C the effects were the opposite exhibiting elevated values. The viscosity decreased with an increase in temperature, and the Arrhenius equation described adequately the effect of temperature on the apparent viscosity of the puree, in which the activation energy (Ea) determined at a shear rate of 100 s-1 was 9.36 kJ.mol-1.

Rheological study of [formula omitted] hydrate slurry in a dynamic loop applied to secondary refrigeration

An original rheological characterisation of CO 2 hydrate slurries in flow is proposed in the present paper. Hydrate slurries are two-phase fluids composed of hydrate crystals in suspension in a liquid phase. One of the applications of CO 2 hydrate slurries relates to secondary refrigeration, principally due to the high latent heat of melting of CO 2 hydrates used as phase change materials and the expected lower cost of gas hydrate production compared to scrapped and brushed surface exchangers (classically used in the field of refrigeration and air-conditioning). In order to be considered as suitable for refrigeration applications, CO 2 hydrate slurries must, however, fulfil other criteria such as satisfying flowing conditions. An experimental loop was used in this work to produce CO 2 hydrate slurries by gaseous CO 2 injection in pre-cooled water and to measure pressure drops as a function of volumetric flow rates for various fractions in solid particles. As most of multiphase solid–liquid fluids, CO 2 hydrate slurry can be rheologically characterised by its pseudo-homogeneous apparent viscosity, strongly depending on the mass fraction, the type and the organisation of the solid particles in the liquid phase related to following parameters: nucleation, growth, shape, size distribution, agglomeration, etc. In order to improve the description of the rheological behaviour of the studied slurry, an empirical model based on the method of the capillary (Ostwald) viscosimeter was applied from our experimental data and provided a Herschel–Bulkley (HB) type equation integrating the solid fraction of the slurry. The results of the empirical HB model were compared to a classical pseudo-homogeneous pressure drop model.

A Unifying Perspective on the Quasi-steady Analysis of Magnetorheological Dampers

A magnetorheological (MR) fluid, modeled as a Bingham plastic (BP) material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a BP model is an idealization to physical MR behavior, albeit a useful one. A better approximation involves modifying both the preyield and postyield constitutive behavior as follows: (1) assume a high viscosity preyield behavior when the shear stress is less than the transition stress, and (2) assume a power law fluid (i.e., strain rate dependent viscosity) when the shear stress is greater than the transition stress. Assuming a power law fluid in postyield allows the model to account for shear thinning behavior exhibited by MR fluids at higher strain rates. Such an idealization for MR fluid constitutive behavior is called an viscous-power law model, or a Herschel—Bulkley (HB) model with preyield viscosity. This study develops a quasi-steady analysis for such a constitutive MR fluid behavior applied to an MR flow mode damper. Closed form solutions are developed for the fluid velocity, as well as key performance metrics, such as damping capacity and dynamic range (ratio of field-on to field-off force). For the given fluid properties and flow mode damper geometry, the fluid velocity profile and gradient, and the relationship of the damper force and piston velocity are analyzed. In addition, specializations to existing models, such as the HB, biviscous, and BP models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.

Experimental and numerical investigations on magnetic fluid jet

The rheological properties of water-based magnetic fluids (MFs) were measured using rotating and capillary rheometers. It is found that the theological behaviors of MFs with high solid content under an applied magnetic field can be described using the Herschel-Bulkley (H-B) model. Two-dimensional numerical simulation was performed to investigate ejection phenomena of the MF from a capillary with the H-B model. Experiments was conducted to observe drop formations. The measured numerical results are validated by the experimental findings.

The influence of texture improver type and its addition level on rheological properties of goat’s milk yogurt

Set yogurt from goat?s milk with addition of two texture improvers DSE 6693 and DSE 6694 from NZMP New Zealand, added in the amount of 1, 2and 3% and control yogurt without addition of texture improvers were produced. In yogurt determined sensory quality, pH, apparent viscosity and rheological properties. Flow curves obtained for produced yogurts were described by three rheological models: Ostwald de Waele, Herschel-Bulkley (H-B) and Casson. Addition of texture improver caused an increase in total solids and total protein content of milk for yogurt. Yogurt with texture improvers gave better sensory quality than control yogurt. The yogurt with 1% addition of DSE 6693 and with 2% addition of DSE 6694 had the best sensory quality. The increase in addition level of texture improvers caused an increase in apparent viscosity, consistency coefficient K, yield stress (except H-B model) and deviation from Newtonian flow (decrease of flow index n). Effect of type of improver was rather negligible, whereas its level addition considerably influenced the evaluated rheological parameters.

Rheological Parameter Estimation for a Ferrous Nanoparticle-based Magnetorheological Fluid using Genetic Algorithms

This study examines identification of rheological parameters for a constitutive model characterizing the rheological behavior of a ferrous nanoparticle-based magnetorheological (MR) fluid. Particle size is nominally 28 nm and the MR fluid has a weight fraction of 27.5% Fe. A constant shear rate rheometer is used to measure flow curves (shear stress vs. shear rate), as a function of applied magnetic field, of an MR suspension of nanometer-sized iron particles in hydraulic oil. The MR fluid is characterized using both Bingham-plastic (BP) and Herschel-Bulkley (HB) constitutive models. These models have two regimes that can be characterized by a field-dependent yield stress: pre-yield implies that the local shear stress is less than the yield stress, and post-yield implies that the local shear stress is greater than the yield stress. Both models of MR fluid behavior assume that the MR fluid is rigid in the pre-yield regime. However, the post-yield behavior is different. The BP model assumes that the post-yield increase in shear stress is proportional to shear rate. However, the HB model assumes that the post-yield increase in shear stress is proportional to a power law of shear rate. Identification of the model parameters is complicated by model non-linearities, as well as variance in experimental data. The rheological parameters of the BP and HB models are identified using both a gradient-based least mean square minimization procedure, as well as a genetic algorithm (GA). The HB model is shown to represent better, the rheological behavior of the ferrous nanoparticle-based MR fluid. Also, the GA performs better than the gradient-based procedure in minimizing modeling error.