Effect of Yield Stress on the Power Law Constants of Fluid Food Materials Determined in Low Shear Rate Viscometers

1963 ◽  
Vol 2 (1) ◽  
pp. 62-65 ◽  
Author(s):  
S. E. Charm
Keyword(s):  
Shear Rate ◽  
Yield Stress ◽  
Power Law ◽  
Low Shear

Viscosity Function for Yield-Stress Liquids

2004 ◽  
Vol 14 (6) ◽  
pp. 296-302 ◽  
Author(s):  
Paulo R. Souza Mendes ◽  
Eduardo S. S. Dutra
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Yield Stress ◽  
Power Law ◽  
Drilling Fluid ◽  
Oil Emulsion ◽  
Viscosity Function ◽  
Coating Formulation ◽  
Low Shear

Abstract A viscosity function for highly-shear-thinning or yield-stress liquids such as pastes and slurries is proposed. This function is continuous and presents a low shear-rate viscosity plateau, followed by a sharp viscosity drop at a threshold shear stress value (yield stress), and a subsequent power-law region. The equation was fitted to data for Carbopol aqueous solutions at two different concentrations, a drilling fluid, an water/oil emulsion, a commercial mayonnaise, and a paper coating formulation. The quality of the fittings was generally good.

Laminar Forced Convection in Viscous Shear-Thinning Liquid Flows Inside Circular Pipes: Case for a Modified Power-Law Rheology

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
J. Subedi ◽  
S. Rajendran ◽  
R. M. Manglik
Keyword(s):  
Heat Transfer ◽  
Shear Rate ◽  
Convective Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Frictional Loss ◽  
Viscous Shear ◽  
Laminar Forced Convection ◽  
Rheology Model ◽  
Low Shear

Abstract Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

Viscosity Models for Drilling Fluids: Viscosity Parameters and Their Use

2019 ◽  
Author(s):  
Arild Saasen ◽  
Jan David Ytrehus
Keyword(s):  
Shear Rate ◽  
Yield Stress ◽  
Yield Point ◽  
Power Law ◽  
Physical Parameters ◽  
Fluid Viscosity ◽  
Reasonable Accuracy ◽  
Bingham Model ◽  
Viscosity Models ◽  
Power Law Exponent

Abstract The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. The scope of the present paper is to outline how to select the individual models, and how the models need to be re-formulated to be able to have parameters with a physical meaning. In principle, the Bingham model itself have physical parameters being the yield point and the plastic viscosity. However, the Bingham model very often only very poorly describe the viscosity in complex fluids. This yield stress can be described within a reasonable accuracy by application of the low-shear yield point. A similar problem exists with the Power-Law model resulting from the model’s absence of a yield stress. The compromise model is the Herschel-Bulkley model which contains a yield stress and a power-law term. This model describes the drilling fluid viscosity with reasonable accuracy and includes both the Bingham and Power-Law models as limit formulations. It is not possible to select fluids based on the Herschel-Bulkley traditional parameters alone. The reason is that the Herschel-Bulkley power-law term’s viscosity parameter has a unit dependent on its power-law exponent. In the present approach the fluid is described using a yield stress, a surplus stress at a characteristic shear rate of the fluid flow and finally a power-law exponent making the fluid applicable in the practical shear rate ranges. The surplus stress is no-longer dependent on other parameters. Hence, we have re-arranged the viscosity model to have independent measurable quantities.

Rheology of pulp suspensions of bleached sugarcane bagasse: Effect of consistency and temperature

TAPPI Journal ◽  
2015 ◽  
Vol 14 (9) ◽  
pp. 601-606 ◽  
Author(s):  
JORGE H. SÁNCHEZ ◽  
GERMÁN C. QUINTANA ◽  
MERY E. FAJARDO
Keyword(s):  
Shear Rate ◽  
Rheological Properties ◽  
Yield Stress ◽  
Sugarcane Bagasse ◽  
Power Law ◽  
Apparent Viscosity ◽  
Power Law Model ◽  
Pulp Suspensions ◽  
Concentric Cylinders ◽  
Rate Controlled

Rheological properties, such as yield stress and apparent viscosity, of pulp suspensions of bleached sugarcane bagasse were studied in a stress-shear rate controlled rheometer using concentric cylinders geometry. Results were statistically analyzed and presented as a function of the suspension consistency (0.5% ≤ Cm ≤ 4.0%) and temperature (20°C, 40°C, and 60°C). The yield stress was influenced by the consistency and temperature. The apparent viscosity was influenced only by the consistency. A power law model was fitted to the experimental results of yield stress. In flow tests, all the suspensions showed shear-thinning behavior, which was in agreement with the Carreau-Yasuda model.

scholarly journals A semi-infinite hydraulic fracture driven by a shear-thinning fluid

2018 ◽  
Vol 838 ◽  
pp. 573-605 ◽  
Author(s):  
Fatima-Ezzahra Moukhtari ◽  
Brice Lecampion
Keyword(s):  
Shear Rate ◽  
Power Law ◽  
Hydraulic Fracture ◽  
Complex Structure ◽  
Shear Thinning ◽  
High Shear Rate ◽  
Asymptotic Region ◽  
High Shear ◽  
Confining Stress ◽  
Low Shear

We use the Carreau rheological model which properly accounts for the shear-thinning behaviour between the low and high shear rate Newtonian limits to investigate the problem of a semi-infinite hydraulic fracture propagating at a constant velocity in an impermeable linearly elastic material. We show that the solution depends on four dimensionless parameters: a dimensionless toughness (function of the fracture velocity, confining stress, material and fluid parameters), a dimensionless transition shear stress (related to both fluid and material behaviour), the fluid shear-thinning index and the ratio between the high and low shear rate viscosities. We solve the complete problem numerically combining a Gauss–Chebyshev method for the discretization of the elasticity equation, the quasi-static fracture propagation condition and a finite difference scheme for the width-averaged lubrication flow. The solution exhibits a complex structure with up to four distinct asymptotic regions as one moves away from the fracture tip: a region governed by the classical linear elastic fracture mechanics behaviour near the tip, a high shear rate viscosity asymptotic and power-law asymptotic region in the intermediate field and a low shear rate viscosity asymptotic far away from the fracture tip. The occurrence and order of magnitude of the extent of these different viscous asymptotic regions are estimated analytically. Our results also quantify how shear thinning drastically reduces the size of the fluid lag compared to a Newtonian fluid. We also investigate simpler rheological models (power law, Ellis) and establish the small domain where they can properly reproduce the response obtained with the complete rheology.

Rheological Modelling of Complex Flow Behaviour of Bitumen-Solvent Mixtures and Implication for Flow in a Porous Medium

2021 ◽  
pp. 1-34
Author(s):  
Olalekan Alade
Keyword(s):  
Shear Rate ◽  
Power Law ◽  
Rheological Model ◽  
Flow Characteristics ◽  
Solvent Mixtures ◽  
Pore Scale ◽  
Rheological Models ◽  
Shear Rates ◽  
Rate Region ◽  
Low Shear

Abstract The viscosity of extra-heavy oils including bitumen can be reduced significantly by adding solvent such as toluene to enhance extraction, production and transportation. Thus, prediction of viscosity and/or rheology of bitumen-solvent mixtures has become necessary. More so, selecting a suitable rheological model for simulation of flow in porous media has an important role to play in engineering design of production and processing systems. While several mixing rules have been applied to calculate the viscosity of bitumen-solvent mixtures, rheological model to describe the flow characteristics has rarely been published. Thus, in this investigation, rheological behaviour of bitumen and bitumen-toluene mixtures (weight fractions of bitumen WB = 0, 0.25, 0.5, 0.6, 0.75, and 1 w/w) have been studied at the flow temperature (75 °C) of the bitumen and in the range of shear rates between 0.001 and 1000 s−1. The data was fitted using different rheological models including the Power Law, Cross Model, Carreau-Yasuda Model, and the newly introduced ones herein named as Cross-Logistic and Logistic models. Then, a computational fluid dynamics (CFD) model was built using a scanning electron image (SEM) of rock sample (representing a realistic porous geometry) to simulate pore scale flow characteristics. The observations revealed that the original bitumen exhibits a Newtonian behaviour within the low shear rate region (0.001 to 100 s−1) and shows a non-Newtonian (pseudoplastic) behaviour at the higher shear rate region (100 to 1000 s−1). Conversely, the bitumen-toluene mixtures show shear thinning (pseudoplastic) behaviour at low shear rate region (0.001 to 0.01), which appears to become less significant within 0.01 to 0.1 s−1, and exhibit shear independent Newtonian behaviour within 0.1 and 1000 s−1 shear rates. Moreover, except for the original bitumen, statistical error analysis of prediction ability of the tested rheological models as well as the results from the pore scale flow parameters suggested that the Power Law might not be suitable for predicting the flow characteristics of the bitumen-toluene mixtures compared to the other models.

An Improved Mathematical Model for Relating Shear Stress to Shear Rate in Drilling Fluids and Cement Slurries

1976 ◽  
Vol 16 (01) ◽  
pp. 31-36 ◽  
Author(s):  
R.E. Robertson ◽  
H.A. Stiff
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Yield Stress ◽  
Power Law ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Drilling Fluids ◽  
Rate Data ◽  
Power Law Model ◽  
Proposed Model

Abstract The Newtonian, Bingham, and power law models previously have been used to approximate the previously have been used to approximate the rheology of drilling fluids and cements. The proposed yield-pseudoplastic model provides more consistently accurate descriptions of the rheology of such fluids. Simple explicit relationships between the wall shear rate and the volumetric flow rate in both pipe and annular flow have been derived from this model for use in engineering calculations. Introduction Two mathematical models have been widely used with drilling fluids and cement slurries for relating shear stress to shear rate. The most popular is that of Bingham,.T = Ty + ny, .............................(1) which describes this relationship as linear after an initial yield. Very few, if any, drilling fluids or cement slurries conform to this model, and no explicit relationship can be derived between the shear rate and the volumetric flow rate in a pipe or an annulus. In recent years, the Ostwald-de Waele or "power law" model,.T = K yn,...................................(2) has gained popularity. Eq. 2 describes a fluid with no yield stress and a constant ratio between the logarithms of the shear stress and the shear rate over a workable range. Simple explicit relationships between the shear rate and the volumetric flow rate in a pipe and an annulus can be derived from the equation, but the model often does not fit actual shear stress and shear rate data. Actual shear stress/shear rate data for many fluids place them in the category of yield-pseudoplastics, fluids that exhibit a yield stress as well as a nonlinear relationship between shear stress and shear rate once flow is initiated. A three-parameter model for such fluids, proposed by Herschel and Bulkley, combines the characteristics of the Bingham and power law models:.T = Ty + K yn ..............................(3) Eq. 3 describes the behavior of yield-pseudoplastics reasonably well, but again, no explicit relationship can be derived between the shear rate and the volumetric flow rate in a pipe or an annulus. Thus, the need exists for a model that will adequately describe yield-pseudoplastics, such as drilling fluids and cement slurries, and that has the analytical utility of the power law model for engineering calculations. PROPOSED MODEL PROPOSED MODEL The proposed model takes the form.T = A (y + C)B,.............................(4) It adequately describes the relationship between shear rate and shear stress for most drilling fluids and cement slurries. A simple explicit equation replacing shear rate to the volumetric flow rate in a pipe or annulus can be derived from Eq. 4. As an pipe or annulus can be derived from Eq. 4. As an added feature, the values of the constants characterize the fluid. Thus, it can be seen that when B = 1.0 and C = 0, Eq. 4 becomes.T = A y, ...................................(5) which describes the flow properties of a Newtonian fluid. When B = 1.0 and C 0, the fluid is a Bingham plastic, as described in Eq. 1. When B 1.0 and plastic, as described in Eq. 1. When B 1.0 and C = 0, the fluid follows the power law model, as shown in Eq. 2. The parameters A and B can be considered similarly to the parameters of the power law model. However, the third parameter, C, has a somewhat different connotation than the yield stress of the Bingham model. SPEJ P. 31

scholarly journals Epitaxial Crystallization of Poly(ε-caprolactone) on Reduced Graphene Oxide at a Low Shear Rate by In Situ SAXS/WAXD Methods

ACS Omega ◽  
2020 ◽  
Vol 5 (49) ◽  
pp. 31535-31542
Author(s):  
Weijun Miao ◽  
Feng Wu ◽  
Shiman Zhou ◽  
Guibin Yao ◽  
Yiguo Li ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Shear Rate ◽  
Reduced Graphene Oxide ◽  
Epitaxial Crystallization ◽  
Reduced Graphene ◽  
Low Shear

Thermorheological Characterization of Elastoviscoplastic Carbopol Ultrez 20 Gel

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Experimental Investigation ◽  
Yield Stress ◽  
Elastic Properties ◽  
Viscous Dissipation ◽  
Power Law ◽  
Effect Of Temperature ◽  
Rheological Parameters ◽  
Frequency Range ◽  
Power Law Index

The temperature and concentration play an important role on rheological parameters of the gel. In this work, an experimental investigation of thermorheological properties of aqueous gel Carbopol Ultrez 20 for various concentrations and temperatures has been presented. Both controlled stress ramps and controlled stress oscillatory sweeps were performed for obtaining the rheological data to find out the effect of temperature and concentration. The hysteresis or thixotropic seemed to have negligible effect. Yield stress, consistency factor, and power law index were found to vary with temperature as well as concentration. With gel concentration, the elastic effect was found to increase whereas viscous dissipation effect was found to decrease. Further, the change in elastic properties was insignificant with temperature in higher frequency range of oscillatory stress sweeps.

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