Herschel-Bulkley Research Articles

A dissipation-based method for improving the accuracy of computational fluid dynamics simulations of high level non-Newtonian wastes

This paper investigates a new viscosity model for laminar, transitional, and turbulent pipe flow simulations of a non-Newtonian slurry using the Star-CCM+ software. Herschel-Bulkley (HB) rheology equation was used in its original and modified forms to model the fluid viscosity. The realizable k-ε model was used for modeling of turbulence. It was observed that simulations using the HB model predicted inaccurate profiles of U (mean velocity) and U+ (mean velocity in wall units). Therefore, we developed alternative values of viscosity obtained directly from non-linearity of stress–strain variation (α) in each iteration. The developed method, “Alpha method”, applied changes in places where dissipation rate of turbulent kinetic energy occurred and was designed based on local or global dissipation rate values. Inverse values of α were used to test effects of more viscosity reduction for all flow regimes. In prediction of the mean velocities, significant improvements were obtained through global adjustment of viscosity in inverse form during simulation of the laminar and turbulent flow cases. For the transitional flow, obtaining improvements in prediction of U and U+ from the same model version faced challenges. While the global adjustments in direct form were found significantly effective in improving the prediction of U, they failed to predict the U+ accurately. For this purpose, Local viscosity adjustments were found significantly effective.

Numerical prediction of flow behavior of cuttings carried by Herschel-Bulkley fluids in horizontal well using kinetic theory of granular flow

The cuttings transport was numerically simulated based on kinetic theory of granular flow in combination with sliding mesh for drill pipe rotation in the horizontal well. The Herschel-Bulkley (H-B) model was implemented to describe the rheological behavior of drilling mud. Three distinguishable flow regions of cuttings and swaying phenomenon of cuttings distribution along the direction of drill pipe rotation were observed. The granular temperature of cuttings is high near the wall of drill pipes, which indicates that the energy from the rotating drill pipe is transferred to cuttings. Effects of three rheological parameters (τ0, KHB and n) on the flow behavior of cuttings and HB fluid were analyzed. With the increase of Herschel-Bulkley fluid rheological parameters, the height of cuttings bed decreases, and the axial flow of cuttings at the lower side is significantly enhanced, but the pressure drop through the annulus is increased. When the value of consistency coefficient and flow behavior index of H-B fluid is low, the cuttings transportation in the wellbore is unstable with the pulsation of cuttings volume fraction in the annulus. Among the three rheological parameters, the flow behavior index plays the most significant role in pressure drop through the annulus.

Effect of superplasticizers on the rheological properties of fly ash incorporated cement paste

The rheology is a study of flow of matter. Rheological behavior of cement paste changes with composition of cement, amount of mineral and chemical admixtures, family of superplasticizer, temperature etc. This paper explores the influence of superplasticizer dosage, superplasticizer family and mineral admixture dosage on the rheological behavior of cement paste. For this purpose cement pastes were prepared at a water cement ratio of 0.37 using OPC and different percentage of fly ash (15, 25, 35) and different dosages of superplasticizer (one from each family). Four families of superplasticizer used for this study are polycarboxylate ether, sulphonate melamine formaldehyde, sulphonate naphthalene formaldehyde and lignosulphates. Rheological tests were performed in a coaxial cylinder viscometer (Brookfield DV-II). Saturation dosage of the superplasticizers in the cement paste mixes with different percentage of fly ash replacement were obtained through marsh cone and mini slump tests on cement paste. Cement pastes were placed in the sample chamber of coaxial cylinder viscometer and shear stress produced measured with known shear rate ranging from 30 S to 65 S-1 applied to the fluid through the spindle. Rheological parameters like yield stress and plastic viscosities were calculated using Bingham and Herschel bulkley model. Change in rheological parameters of the cement paste with fly ash replacement percentage, superplasticizers dosage and family were measured and comparison is made

Rheological behaviour of different grades of self-compacting concrete containing recycled aggregates

Rheological behaviour of three grades of Self-Compacting Concrete (SCC) containing selected volumetric replacement levels of coarse recycled concrete aggregates (SCRCA) is reported. The binder in the control SCC was cement. Fly ash and silica fume were added to the control mix in binary and ternary blends to achieve the normal-, the medium- and the high-strength SCRCAs. Like the SCC made with the natural aggregates, the normal-strength SCRCA showed a shear thickening response. Its flow behaviour could be described using the Modified Bingham (MB) as well as the Herschel-Bulkley (HB) model. Although rheology of the medium- and the high-strength SCRCAs could be represented by the Bingham model, a more detailed analysis of their flow data using the MB and the HB model indicated shear thinning behaviour. This response is attributed to the presence of silica fume in these two concrete grades. The results of this investigation have implications for formwork pressure, multi-lift casting, pumping and segregation resistance of SCRCA.

Peristaltic flow and heat transfer of a Herschel-Bulkley fluid in an inclined non-uniform channel with wall properties

In the present work, we obtained analytical solutions for peristaltic flow and heat transfer of a Herschel-Bulkley (HB) fluid in an inclined non-uniform conduit with elastic walls. The effects of the physical parameters on the axial velocity, the streamlines, the temperature and the rate of heat transfer are discussed through graphs. Further, we discussed the results for the peristaltic transport of Newtonian, Bingham and power-law fluids. The variation in the power-law index n shows that the values of the velocity and the temperature fields are grater for shear thinning (n < 1) HB fluids than the shear thickening (n > 1) HB fluids. Also for n = 1, the results agree very well with the available results in the literature. Further, the inclination angle has a strong influence on the velocity and the temperature fields.

Rheological properties of synthetic mucus for airway clearance.

In this work, a complete rheological characterization of bronchial mucus simulants based on the composition proposed by Zahm et al. (Eur Respir J 1991; 4:311-315) is presented. Dynamic small amplitude oscillatory shear (SAOS) experiments, steady state (SS) flow measurements and three intervals thixotropy tests (3ITT), are carried out to investigate the global rheological complexities of simulants (viscoelasticity, viscoplasticity, shear-thinning, and thixotropy) as a function of scleroglucan concentrations (0.5-2 wt %) and under temperatures of 20 and 37°C. SAOS measurements show that the limit of the linear viscoelastic range as well as the elasticity both increase with increasing sclerogucan concentrations. Depending on the sollicitation frequency, the 0.5 wt % gel response is either liquid-like or solid-like, whereas more concentrated gels show a solid-like response over the whole frequency range. The temperature dependence of gels response is negligible in the 20-37°C range. The Herschel-Bulkley (HB) model is chosen to fit the SS flow curve of simulants. The evolution of HB parameters versus polymer concentration show that both shear-thinning and viscoplasticity increase with increasing concentrations. 3ITTs allow calculation of recovery thixotropic times after shearings at 100 or 1.6 s-1 . Empiric correlations are proposed to quantify the effect of polymer concentration on rheological parameters of mucus simulants. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 106A: 386-396, 2018.

Rheological characteristics of muskmelon (cantaloupe) pulp

The rheological characteristics of musk melon (cantaloupe) pulp was evaluated with a view to determine its flow behaviour, yield stress and applicability of common rheological models. The experimental data on rheological behaviour were analyzed on the basis of four models viz., Ostwald, Casson, Bingham and Herschel-Bulkley (H-B). However, Herschel-Bulkley model showed best fit. Consistency index (K) was found to decrease with increase in temperature. The yield stress value determined by three methods showed in the range of 3.6 to 4.1 Pa. Yield stress calculated from stress-strain plot showed the maximum value. Overall the rheological behaviour of musk melon pulp followed the pseudo plastic with yield stress.

Rheological Characterization of Suspension of Hollow Glass Beads

Summary Hollow glass spheres (beads) are widely used as density and rheological modifiers for various oil and gas process fluids, particularly cement. One of the primary uses is to achieve lightweight slurries with good mechanical properties of the set cement. This paper discusses a concentrated, yet pumpable, suspension of these spheres for offshore cementing applications. Providing the lightweight spheres in a liquid suspension eliminates the risks associated with dry blending these materials. The development of the liquid suspension of hollow beads enables on-the-fly mixing of cement slurries with desired density profiles. Currently, the beads are premixed in the cement powder before they are shipped to offshore locations, which could result in the segregation of the beads during delivery and storage, and limits operations to the predetermined density (concentration of beads) of the slurry. This paper presents the rheological behavior of the concentrated suspension (up to 60% vol/vol) of hollow glass spheres suspended in a dilute aqueous solution of bentonite and soda ash. In addition, an attachment to the viscometer (called Fann Yield Stress Adaptor or FYSA) was used to characterize the flow behavior. A rheological model was developed to highlight the bead/bead surface interactions as a major component controlling flow behavior. Four different variants of beads were studied. These were selected to represent a range in surface area per unit volume of beads. Increasing the concentration of beads or the bentonite in solution correlated to increased yield stress and fluid viscosity at operational shear rates. In addition, a Krieger-Dougherty-type relation captured well the effect of the bead concentration, with the maximum packing fraction of beads as a function of surface area per unit volume of the beads. Overall, the Herschel-Bulkley (HB) model best described the suspension rheology with the shear-thinning exponent in the range of ≈0.8 to 1.0. Surface area of the beads linearly correlated to the yield stress of the corresponding concentrated bead solution. Results of this study and the model developed can be used to develop variants of the system with minimal experimentation, thus significantly shortening the design time.

Stiffness and Damping Properties of (Semi) Floating Ring Bearing Using Magnetorheological Fluids as Lubricant

Magnetorheological fluids (MRFs) are applicable for achieving semi-active control in smart bearings. For hydrodynamic bearings lubricated with MRF, changes of the viscosity induced by magnetic field lead to changes of the dynamic characteristics such as stiffness and damping properties, providing the controllability to the bearings in rotor applications. Two main defects of the MRF, however, may potentially limit the use of this kind of bearings. One is that the magnetic field-induced viscosity alteration capability decreases as the shear rate increases; the other is the extra friction introduced by iron particles in the MRF in external magnetic field. In this study, the floating ring bearing (FRB) and semi-floating ring bearing (sFRB) are introduced to replace common journal bearing for MRF-lubricated smart bearings. Performance enhancement is achieved using FRB and sFRB. The lubrication behavior of MRF is studied using the Herschel–Bulkley (HB) model that incorporates the yield stress and the shear-thinning effect, which are the two main features of the MRF under shearing. A kind of MRF is developed for lubrication application, and a test rig is setup to measure its shear rate–stress relationship and then to identify its HB model parameters. With the identified HB model, stiffness and damping characteristics of the MRF-lubricated FRB and sFRB are studied. Results show that, compared to MRF-lubricated common journal bearings, the MRF-lubricated FRB and sFRB both achieve better performances in damping enhancement, while limiting the journal friction to a relatively lower degree.

Comparative study between microvascular tone regulation and rheological properties of blood in patients with type 2 diabetes mellitus.

The aim of the study is to investigate the changes of the skin blood flow responses to cold stress in patients with diabetes mellitus type 2 through wavelet analysis of the peripheral skin temperature oscillations and to estimate their relationship with the blood viscosity values. The amplitudes of the skin temperature pulsations (ASTP) were monitored by "Microtest" device ("FM-Diagnostics", Russia); the whole blood viscosity and the shear stresses were measured by Contraves LS30 viscometer (Switzerland) at a steady flow in 9 healthy subjects and in 30 patients with type 2 diabetes mellitus. Power law and Herschel-Bulkley (HB) equations were applied to describe the blood rheology. Both models include consistency (k) and flow index (m), and the HB also gives the yield stress (τ0). The Spearman rank correlations between these parameters and the ASTP in the frequency ranges, corresponding to the myogenic, neurogenic and endothelial mechanisms of the microcirculation tone regulation were calculated. The ASTP values decreased when the blood viscosity increased. The correlation analysis revealed good ASTP-m (r > 0.5) and ASTP-k (r < -0.5) relationships in the endothelial range, while the ASTP-τ0 correlation was weaker (r≈-0.4). These correlations became lower for the ASTP during the cold stress. The results prompt manifestation of endothelial dysfunction in patients with type 2 diabetes.

Rheological behavior of fresh cement pastes with a graphene oxide additive

The rheological properties and morphology of fresh cement pastes with different contents of graphene oxide (GO) were investigated by a rheometer and a laser confocal scanning microscope, respectively. The rheological data were fitted by the Modified-Bingham (M-B) model and Herschel-Bulkley (H-B) model. A mechanism for the effect of GO on the rheological properties is proposed. Results show that the cement particles are re-agglomerated and new flocculation structures are generated by the addition of GO. The new flocculation structures significantly alter the rheological properties of the pastes. The degree of re-agglomeration and the number of new flocculation structures increase with increasing GO content, leading to a sharp increase in the yield stress, plastic viscosity and the area of the hysteresis loop. GO can effectively reduce the degree of shear-thickening, and increase the critical shear rate and the stability of the pastes.

The influence of effusion rate and rheology on lava flow dynamics and morphology: A case study from the 1971 and 1988–1990 eruptions at Villarrica and Lonquimay volcanoes, Southern Andes of Chile

We analyzed two historical lava flows from the Southern Andes of Chile: The lava flows from the 1971 Villarrica volcano eruption and the 1988–1990 Lonquimay volcano eruption. The 1971 lava flow has a volume of 2.3×107m3, a maximum length of 16.5km and was emplaced in two days, with maximum effusion rates of ~800m3/s. The lava has a mean width of 150m and thicknesses that decrease from 10 to 12m at 5km from the vent to 5–8m at the flow front. The morphology is mainly ‘a‘ā. The 1988–1990 lava flow has a volume of 2.3×108m3, a maximum length of 10.2km and was emplaced in 330days, with peak effusion rates of ~80m3/s. The flow has a mean width of 600m and thicknesses that increase from 10 to 15m near the vent to >50m at the front. The morphology varies from ‘a‘ā in proximal sectors to blocky in the rest of the flow. We modelled the advance rate and thickness of these flows assuming two possible dynamical regimes: An internal rheology regime modelled as a Herschel-Bulkley (HB) fluid and a Yield Strength in the Crust (YSC) regime. We compared our results with the widely used Newtonian and Bingham rheologies. Our results indicate that the 1971 flow can be modelled either by the HB, Bingham or Newtonian rheologies using a single temperature, while the 1988–1990 flow was controlled by the YSC regime. Our analysis and comparison of models shows that care should be taken when modelling a lava flow, as different rheologies and assumptions can reach the same results in terms of advance rate and flow thickness. These examples suggest that the crustal strength should be taken into account in any model of lava flow advance.

On the propagation of viscous gravity currents of non-Newtonian fluids in channels with varying cross section and inclination

This paper presents a model for the laminar propagation of gravity currents of rheologically complex fluids over natural slopes. The study is motivated by the ubiquitous occurrence of gravity currents in environmental applications that are confined by channels that widen and have reduced slopes in the flow direction; typical examples are mud and lava flows. In these applications, many fluids exhibit nonlinear relationships between shear stress and shear rate, with or without the appearance of a yield stress. We consider Ostwald-de Waele and Herschel-Bulkley (HB) fluids. A power-law equation is used to capture the variations in the channel shape and slope in the flow direction. We study the motion of constant and time-dependent volumes of these fluids on smoothly varying topographies. Approximate similarity solutions are obtained for Ostwald-de Waele fluids, while for HB fluids, we use the methods of characteristics to compute front propagation. Constant volume and constant influx tests were conducted in a channel with a widening parabolic cross-section and an inclination decreasing downstream from ≈ 7° to ≈ 3.2°. The front position was measured continuously over time, and the current thickness and the surface velocity were recorded for a subset of experiments in some cross sections. The experimental study confirms the theoretical formulation, with a better agreement for constant influx than constant volume currents.

Surface chemistry and rheological properties of API bentonite drilling fluid: pH effect, yield stress, zeta potential and ageing behaviour

API bentonite, a key ingredient of drilling muds, displayed a negative zeta potential across the whole pH range of 2.5–12.3. It contained two very rheological active ingredients, sodium montmorillonite or Na+Mt (40.4%) and needle-shape sepiolite (16%). Due to the interplay of these two ingredients, the rheological behaviour displayed by the API bentonite suspensions is quite different to other bentonite suspensions. The gel displayed a very low or no yield stress at low acidic pH and a maximum yield stress at pH 8–12. Magnesium leaching from sepiolite at low pH and its hydrolysis plays a role in affecting the rheological properties at high pH. Yield stress and ageing behaviour was observed in suspensions with at least 3wt% solids. The Herschel-Bulkley (HB) model described the flow behaviour of these gels. Both the HB yield stress and viscosity at a fixed shear rate of the 7wt% gel peaked at pH 8.5 and were smallest at pH 5.2. The ageing or structural recovery behaviour is most pronounced at high pH for the most concentrated gels. Both the Leong and Nguyen-Boger ageing models described the structural recovery behaviour well. The recovery of the recently discovered very open honeycomb structure formed by Na+MT gel, after breakdown by shear was invoked to explain the ageing behaviour.

Rheology Study on Low-Sugar Apple Jam by a New Nonlinear Regression Method of Herschel-Bulkley Model

Structure break was found in shearing process of static prepared low-sugar apple jam, which is a thixotropic and shear-thinning fluid. In order to investigated this jam, a new nonlinear regression method of Herschel–Bulkley (H-B) model without measuring yield stress was set up using R2 as optimizing criterion, and compared with Casson model. Dynamic yield stress was calculated using the regression of downward curve. Casson model was found fit in high shear rate (in one case, R2 0.9986, still lower than H-B model, 0.9997). Break stress (from 113 to 497 Pa) could be largely increased by soluble solid concentration rising, and dynamic yield stress of H-B model changed from 0.004 to 20.75 Pa, mainly depending on sugar and soluble solid concentration. Consistency index (24.50–102.3 Pa·sn) was increased with adding soluble solid and decreased with adding sugar. Flow behavior index (0.229–0.363) was increased evidently with adding pectin and sugar. Practical Applications The low-sugar jams are more nutrition-reasonable since they generally provide fewer calories, now short of deep research. Rheological properties are of great significance for processed food fluids. Traditional steady-state test was applied widely in rheologic study of food fluids. However, information under flow curves could not be explored in detail because definition of yield stress was confused for a long time and the most common model of fluid, Herschel–Bulkley model, lacked suitable regression method. Additionally, upward curve was often ignored. In this work, a new simple nonlinear regression of Herschel–Bulkley model was set up without measuring yield stress investigated. Then the influences of ingredients on rheologic properties of low-sugar apple jam could be investigated in detail. It is expected that the new method and observation would be applied by other rheologic researchers, and it is useful for finding relationships between mouth feel and indexes of Herschel–Bulkley model.

Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids

In this study, we present a homogenization model for the macroscopic rheological behavior of non-colloidal suspensions of initially spherical, viscoelastic particles in yield stress fluids, which are subjected to uniform flow conditions. The constitutive behavior of the suspending fluid is characterized by the Herschel–Bulkley (HB) model, and the particles are assumed to be neutrally buoyant solids characterized by the finite-strain Kelvin–Voigt viscoelastic model. We make use of the “linear comparison composite” variational technique of Ponte Castañeda (1991) to approximate the instantaneous response of the suspensions of viscoelastic particles in the HB fluid by that of a fictitious suspension consisting of the same particles distributed identically in a Newtonian fluid with a suitably-chosen viscosity. The response of the latter suspension is then estimated by the homogenization model recently developed by Avazmohammadi and Ponte Castañeda (2015), which, when combined with appropriate evolution laws for the relevant microstructural variables, provides a complete characterization of the time-dependent response of the actual suspensions. With the objective of illustrating the key features of our model, we consider the particular case of suspensions of elastic particles in HB fluids under shear flow conditions. The results provide a broad picture of the influence of the HB fluid and particle constitutive properties, as well as of the particle volume fraction on the effective time-dependent and steady-state behaviors of the suspensions. For the special case of non-deformable particles, our model predicts that the suspensions behave like HB fluids with modified properties, consistent with the results of Chateau et al. (2008).

Numerical simulation and experimental validation of liquid‐film‐flow characteristics in dip coating for non‐Newtonian fluids

The film‐flow problem in dip coating is simulated numerically for non‐Newtonian fluids based on Carreau–Yasuda (CY) and Herschel–Bulkley (HB) constitutive equations, with particular focus on coating‐film‐thickening phenomena and on the evolution of free surface and flow field under different sets of conditions. Finite element method (FEM) is combined with remeshing technique using a commercial code (Polyflow). Numerical predictions of the final film thickness and free surface for HB and CY fluids are successfully compared with experiments under the given conditions. Results show that the combination of FEM‐remeshing technique could be useful for dip‐coating design and optimization. Effects of coating fluid properties and withdrawal speed on film thickening and free surface shape and location are also discussed. Flow fields under different conditions are presented to analyze the evolution of the entire flow field and flow characteristics in detail. POLYM. ENG. SCI. 56:1070–1078, 2016. © 2016 Society of Plastics Engineers

Effect of Temperature on Grease Flow Properties in Pipes

ABSTRACTThe effect of temperature on grease flow properties in pipes was investigated using both theoretical and experimental methods. A theoretical model for pipe flow was obtained by using the Herschel-Bulkley (H-B) rheology model. The H-B parameters at different temperatures were obtained from flow curves measured on a rheometer. The flow properties in the pipes were studied and combined with the theoretical model and H-B parameters. In addition, pressure drop experiments were carried out to verify the theoretical model. The model can be used to predict the critical temperature at which a lubrication system would no longer be able to deliver a sufficient grease flow rate.

Viscoelastic capillary flow: the case of whole blood

The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR) law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.<br />In this work we consider the Herschel-Bulkley (HB) rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids), the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM) law for power-law fluids. Although HB model cannot reduce to Casson’s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.<br />Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.

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.