Shear-dependent Viscosity Research Articles

The rheological assumptions of classical EHL: What went wrong?

Abstract The field of elastohydrodynamic lubrication (EHL) now has two very different approaches to the problem. For the first approach, two assumptions regarding the pressure, temperature and shear dependence of viscosity have been essential to the way that classical EHL developed over the last forty years. 1. The liquid in the inlet zone responds in Newtonian fashion. 2. The shear stress versus shear rate relationship of the liquid has the same form as the average shear stress versus average shear rate obtained from a traction curve. The new, quantitative, approach employs viscosities measured in instruments which do not rely upon these assumptions. There has been a rapid succession of advances in understanding of film forming and friction under the new approach.

The Viscosity of Polyalphaolefins Mixtures at High Pressure and Stress

Understanding the pressure and shear dependence of viscosity is essential to an understanding of the mechanisms of film forming and friction in concentrated contacts. The blending of different molecular mass polyalphaolefins (PAOs) may permit the formulator to arrive at a desired combination of film thickness and friction. The viscosities of PAO base oils and their blends were measured versus temperature, pressure, and shear stress to 1 GPa in pressure. The Grunberg–Nissan mixing rule, with effective mole fractions, provides an excellent mixing rule for the temperature and pressure-dependent low-shear viscosity. This work provides the first look at a possible mixing rule for the non-Newtonian response of mixtures of base oils.

The energy equality for weak solutions to the equations of non-Newtonian fluids

In this short paper, we extend the result of Shinbrot (1974) to an incompressible fluid with shear dependent viscosity. It is shown that a weak solution to the equations of non-Newtonian fluids lying in a space Lq(0,T;Lp) satisfies an energy equality, where 2rr−1≤p≤2rr−2 and 1p+1q≤r−1r, if r>2; p≥2rr−1 and r−1p+1q=r−12, if 2(n+1)n+2<r≤2. In particular, our result implies that the weak solution must satisfy the energy equality when r≥3n+2n+2, which is consistent with the known fact.

Ultrasonic Characterization of Newtonian and Non-newtonian Fluids

Viscous liquid causes a loss of acoustic energy for acoustic wave propagation through the liquid. From an acoustical point of view, Glycerin being Newtonian is a more complex medium as it is heterogeneous, anisotropic and viscoelastic. Non-Newtonian liquids like PEG-SiO2, DMF-SiO2 solutions show shear-dependent nonlinear Viscosity. Apparent molar adiabatic compressibility ( ), as well as bulk moduli (K) and apparent molar volumes ( ) of different glycerin-water solutions, are evaluated in the present investigation. At the lower concentration region for glycerin-water solutions apparent molar adiabatic compressibility ( ) varies linearly with the independent variable either molality or m1/2. The pulse-echo method has been followed to measure attenuation coefficient and sound velocity in these liquids at room temperature. This sound velocity has been compared with the measurement from high precision density and velocity meter (Anton Paar DSA 5000 M for the same temperature. The measurement technique has been reported to quantify adiabatic compressibility as 10% glycerin in water was found to be 41.1×10-11 Pa-1 (K=2.43GPa) including 1.86dB/cm/MHz of attenuation, less compared to pure water but the ultrasonic absorption coefficient (μa ≈ 0.53) of 10% glycerin in water is nearer to pure water whereas the Non-Newtonian fluids show higher attenuation (>3dB/cm) and higher absorption (μa≈0.6).

Effect of disorder in the pore-scale structure on the flow of shear-thinning fluids through porous media

Modeling the flow of fluids with shear-dependent viscosity through porous media is a challenging fundamental and engineering problem. At continuum-scale, such flows are usually described using modified versions of Darcy’s law, which are obtained by considering either an apparent viscosity or an apparent permeability. In the two cases, Darcy’s law becomes nonlinear as the apparent viscosity or permeability both depend on the velocity or pressure gradient. The main difference between these two approaches is the impact of non-Newtonian effects on the flow direction. With the apparent viscosity, the flow direction is determined by the standard permeability tensor and unaltered by non-Newtonian effects. On the other hand, with the apparent permeability, the flow direction may be modified by non-Newtonian effects contained in the second-order tensor. Here, we ask the question of whether it is necessary to use a general tensorial correction including changes of flow direction or if the (scalar) apparent viscosity approach is sufficient. To study this, we solve numerically the non-Newtonian flow problem in a variety of isotropic porous structures for a model fluid where the viscosity depends on the shear rate following a power law with a Newtonian cut-off in the limit of low shear rates. We find that the structure of the porous medium plays a fundamental role and that there is a competition between the nonlinearity of the flow, induced by the non-Newtonian rheology, and the disorder of the porous structure. Our main result is that an apparent viscosity is sufficient in cases of sufficiently disordered porous media, as is the case of some sandstones found in petroleum engineering. Fundamentally, this suggests that the disorder in the geometry of the porous structure is mitigating part of the nonlinear effects due to the rheology.

Influence of Frequency-Dependent Dielectric Loss on Electrorheology of Surface Modified ZnO Nanofluids

The shear dependent viscosity change in dielectric nanofluids under the applied electric field, provide potentials for prospect applications especially in enhanced oil recovery. When nanofluids are activated by an applied electric field, it behaves as a non-Newtonian fluid under electrorheological effect (ER) by creating the chains of nanoparticles. In this research, the effect of dielectric loss on the electrorheological characteristic of dielectric nanofluids (NFs) was studied, corresponding to the applied frequency of 167 and 18.8 MHz. For this purpose, electrorheological characteristics of ZnO (55.7 and 117.1 nm) nanofluids with various nanoparticles (NPs) concentration (0.1, 0.05, 0.01 wt. %) were measured. The measurement was done via solenoid based EM transmitter under salt water as a propagation medium. The result shows that the applied electric field caused an apparent increase on the relative viscosity of ZnO NFs due to electrorheological effect. However, the relative viscosity shows a higher increment at 167 MHz due to the greater dielectric loss, compared to 18.8 MHz. The high dielectric loss allows the dipole moments to rotationally polarize at the interfaces of nanoparticles, which create stronger chains that align with the applied electric field. Additionally, the relative viscosity demonstrated an increment with the increase in particle size of ZnO nanoparticles from 55.7 to 117.1 nm. While the viscosity of nanofluid also indicated the high dependence on particle loading.

Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids

The understanding of hydrodynamic forces around particles, drops, or bubbles moving in Newtonian liquids is modestly mature. It is possible to obtain predictions of the attractive–repulsive interaction for moving ensembles of dispersed particulate objects. There is a certain intuition of what the effects of viscous, inertial, and surface tension forces should be. When the liquid is non-Newtonian, this intuition is gone. In this review, we summarize recent efforts at gaining fundamental understanding of hydrodynamic interactions in non-Newtonian liquids. Due to the complexity of the problem, most investigations rely on experimental observations. However, computations of non-Newtonian fluid flow have made increasingly significant contributions to our understanding of particle, drop, and bubble interactions. We focus on gravity-driven flows: rise or sedimentation of single spheroidal objects, pairs, and dispersions. We identify the effects of two main rheological attributes—viscoelasticity and shear-dependent viscosity—on the interaction and potential aggregation of particles, drops, and bubbles. We end by highlighting the open questions in the subject and by suggesting future directions toward the fundamental physics as well as applications.

Nonlocal Cahn–Hilliard–Navier–Stokes systems with shear dependent viscosity

We consider a diffuse interface model for the phase separation of an incompressible and isothermal non-Newtonian binary fluid mixture in three dimensions. The averaged velocity u is governed by a Navier–Stokes system with a shear dependent viscosity controlled by a power p>2. This system is nonlinearly coupled through the Korteweg force with a convective nonlocal Cahn–Hilliard equation for the order parameter φ, that is, the (relative) concentration difference of the two components. The resulting equations are endowed with the no-slip boundary condition for u and the no-flux boundary condition for the chemical potential μ. The latter variable is the functional derivative of a nonlocal and nonconvex Ginzburg–Landau type functional which accounts for the presence of two phases. We first prove the existence of a weak solution in the case p≥11/5. Then we extend some previous results on time regularity and uniqueness if p>11/5.

Effects of Rheological Factors on Perceived Ease of Swallowing

This study is a contribution to the understanding of how rheological properties of a fluid influences swallowing, especially people suffering from swallowing disorders (dysphagia). Our hypothesis was that fluid elasticity contributes to safe and pleasant swallowing. In the present study three food grade model fluids with specific rheological properties were developed and used: A Newtonian fluid with constant shear viscosity, an elastic Boger fluid with constant shear viscosity and a shear-thinning fluid which was elastic and had rate dependent shear viscosity. By comparing the swallowing of these model fluids the specific rheological effects could be distinguished. Sensory analysis of the perceived ease of swallowing was performed by a panel of healthy individuals, and by a group of dysphagic patients. The swallowing of the latter group was also characterized by videoflouroscopy and the transit times in the mouth and pharynx were determined. The hypothesis was confirmed by dysphagic patients who perceived swallowing easier for the elastic model fluids. A sensory panel of healthy individuals could not distinguish differences in swallowing, likely because their swallowing functions well and is an involuntary process. Quantitative videofluoroscopic measurements of swallowing transit times for the dysphagic patients suggested that fluid elasticity contributed to easy and safe swallowing, but the effect was not statistically significant due to the large spread of type of swallowing disorder.

Analysis of micromixing of non-Newtonian fluids driven by alternating current electrothermal flow

Biochemical applications pertaining to chip scale mixing often deal with fluids which exhibit non-Newtonian behavior. This paper presents numerical investigations on the characterization of the effect of shear dependent apparent viscosity of non-Newtonian fluids on the mixing efficiency and volume flow rate in an alternating current electrothermal micromixer driven by electrothermal micropump. The micromixer consists of thin film asymmetric pairs of electrodes on a microgrooved channel floor and an array of electrode pairs on the top wall. The results show that mixing quality and flow rate have a strong dependence on shear dependent viscosity of the non-Newtonian fluid. Using a power law based constitutive model, it is found that for specific design parameters, more uniform and homogeneous mixing is achieved with increasing flow behavior index. Thus, electrothermal mixing in a microfluidic device has higher efficiency and effectiveness in the regime of dilatant fluids compared to Newtonian and pseudoplastic fluids. Our results also demonstrate that an optimal voltage for maximum mixing efficiency progressively reduces, while the flow rate continues to increase monotonically, with enhancements in the applied AC potential. These results hold practical implications in several emerging applications, including chemical analysis of biological fluids in general, and biomedical diagnostics in particular.

Quality by Design approach for an in situ gelling microemulsion of Lorazepam via intranasal route

The present study illustrates the application of the concept of Quality by Design for development, optimization and evaluation of Lorazepam loaded microemulsion containing ion responsive In situ gelator gellan gum and carbopol 934. A novel approach involving interactions between surfactant and polymer was employed to achieve controlled drug release and reduced mucociliary clearance. Microemulsion formulated using preliminary solubility study and pseudo ternary phase diagrams showed significantly improved solubilization capacity of Lorazepam with 54.31±6.07nm droplets size. The effect of oil to surfactant/cosurfactant ratio and concentration of gelling agent on the drug release and viscosity of microemulsion gel (MEG) was evaluated using a 32 full factorial design. The gel of optimized formulation (MEG1) showed a drug release up to 6h of 97.32±1.35% of total drug loaded. The change in shear-dependent viscosity for different formulations on interaction with Simulated Nasal Fluid depicts the crucial role of surfactant-polymer interactions on the gelation properties along with calcium ions binding on the polymer chains. It is proposed that the surfactant-polymer interactions in the form of a stoichiometric hydrogen bonding between oxyethylene and carboxylic groups of the polymers used, provides exceptional ME stability and adhesion properties. Compared with the marketed formulation, optimized MEG showed improved pharmacodynamic activity. Ex vivo diffusion studies revealed significantly higher release for MEG compared to microemulsion and drug solution. MEG showed higher flux and permeation across goat nasal mucosa. According to the study, it could be concluded that formulation would successfully provide the rapid onset of action, and decrease the mucociliary clearance due to formation of in situ gelling mucoadhesive system.

Temperature dependence of shear viscosity ofSU(3)-gluodynamics within lattice simulation

This report is devoted to the study of temperature dependence of shear viscosity in SU (3)-gluodynamics. To calculate shear viscosity we measured the correlation function of the energy-momentum tensor T12 T12 for a set of temperatures in the region T/Tc ϵ (0.9, 1.5). The measurements were carried out using multilevel algorithm which considerably improves the accuracy of the data. For determination of the shear viscosity two methods were used: physically motivated ansatz and non-parametrical Backus-Gilbert method. Both methods give consistent results. The calculation allows to determine temperature dependence of the ratio of shear viscosity to the entropy density η/s .

Systematic Extraction of QGP Properties

We investigate the collision energy dependence of shear viscosity over the entropy density ratio $\eta/s$ in Au+Au collisions at $\sqrt{s_{NN}}=19.6, 39$, and $62.4$ GeV, using Bayesian statistical analysis and Gaussian process emulators to explore the full input parameter space of a transport+hydrodynamics hybrid model. The ratio is found to decrease as a function of collision energy, supporting the results from previous studies performed with the same hybrid model.

Steady flow for shear thickening fluids in domains with unbounded sections

We solve the stationary Stokes and Navier–Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonian fluids using the techniques found in [3, Dias and Santos].

A microfluidic method and custom model for continuous, non-intrusive biofilm viscosity measurements under different nutrient conditions.

Straight, low-aspect ratio micro flow cells are used to support biofilm attachment and preferential accumulation at the short side-wall, which progressively reduces the effective channel width. The biofilm shifts downstream at measurable velocities under the imposed force from the constant laminar co-flowing nutrient stream. The dynamic behaviour of the biofilm viscosity is modeled semi-analytically, based on experimental measurements of biofilm dimensions and velocity as inputs. The technique advances the study of biofilm mechanical properties by strongly limiting biases related to non-Newtonian biofilm properties (e.g., shear dependent viscosity) with excellent time resolution. To demonstrate the proof of principle, young Pseudomonas sp. biofilms were analyzed under different nutrient concentrations and constant micro-flow conditions. The striking results show that large initial differences in biofilm viscosities grown under different nutrient concentrations become nearly identical in less than one day, followed by a continuous thickening process. The technique verifies that in 50 h from inoculation to early maturation stages, biofilm viscosity could grow by over 2 orders of magnitude. The approach opens the way for detailed studies of mechanical properties under a wide variety of physiochemical conditions, such as ionic strength, temperature, and shear stress.

Flow of blood in micro-channels: recent results based on mixture theory

Blood, composed of red blood cells (RBCs), white blood cells, platelets and plasma, is a non-linear fluid exhibiting complex behavior, such as plasma-skimming and the Fahraeus effect, which are observed especially in microscale applications. In this paper, we use Mixture Theory to model blood as a two-fluid (two-component) system. Plasma is treated as a viscous fluid and the RBCs are modeled as a nonlinear fluid with a shear dependent viscosity, with the effect of the hematocrit included. The drag force and the shear lift force between the RBCs and plasma are also accounted for. We present an overview of our recent studies which show very good agreement between our numerical results and available experimental results.

On the pressure-driven flow of suspensions: Particle migration in shear sensitive liquids

Fundamental understanding of flow of suspensions is key in many different areas such as bioengineering, oil, food, pharmaceutical and cosmetic industries. Two important phenomena may occur in the flow of particle suspensions. The first is associated with the relaxation process of particles toward a rest state after the flow is stopped that leads to shear-sensitive viscosity. The second is associated with particle-particle interaction that leads to shear-induced particle migration. The intensity of each of these effects is directly associated with particle size and imposed deformation rate. The available analyses are usually limited to one of these phenomena. A common approach is to consider that the suspension viscosity varies with shear rate, using a viscosity function to describe this dependency, and that the particle concentration is uniform throughout the flow. Most of the studies that consider shear-induced particle migration assume that the viscosity varies only with the local particle concentration and is not a function of shear rate. The range of validity and accuracy of these two approaches is not well understood. In this work, we analyze the fully-developed flow of particle suspensions in a tube using different flow models to evaluate the effect of both particle migration and shear dependent viscosity. The results show that, at certain conditions, accurate predictions on the flow rate-pressure gradient relation can only be made by considering both phenomena in a fully coupled, non-linear flow model.

INFLUENCE OF ELECTROMAGNETIC WAVES ON VISCOSITY AND ELECTRORHEOLOGY OF DIELECTRIC NANOFLUIDS-SCALE-BASED APPROACH

The appearance of electric field and shear dependent viscosity change in dielectric nanofluids provide potential for prospective applications especially in enhanced oil recovery. When nanofluids are activated by an applied electric field, it behaves as a non-Newtonian fluid under electrorheological effect, where the augment of electric field intensity increases the interaction among nanoparticles. Hence the mobility of the fluid can be efficiently controlled by regulating the applied field. Electrorheological characteristics of ZnO and Al2O3 nanofluids with various nanoparticles concentration (0.1, 0.05, 0.01 wt%) were measured. Results show that all the nanofluids exhibit pseudoplastic (shear thinning) behavior, while the electric field causes a visible increase in viscosity at a high shear rate. From the experimental results, it is also explained how the polarization of induced dipoles affects the electrorheology of nanofluids, by creating chains that align with the applied electric field. This paper also describes the designing and experimental aspects of the electromagnetic system, to investigate the change in viscosity of nanofluids.

Anisotropic flows and the shear viscosity of the QGP within an event by event transport approach

We study the effect of a temperature dependent shear viscosity to entropy density ratio η/s(T) on the build-up of the anisotropic flows vn(pT) within a relativistic kinetic transport approach that incorporates initial state fluctuations. We find that only in ultra-central collisions (0 – 0.2%) the vn(pT) have a stronger sensitivity to the T dependence of η/s in the QGP phase and this sensitivity increases with the order of the harmonic n. We study the linear correlation coefficient C(ϵn,vn) for different impact parameters and for two different beam energies: Au+Au at s=200 GeV at RHIC and Pb + Pb at s=2.76 TeV at LHC. The study of the correlations shows that at LHC energies there is more correlation than at RHIC energies. At LHC energies and for ultra-central collisions the linear correlation coefficient C(ϵn,vn)≈1 for n = 2, 3, 4 and 5.

Local well-posedness for Boussinesq approximation with shear dependent viscosities in 3D

In this paper, we prove the existence and uniqueness of regular weak solutions for a nonlinear Boussinesq system in a small time interval. The viscosity is assumed to be with a p-structure depending on the shear rate. We mainly work on 3D case with periodic boundary and initial value conditions. The W2,p-type regularity for velocity and H2-type regularity for temperature were obtained for 75<p≤2.