A Rational Friction Factor Correlation for Laminar Fully-Developed Pipe Flows of Shear-Thinning Non-Newtonian Fluids

2021 ◽  
Author(s):  
Robert Brewster
Keyword(s):  
Shear Rate ◽  
Friction Factor ◽  
Power Law ◽  
Fluid Model ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Cross Model ◽  
Pipe Flows ◽  
Design Calculations ◽  
Friction Factor Correlation

Abstract A friction factor correlation for laminar, hydrodynamically fully-developed pipe flows of shear-thinning non-Newtonian fluids is derived through analysis and asymptotic considerations. The specific non-Newtonian fluid model used is the Extended Modified Power Law (EMPL) model, which is functionally equivalent to the Cross model. The EMPL model spans the entire shear rate range from the low to the high shear rate Newtonian regions, and includes the intermediate shear rate power law region. The friction factor correlation has an explicit form and is a function of three dimensionless parameters, making it well-suited to design calculations. The overall accuracy of the correlation is 6.6%, though it is much better in most cases. Graphical results for the correlation, and deviations with respect to high-accuracy numerical calculations are presented and discussed.

Theoretical Analysis of Turbulent Flow of Power-Law Fluids in Coiled Tubing

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 447-457 ◽  
Author(s):  
Yunxu Zhou ◽  
Subhash Nandlal Shah
Keyword(s):  
Boundary Layer ◽  
Theoretical Analysis ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Power Law ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Boundary Layer Approximation ◽  
Coiled Tubing ◽  
Friction Factor Correlation

Summary A comprehensive theoretical analysis of turbulent flow of a power-law fluid in coiled tubing was conducted with the approach of boundary layer approximation. Equations of momentum integrals for the boundary layer flow were derived and solved numerically. Based on the results of the numerical analysis, a new friction-factor correlation was developed which is applicable to a wide range of flow behavior index of power-law fluid model. The new correlation was verified by comparing it with the published Ito correlation for the special case of Newtonian fluid. For non-Newtonian fluids, there is also a close agreement between the new correlation and the experimental data from recent full-scale coiled tubing flow experiments. Introduction Many fluids that are pumped through coiled tubing are typically non-Newtonian fluids, such as polymer gels or drilling muds. Understanding their flow behavior and being able to accurately predict frictional pressure through coiled tubing are essential for better operations design. A recent literature review (Zhou and Shah 2004) indicates that though there are numerous studies on the flow of Newtonian fluids in coiled pipes, there is, however, very little information with regard to the corresponding flow of non-Newtonian fluids. Among the various approaches of investigating fluid flow in coiled pipes, there is one important method called boundary layer approximation analysis. It is especially useful for high-Dean (1927, 1928) number flows where the effect of secondary flow is largely confined in a thin boundary layer adjacent to the pipe wall (Dean number is commonly defined as: (equation). According to this approach, the tubing cross-section can be divided into two regions: the central in viscid core, and the thin viscous boundary layer. This leads to much simplified flow equations for high-Dean number flows in curved geometry. This approach has been used by a number of researchers, for example, by Adler (1934), Barua (1963), Mori and Nakayama (1965), and Ito (1959, 1969) for Newtonian fluids, and by Mashelkar and Devarajan (1976, 1977) for non-Newtonian fluids. In a previous attempt, Zhou and Shah (2007) applied the method of boundary layer approximation to solve the laminar flow problem of a power-law fluid in coiled tubing and obtained an empirical friction-factor correlation based on the theoretical analysis and numerical solutions. In the present study, we take the same analysis approach but consider the turbulent flow of a power-law fluid in coiled tubing. A friction-factor correlation for turbulent flow in coiled tubing is developed, and its validity is evaluated with a published correlation (Ito 1959) and recent full-scale experimental data.

Rheological Behavior of Seed Gum from Cassia fistula

2019 ◽  
Vol 818 ◽  
pp. 16-20
Author(s):  
Wancheng Sittikijyothin ◽  
Khanaphit Khumduang ◽  
Keonakhone Khounvilay ◽  
Rattanaphol Mongkholrattanasit
Keyword(s):  
Shear Rate ◽  
Flow Behavior ◽  
Critical Concentration ◽  
Shear Thinning ◽  
Zero Shear Viscosity ◽  
Specific Viscosity ◽  
Cross Model ◽  
Linear Slope ◽  
Mechanical Spectra ◽  
Seed Gum

The C. fistula gums in aqueous solutions clearly exhibited shear-thinning flow behavior at high shear rate, however, at higher concentrations, pronounced shear thinning was observed. The value of zero shear viscosity [h0] was predicted by fitting Cross model. A plotting of specific viscosity at zero shear rate (hsp0) against coil overlap parameter (C[h]) was shown the linear slope of dilute and simi-dilute as 1.43 and 4.10, respectively, which found the critical concentration (C*) about 7.08/[h]. While, the mechanical spectra in the linear viscoelastic region of gum solutions showed the typical shape for macromolecular solutions.

Rheology of Polyaniline-Dinonylnaphthalene Disulfonic Acid (DNNDSA) Montmorillonite Clay Nanocomposites in the Sol State: Shear Thinning versus Pseudo-Solid Behavior

2008 ◽  
Vol 8 (4) ◽  
pp. 1842-1851 ◽  
Author(s):  
Ashesh Garai ◽  
Arun K. Nandi
Keyword(s):  
Shear Rate ◽  
Storage Modulus ◽  
Power Law ◽  
Network Formation ◽  
Loss Modulus ◽  
Shear Thinning ◽  
Disulfonic Acid ◽  
Clay Nanocomposites ◽  
Crossover Point ◽  
Clay Concentration

The melt rheology of polyaniline (PANI)-dinonylnaphthalenedisulfonic acid (DNNDSA) gel nanocomposites (GNCs) with organically modified (modified with cetyl trimethylammonium bromide)-montmorillonite (om-MMT) clay has been studied for three different clay concentrations at the temperature range 120–160 °C. Field emission scanning electron microscopy (FE-SEM), wide angle X-ray scattering (WAXS), differential scanning calorimetry (DSC) and dc-conductivity data (∼10–3 S/cm) indicate that the PANI-DNNDSA melt is in sol state and it is not de-doped at that condition. The WAXS data indicate that in GNC-1 sol clay tactoids are in exfoliated state but in the other sols they are in intercalated state. The zero shear viscosity (η0), storage modulus (G′) and loss modulus (G″) increase than that of pure gel in the GNCs. The pure sol and the sols of gel nanocomposites (GNCs) exhibit Newtonian behavior for low shear rate (<6 × 10–3 s–1) and power law variation for the higher shear rate region. The characteristic time (λ) increase with increasing clay concentration and the power law index (n) decreases with increase in clay concentration in the GNCs indicating increased shear thinning for the clay addition. Thus the sols of om-clay nanocomposites of PANI-DNNDSA system are easily processible. The storage modulus (G′) of GNC sols are higher than that of pure PANI-DNNDSA sol, GNC1 sol shows a maximum of 733% increase in storage modulus and the percent increase decreases with increase in temperature. Exfoliated nature of clay tactoids has been attributed for the above dramatic increase of G′. The PANI-DNNDSA sol nanocomposites behave as a pseudo-solid at higher frequency where G′ and loss modulus (G′′) show a crossover point in the frequency sweep experiment at a fixed temperature. The crossover frequency decreases with increase in clay concentration and it increases with increase in temperature for GNC sols. The pseudo-solid behavior has been explained from jamming or network formation of clay tactoids under shear. A probable explanation of the two apparently contradictory phenomena of shear thinning versus pseudo-solid behavior of the nanocomposite sols is discussed.

Correlation of Polysiloxane Molecular Structure to Shear-Thinning Power-Law Exponent Using Elastohydrodynamic Film Thickness Measurements

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Thomas J. Zolper ◽  
Paul Shiller ◽  
Manfred Jungk ◽  
Tobin J. Marks ◽  
Yip-Wah Chung ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Shear Rate ◽  
Film Thickness ◽  
Power Law ◽  
Shear Thinning ◽  
Macromolecular Structure ◽  
Polymeric Fluid ◽  
Power Law Exponent ◽  
Elastohydrodynamic Film Thickness ◽  
Thickness Measurements

Siloxane-based polymers (polysiloxanes) are susceptible to temporary shear-thinning that manifests as a reduction of elastohydrodynamic film thickness with increasing entrainment speed or effective shear rate. The departure from Newtonian film thickness can be predicted with the power-law exponent ns, an indicator of the severity of shear-thinning in a polymeric fluid that is influenced by the macromolecular structure. In this paper, a combination of extant rheological and tribological models is applied to determine the power-law exponent of several polysiloxanes using film thickness measurements. Film thickness data at several temperatures and slide-to-roll ratios are used to validate the methodology for several siloxane-based polymers with alkyl and aryl branches.

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.

New power-law scaling for friction factor of extreme Reynolds number pipe flows

2020 ◽  
Vol 32 (9) ◽  
pp. 095121
Author(s):  
H. R. Anbarlooei ◽  
D. O. A. Cruz ◽  
F. Ramos
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Power Law ◽  
Pipe Flows

scholarly journals Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

2017 ◽  
Vol 826 ◽  
pp. 918-941 ◽  
Author(s):  
A. Bougouin ◽  
L. Lacaze ◽  
T. Bonometti
Keyword(s):  
Power Law ◽  
Temporal Evolution ◽  
Volume Fraction ◽  
Fluid Model ◽  
Particle Diameter ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Rheological Parameters ◽  
Power Law Fluids ◽  
Neutrally Buoyant

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

scholarly journals Hydrodynamic drag reduction of shear-thinning liquids in superhydrophobic textured microchannels

2021 ◽  
Vol 25 (9) ◽  
Author(s):  
Anvesh Gaddam ◽  
Himani Sharma ◽  
Ratan Ahuja ◽  
Stefan Dimov ◽  
Suhas Joshi ◽  
...  
Keyword(s):  
Friction Factor ◽  
Power Law ◽  
Shear Thinning ◽  
Flow Behaviour ◽  
Friction Reduction ◽  
Hydrodynamic Drag ◽  
Micro Channels ◽  
Factor Ratio ◽  
Newtonian Liquids ◽  
Power Law Index

AbstractSuper-hydrophobic textured surfaces reduce hydrodynamic drag in pressure-driven laminar flows in micro-channels. However, despite the wide usage of non-Newtonian liquids in microfluidic devices, the flow behaviour of such liquids was rarely examined so far in the context of friction reduction in textured super-hydrophobic micro-channels. Thus, we have investigated the influence of topologically different rough surfaces on friction reduction of shear-thinning liquids in micro-channels. First, the friction factor ratio (a ratio of friction factor on a textured surface to a plain surface) on generic surface textures, such as posts, holes, longitudinal and transverse ribs, was estimated numerically over a range of Carreau number as a function of microchannel constriction ratio, gas fraction and power-law exponent. Resembling the flow behaviour of Newtonian liquids, the longitudinal ribs and posts have exhibited significantly less flow friction than the transverse ribs and holes while the friction factor ratios of all textures has exhibited non-monotonic variation with the Carreau number. While the minima of the friction factor ratio were noticed at a constant Carreau number irrespective of the microchannel constriction ratio, the minima have shifted to a higher Carreau number with an increase in the power-law index and gas fraction. Experiments were also conducted with aqueous Xanthan Gum liquids in micro-channels. The flow enhancement (the flow rate with super-hydrophobic textures with respect to a smooth surface) exhibited a non-monotonic behaviour and attenuated with an increase in power-law index tantamount to simulations. The results will serve as a guide to design frictionless micro-channels when employing non-Newtonian liquids.

Pressure Drop Predictions for Laminar Fully-Developed Flows of Purely-Viscous Non-Newtonian Fluids in Circular Ducts

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Robert A. Brewster
Keyword(s):  
Fluid Model ◽  
Constitutive Models ◽  
Newtonian Fluids ◽  
Alternative Formulation ◽  
Cross Model ◽  
Pressure Drops ◽  
Friction Factors ◽  
Wide Range ◽  
Piping Systems ◽  
The Cross

This paper provides the results of numerical calculations of pressure drops and centerline velocities for laminar fully-developed flows of non-Newtonian fluids in circular ducts. The particular non-Newtonian fluid model considered is the Cross model, which has shown the ability to model the behavior of time-independent purely-viscous fluids over a wide range of shear rates. It is shown that the Cross model is equivalent to the more recently proposed extended modified power law (EMPL) model, and an alternative formulation of the nondimensional parameters arising from the use of these models is explored. Results are presented for friction factors and nondimensional centerline velocities over a wide range of fluid and flow conditions, and it is shown that simpler constitutive models can be used in cases where the ratios of the limiting Newtonian viscosities are extreme. The implications of the results to the design and analysis of piping systems is considered, and simple and accurate correlations are provided for engineering calculations.

scholarly journals Two-phase power-law modeling of pipe flows displaying shear-thinning phenomena

1993 ◽  
Author(s):  
Jianmin Ding ◽  
R.W. Lyczkowski ◽  
W.T. Sha
Keyword(s):  
Power Law ◽  
Shear Thinning ◽  
Two Phase ◽  
Pipe Flows
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