scholarly journals An Empirical Approach to Correlate Power Law Fluid Parameters Obtained from Low Shear Rate Rotational Viscometers and Tube Flow Viscometers

2001 ◽  
Vol 2 (1) ◽  
pp. 27-33
Author(s):  
Benu ADHIKARI ◽  
V.K. JINDAL
Keyword(s):  
Shear Rate ◽  
Power Law ◽  
Empirical Approach ◽  
Tube Flow ◽  
Power Law Fluid ◽  
Fluid Parameters ◽  
Low Shear

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.

Heat transfer to a power-law fluid in tube flow: Numerical and experimental studies

1987 ◽  
Vol 6 (2) ◽  
pp. 143-151 ◽  
Author(s):  
I. Filkova ◽  
A. Lawal ◽  
B. Koziskova ◽  
A.S. Mujumdar
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Experimental Studies ◽  
Tube Flow ◽  
Power Law Fluid

scholarly journals Deformation of a Capsule in a Power-Law Shear Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Fang-Bao Tian
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lattice Boltzmann Method ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

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.

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.

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.

A Comparison of Differential and Integral Descriptions of the Annular Flow of a Power-Law Fluid

1969 ◽  
Vol 9 (03) ◽  
pp. 311-315
Author(s):  
G.C. Wallick ◽  
J.G. Savins
Keyword(s):  
Shear Rate ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Problem ◽  
Axial Flow ◽  
Past Experience ◽  
Radial Coordinate ◽  
Power Law Model ◽  
Power Law Fluid ◽  
Model Parameter

Abstract Some physical processes may be described mathematically in both differentialand integral equation form. Formulation choice for numerical solution often isbased upon personal preference rather than upon problem characteristics. Wecompare differential and integral methods for the numerical description of thesteady-state flow of a non-Newtonian, power-law fluid through an annulus. Forthis application, our data indicate that the integral formulation is superiorboth in solution accuracy and computational efficiency. Our integral solutionmethod is a generalization of an earlier analytic solution that was restrictedto integer values of the power-law model parameter N. The new method ispower-law model parameter N. The new method is more directly applicable inpractical applications and is valid for all N, integer and non-integer. Introduction In many instances differential and integral equations may be used with equalvalidity for the mathematical description of a physical precess. The choice ofmethods often is dictated more by the past experience and predilection of theanalyst than past experience and predilection of the analyst than by the natureof the problem. Yet the efficiency and efficacy of the solution process may bestrongly dependent upon the problem formulation selected. As an example of thisprocedural dichotomy we will consider the numerical description of thesteady-state isothermal axial flow of an incompressible time independentnon-Newtonian fluid through the annular spacing between two fixed concentriccylinders of radii Ri and R, R greater than Ri.* We assume that the cylindersare infinite in length (no end effects) and that the flow is produced by theapplication of a constant pressure gradient in the axial z-direction. This flowproblem has been treated by a number of investigators, and has practicalapplication, e.g., flow of drilling fluids, extrusion of molten plastics, etc. Fredrickson and Bird have shown that, subject to the above assumptions, theflow equation may be written in the form ...........(1) where J = -dp/dz= constant p represents the pressure, the radial coordinate, and = z pressure, the radial coordinate, and = z represents the shearingstress. We seek a solution of Eq. 1 subject to the adherence boundaryconditions ...........(2) where v = vz is the axial flow velocity. For this flow problem it can beshown that .............(3) where is the shear-dependent viscosity function, and that the shear rate maybe expressed in the forms ..............(4) The minus sign is used in Eq. 4 to insure that and always have the samesign, greater than 0. In principle, the flow problem outlined here may besolved for any non-Newtonian fluid for which the shear-dependent viscosityfunction can be established as a known analytic function of the rate of shearfrom an investigation of any of the viscometric flows. However, it isconvenient for our purpose to use the particular viscometric function .............(5) which is referred to as the power-law model. The parameters n and Kcharacterize the relationship between shear rate and shear stress for a powerlaw liquid. The parameter n is a measure of the departure from Newtonianbehavior. If n less than 1, the flow behavior is of the "shearthinning" type; if n greater than 1, it is of the "shearthickening" category.

Effects of Non-Newtonian Fluid Characteristics on Flow Dynamics in Polymer Flooding: a Lattice Boltzmann Study

2021 ◽  
Author(s):  
Bei Wei ◽  
Jian Hou ◽  
Ermeng Zhao
Keyword(s):  
Porous Media ◽  
Shear Rate ◽  
Newtonian Fluid ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Polymer Flooding ◽  
Lattice Boltzmann Model ◽  
Fluid Viscosity ◽  
Power Law Fluid ◽  
Boltzmann Model

Abstract The flow dynamics of non-Newtonian fluid in porous media is much different from the Newtonian fluid. In this work, we establish a lattice Boltzmann model for polymer flooding taking into both the power law fluid properties and viscoelastic fluid properties. Using this model, we investigate the viscosity distribution in porous media, the local apparent permeability in porous media, and the effect of elastic force on the remaining oil in dead ends. Firstly, we build a single phase lattice Boltzmann model to evolve the fluid velocity field. Then the viscosity and shear rate in each lattice can be calculated based on the relaxation time and velocity field. We further make the fluid viscosity change with the shear rate according to the power-law fluid constitutive equation, consequently establish the lattice Boltzmann model for power law fluid. Moreover, we derive the Maxwell viscoelastic fluid model in integral form using Boltzmann superposition principle, and the elastic force is calculated from the divergence of the stress tensor. We then couple the elastic force into the lattice Boltzmann model by Newton's second law, and finally establish the lattice Boltzmann model of the viscoelastic fluid. Both the models are validated against analytical solutions. The simulation results show that when the power-law index is smaller than 1, the fluid viscosity shows a distribution of that viscosity is higher in pore center and lower near the wall; while when the index is larger than 1, the fluid viscosity shows a opposite distribution. This is because the pore center has a high velocity but a low shear rate, while the boundary has a low velocity but a high shear rate. Moreover, the local apparent permeability decreases with the power law index, and the number of hyper-permeable bands also decreases. In addition, the local permeability shows pressure gradient dependence. Considering the viscoelasticity effects, the displacement fluid has a clear tendency to sweep deeply into the dead end, which improves the oil washing efficiency of the dead end. The model provides a pore scale simulation tool for polymer flooding and help understand the flow mechanisms and enhanced oil recovery mechanisms during polymer flooding.

Power-Law Fluid Flow Over a Sphere: Average Shear Rate and Drag Coefficient

2008 ◽  
Vol 82 (5) ◽  
pp. 1066-1070 ◽  
Author(s):  
Maurice Renaud ◽  
Evelyne Mauret ◽  
Rajendra P. Chhabra
Keyword(s):  
Fluid Flow ◽  
Shear Rate ◽  
Drag Coefficient ◽  
Power Law ◽  
Power Law Fluid ◽  
Average Shear Rate ◽  
Average Shear
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