non-Newtonian Shear Viscosity Research Articles

The Pressure and Temperature Dependency of Relative Volume, Low Shear Viscosity, and Non-Newtonian High Shear Viscosity in SAE AS5780 HPC, MIL-PRF-23699 HTS, and DOD-PRF-85734 Lubricants

This work quantifies the high-pressure rheological performance of two jet engine turbine oils and three helicopter transmission oils. The jet engine oils are qualified for both the MIL-PRF-23699 high thermal stability and AS5780 high performance classifications, and the helicopter oils are classified against DOD-PRF-85734. Rheological properties include relative volume, low shear, and high shear viscosity. Relative volume measurements are presented for temperatures ranging from 20 to 100 °C and up to 300 MPa. Low shear viscosity measurements range from 20 to 100 °C and up to 1 GPa. Apparent shear or high shear viscosity measurements varied pressure up to 550 MPa and shear stresses up to 5 MPa. The non-Newtonian limit for each lubricant was observed. Rheological models obtained from the measurements include the Tait and Murnaghan relative volume models, the Williams-Landel-Ferry (WLF) modified Yasutomi low shear viscosity model, and both the modified Carreau-Yasuda and double modified Carreau-Yasuda shear viscosity models. The regressed models highlight shortcomings of classical elastohydrodynamic lubrication (EHL) expressions in describing the measured lubricants’ rheological response. These property models support the development of modern EHL calculations as they relate to high-performance aerospace applications.

Non-Newtonian shear viscosity of confined water in forsterite nanoslits: insights from molecular dynamics simulations

ABSTRACT The confined water flow through forsterite nanoslits is vital to the security of CO2 geological sequestration in deep saline aquifers. Molecular dynamics simulations for confined water in the forsterite nanoslits are performed in this work. We investigate the effects of nanoslit height, hydraulic pressure drop, temperature and hydrostatic pressure on the water flow characteristics. Firstly, equilibrium molecular dynamics simulations are conducted to select a minimum nanoslit height for the subsequent non-equilibrium molecular dynamics (NEMD) simulations, to weaken the ultra-dominant nano-confinement effect on water flow. NEMD simulations reveal that the velocity profiles transfer from parabolic to plug-like shape with the increase in hydraulic pressure drop. The distance-dependent shear viscosity is determined by analyzing velocity profiles. The results indicate that the confined water gradually deviates from the Newtonian to non-Newtonian fluid, resulting from the more condensed water molecule layers introduced by the large hydraulic pressure drop. Additionally, we demonstrate that the water flow is enhanced with the temperature increasing. The enhancement in water flow is attributed to the shear viscosity reduction, resulting from the looser hydrogen-bonding network. Comparatively, the impact of variations in the hydrostatic pressure on the velocity profiles and shear viscosity is insignificant. This work provides atomistic insights into the non-Newtonian transport behaviour of high velocity water flow under nano-confinement or extreme environmental conditions.

Foam drainage. Possible influence of a non-newtonian surface shear viscosity

We describe forced drainage experiments of foams made with model surfactant solutions with different surface rheology. We analyze the origin of two distinct drainage transitions reported in the literature, between regimes where the bubble surfaces are mobile or rigid. We propose that both transitions are related to the surface shear viscosity and to its shear thinning behavior. Shear thinning could also account for the huge discrepancies between measurements reported in the literature. The role of surface tension gradients, i.e. Marangoni effect, could not possibly explain the behavior observed with the different solutions.

Flow of complex suspensions

The flow of complex suspensions is ubiquitous in nature and industrial applications. These suspensions are made of complex particles (anisotropic, deformable, or active) suspended in simple fluids. The macroscopic non-Newtonian properties of these suspensions depend on the nature of the suspended particles and their interaction with given flows. Here, we describe how one can make use of novel micro-fabrication techniques and microfluidic rheometers to determine their flow properties under well controlled experimental conditions. We discuss three different aspects important for the study of the flow of complex suspensions. First, we use a well known complex fluid to design a novel microfluidic rheometer. Then we measure the non-Newtonian shear viscosity of a dilute suspension of microswimmers adapting an existing microfluidic rheometer. And finally we use a micro-fabrication technique to produce well controlled model fibers inside microfluidic channels and give some examples of the flow dynamics when these model fiber suspensions are forced through constrictions.

Transition from Newtonian to non-Newtonian surface shear viscosity of phospholipid monolayers

The surface shear viscosity of DPPC (dipalmitoylphosphatidylcholine) monolayers on the air/water interface was determined over a wide range of surface concentrations in an annular channel. DPPC is studied widely because it is ubiquitous in biological systems. Brewster angle microscopy (BAM) was found to be capable of measuring the monolayer velocity field, even in the absence of co-existing phase domains. Interfacial velocimetry via cross correlations of BAM images provides accurate and non-invasive measurements, useful for both macro and microrheology. The measured velocity profiles are compared with computed profiles obtained over a range of surface shear conditions using the Boussinesq-Scriven surface model, from which the surface shear viscosity was determined. For monolayers in the liquid expanded (LE) and liquid expanded/liquid condensed (LE/LC) co-existing phases, we observe Newtonian behavior. We also show how the flow departs from the Newtonian regime for monolayers with larger surface concentration, corresponding to LC phase transition to solid phase.

Friction Theory Modeling of the Non-Newtonian Viscosity of Crude Oils

Rheological behavior is key for the evaluation, simulation, and development of petroleum reservoirs. In previous papers, friction theory models have been used to develop accurate, even reference quality, descriptions of the Newtonian shear viscosity of fluids. The friction theory has also been successfully used to accurately model an ample range of reservoir fluids ranging from natural gas to heavy oils (with viscosities up to thousands of mPa s). In this work, the basic friction theory approach has been further extended to the description of the non-Newtonian shear viscosity of crude oils. The extension is carried out by modifying the basic approach by further introducing a shear rate dissipation parameter for the scaling of the non-Newtonian behavior and a wax-appearance-related temperature. The resulting approach is straightforward and can reproduce the non-Newtonian behavior of crude oils with an accuracy close to the experimental uncertainty. The extended model is consistent with the overall friction theory approach and can be applied to the full range of oil reservoir production conditions, which is demonstrated by the ability of the model to calculate the expected rheological properties of a reconstituted reservoir fluid. In its current form, the proposed model has three adjustable parameters for a full characterization of the investigated oils, and no further parameters are needed in case the fluid is reconstituted. The model is able to reproduce the experimental Newtonian and non-Newtonian rheology over the wide temperature ranges of the studied waxy oils to within an overall average absolute percentage deviation under 15%. Consistent with previous investigations, the addition of a natural gas should yield lower deviations for the reconstituted fluid.

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.

Viscosity models for silicate melts

Rheology of silicates (melts or super cooled as glasses) is one of the most important fields to mankind, as geological activity largely influences life. In this paper, unifying empirical models for the non-Newtonian shear viscosity and the extensional viscosity are proposed. The models have only one parameter, the zero-shear viscosity (the Newtonian plateau), and are valid for a wide range of chemical compositions.

Quantifying Relationships among the Molecular Weight Distribution, Non-Newtonian Shear Viscosity, and Melt Index for Linear Polymers

This paper presents methodologies to quantify the relationships among the molecular weight distribution (MWD), steady-shear non-Newtonian viscosity (i.e., flow curve), and melt index (MI) of three linear low-density polyethylenes manufactured using the same technology. With the aid of computer-aided process simulation tools (such as POLYMERS PLUS), polymer producers can predict accurately the MWD from manufacturing conditions. Our methodologies help the polymer producers to extend their simulation model to predict flow curves and MI from the MWD. To do this, this paper employs (1) a modified Carreau-Yasuda (CY) model or Bersted's partition model to relate the MWDs and flow curves, (2) Bremner and Rudin's model to relate the weight-average molecular weight (MWW) and MI, and (3) Rohlfing and Janzen's model to relate the flow curve and MI. We show that the Carreau-Yasuda, Bersted, and Bremner and Rudin models work very well for correlating our data, predicting flow curves that average 3−7% error and MI value...

Combining molecular and continuum mechanics concepts for constitutive equations of polymer melt flow

Molecular-level modelling of linear viscoelastic properties of a polymer melt is combined with a continuum-based model for the recoverable deformation in domains of fluid in a flow field to predict nonlinear viscoelastic properties. A nonlinear differential constitutive equation is derived, whose parameters are elemental linear viscoelastic properties which can be calculated as a function of polymer composition and environmental conditions. The model is demonstrated by means of examples of important nonlinear effects: recoverable strain and Non-Newtonian shear viscosity, extrudate swell, nonlinear stress relaxation, the onset of shear, and elongational viscosity.

Role of viscoelasticity in tube model of airway reopening. I. Nonnewtonian sols.

This investigation used a previously described bench-top device (Gaver et al., J. Appl. Physiol. 69: 74-85, 1990) to examine the role of nonnewtonian and viscoelastic fluids on events at reopening of a closed flexible tube. Aqueous sodium alginate solutions with and without calcium chloride and sodium dodecyl sulfate in desired concentrations provided fluids with a wide range of surface tensions, storage and loss moduli, and nonnewtonian steady shear viscosity. Dimensionless analysis, using the shear rate-dependent viscosities, was applied to reduce reopening pressure-meniscus velocity data to a master curve. With regard to fluid properties, we found that 1) fluid elasticity strongly changes the pressure-velocity relationship, causing flow instability at higher meniscus velocities; 2) decreasing surface tension gives rise to a smaller yield pressure for reopening; and 3) whereas larger tubes are easier to open, smaller tubes produce additional shear thinning of the lining fluid. These results suggest that, for both the upper (large) and lower (small) airways, nonnewtonian and viscoelastic properties of the mucosal fluid modify the time of closure and rate of reopening.

Rheological predictions of a transversely isotropic fluid model with extensible microstructure

A continuum extensible director theory was formulated to describe the isothermal, incompressible flow of uniaxial rodlike semiflexible liquid crystalline polymers. The model is strictly restricted to material that flow-align in shear, and that, in the absence of flow, are sufficiently far from the nematic-isotropic phase transition. The microstructure of the continuum is described by a variable length director, but the extensibility is finite. The model is an extension of the TIF (Transversely Isotropic Fluid) model of Ericksen (1960). The thermodynamic restrictions on the model parameters are found using the non-negative definiteness of the entropy production. The rheological material functions predicted by the model are calculated for steady simple shear and steady uniaxial extensional flows. In the rigid rod limit the model predictions agree with those of the TIF model, and for the finite extensibility case the model predictions are in agreement with those associated with flexible isotropic polymers: strong non-Newtonian shear viscosity, positive first normal stress differences, recoverable shear of order one, negative second normal stress differences, and a maximum in the steady uniaxial extensional viscosity.

Circular birefringence and dichroism due to shear stress: Optical measurement of non-Newtonian viscosity

The semi-classical molecular theory is given of circular birefringence, dichroism and laser ellipticity due to shear stress, the angle of rotation being given in terms of the shear strain rate and non-Newtonian shear viscosity through a perturbation of the imaginary part of the dynamic frequency dependent molecular polarisability. The non-Newtonian shear viscosity can be measured spectroscopically in terms of the angle of rotation at a given frequency (for example a visible laser line) for a given strain rate and sample dimension.

Conjectures on Elongation of a Polymer in Shear Flow

The behavior of a polymer in dilute solution is examined in a Couette flow. It will be gradually stretched as the shear is increased above the smallest relaxation rate of a chain (∝ξ -3 , ξ being the equilibrium size). Predictions are made on the non-Newtonian shear viscosity, light scattering, and birefringence.

Non-newtonian shear viscosity, normal stress coefficients and corresponding states in rheology

A set of mutually consistent material functions, i.e., shear viscosity, primary normal stress, and secondary normal stress coefficients, is presented. They were originally derived by means of a dense-simple-fluid kinetic theory. It is shown that in spite of their origin the material functions can account for the shear rate dependences of rheological material functions for some polymer solutions, if the formulas are treated as phenomenological functions of shear rate. It is also shown that the material functions used are in fact a set of corresponding state rheological equations of state to a good accuracy for the materials examined.

Theory of nonlinear transport processes and irreversible thermodynamics in multicomponent dense fluids

The kinetic equation for a single component dense fluid reported previously is extended to a multicomponent dense fluid and the evolution equations are derived therefrom for macroscopic fluxes. The extended Gibbs relation is derived for dense mixtures from the entropy balance and evolution equations by applying the modified moment method. The evolution equations yield nonlinear transport equations whose solutions in terms of thermodynamic forces give nonlinear constitutive relations as well as nonlinear transport coefficients. The nonlinearity and nonlinear couplings between different irreversible processes generally tend to decrease the transport coefficients according to the results obtained. The non-Newtonian shear viscosity is a typical example.

Non-newtonian effect and long-range correlation in shear flow in two dimensions

A steady state of a two-dimensional incompressible fluid with shear flow is considered. The nonlinear (non-newtonian) shear viscosity is obtained and the correlation of velocity field fluctuations is found to become long-ranged.

Rheology of concentrated disperse systems II. A model for non-newtonian shear viscosity in steady flows

A relative viscosity — volume concentration relationship,η r =η r (φ) deduced from an energy principle, which operates in newtonian range, is phenomenologically extended to the description of non-newtonian behaviour. Such an extension is performed, using a structural intrinsic viscosity $$\tilde k$$ , which depends on volume concentrationφ and shear rate $$\dot \gamma $$ . At constant $$\dot \gamma $$ , some new results concerningk(φ) are given, leading to determination of the thickness of a surfactant layer onto particle surface, and allowing good agreement to the semi-empirical viscosity relation given byThomas. At constantφ, a rate equation governs the evolution of $$\tilde k$$ as a structural parameter. In steady conditions ( $$\dot \gamma $$ = const.), an equilibrium value $$\tilde k(\dot \gamma _r )$$ is reached, $$\dot \gamma _r $$ being a relative shear rate, depending on the overall time relaxation of the structure. A non-newtonian shear viscosity for steady flows is then obtained, depending on $$(\dot \gamma _r )^p $$ . For systems of non-spherical particles, an empirical determination ofp givesp ≈ 0.5.

Transient and Steady Shear Behavior of SBR Polymers

The low shear rate viscosity behavior of SBR random copolymers is investigated in steady and transient shear flow. The polymers studied have high enough molecular weights to make them of commercial interest. The measurements were performed on an apparatus specially designed but readily available and easy to operate. The results showed that even at very low shear rates, the polymers exhibit non-Newtonian steady shear viscosities. A log-log plot of zero shear rate viscosity vs weight-average molecular weight yields a straight line of slope 3.5. The transient shear data show no stress overshoot at shear rates when the viscosity is non-Newtonian. A theoretical discussion of the independence of these two nonlinear effects is provided. The discussion is based on some popular single-integral constitutive equations. It is shown that a recent modification by Carreau to the Lodge elastic liquid model is very realistic. That is, Carreau's model allows one to obtain separately transient shear stress overshoot and non-Newtonian steady shear viscosity.