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.

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.

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.

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.

Elastohydrodynamic film thickness for shear-thinning lubricants

1998 ◽  
Vol 212 (3) ◽  
pp. 179-191 ◽  
Author(s):  
J. A. Greenwood ◽  
J. J. Kauzlarich
Keyword(s):  
Shear Rate ◽  
Film Thickness ◽  
Gas Turbines ◽  
Shear Thinning ◽  
Mineral Oil ◽  
High Shear ◽  
Newtonian Viscosity ◽  
Special Cases ◽  
Rolling Element ◽  
Low Shear

Mineral oils and synthetic lubricants that are thickened by polymers of large molecular weight are being promoted for automobiles as well as aircraft gas turbines. These multiweight lubricants are found to have a complicated Newtonian and non-Newtonian viscosity depending upon shear rate in the bearing. In general, polymer-thickened mineral oil lubricants show a first Newtonian behaviour at a low shear rate, shear-thinning non-Newtonian behaviour at a higher shear rate and a second Newtonian behaviour at a very high shear rate, with a second Newtonian viscosity approximately equal to the base oil viscosity. Because of high shear thinning in the inlet region of rolling element bearings, predicting the film thickness using the low shear rate first Newtonian viscosity can be in error, in particular examples, by a factor of ½ for mineral oil plus 4% methacrylate thickener and 1/7 for mineral oil plus 20% polybutene thickener. The case of naturally shear-thinning silicone fluids is analysed and it is shown that the elastohydrodynamic (EHD) film thickness is nearly the same for silicones with widely varying first Newtonian viscosity. A general EHD analysis for shear-thinning lubricants in pure rolling is presented and shown to agree with known special cases. A closed-form EHD equation for power law shear-thinning lubricants is derived, which gives very accurate results for a bearing where the inlet state of the rolling element falls in the region where the non-Newtonian viscosity is expected. A comparison with some published experimental results by Bair and Khonsari is presented.

Film Thicknesses in Circular Elastohydrodynamic Contacts

1988 ◽  
Vol 202 (1) ◽  
pp. 11-17 ◽  
Author(s):  
J A Greenwood
Keyword(s):  
Film Thickness ◽  
Excellent Agreement ◽  
Power Law ◽  
Point Contact ◽  
Elastohydrodynamic Film Thickness ◽  
Different Sources

A new elastohydrodynamic film thickness chart is introduced, with advantages over the Johnson chart for the true elastohydrodynamic regime. Collected results of point-contact calculations from different sources are plotted, and show excellent agreement, but do not fit an obvious power law formula.

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.

Stress and texture in sputter deposited Cr films

2003 ◽  
Vol 795 ◽  
Author(s):  
S. Yu. Grachev ◽  
J.-D. Kamminga ◽  
G. C. A. M. Janssen
Keyword(s):  
Tensile Stress ◽  
Film Thickness ◽  
Grain Growth ◽  
Power Law ◽  
Fiber Type ◽  
Intrinsic Stress ◽  
Stress Evolution ◽  
Power Law Exponent ◽  
Sputter Deposited ◽  
Chromium Films

ABSTRACTIntrinsic stress in coatings is often responsible for its performance. We studied tensile stress in sputter deposited chromium films as a function of film thickness and Ar pressure during deposition. We correlate the stress evolution to the grain growth in the polycrystalline films. Both grain growth and stress evolution obey the same power law dependence on thickness. We conclude that the tensile stress is generated at the grain boundaries. The power law exponent did not depend on pressure of Ar and remained 0.36. However, texture and microstructure in the layers changed when pressure was increased from 2×10-2 to 6×10-2 mbar. Texture switched from 110 to 111 fiber type. Grooves and sharp star-like grains were observed at higher pressure. We explain changes in terms of suppressed shadowing and less surface diffusion.

Sign in / Sign up

Export Citation Format

Share Document