Newtonian Rheology Research Articles

Numerical Modeling of Non-Isothermal Laminar Flow and Heat Transfer of Paraffinic Oil with Yield Stress in a Pipe

This paper presents the results of a study on the non-isothermal laminar flow and heat transfer of oil with Newtonian and viscoplastic rheologies. Heat exchange with the surrounding environment leads to the formation of a near-wall zone of viscoplastic fluid. As the flow proceeds, the transformation of a Newtonian fluid to a viscoplastic state occurs. The rheology of the Shvedoff–Bingham fluid as a function of temperature is represented by the effective molecular viscosity apparatus. A numerical solution to the system of equations of motion and heat transfer was obtained using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The calculated data are obtained at Reynolds number Re from 523 to 1046, Bingham number Bn from 8.51 to 411.16, and Prandl number Pr = 45. The calculations’ novelty lies in the appearance of a “stagnation zone” in the near-wall zone and the pipe cross-section narrowing. The near-wall “stagnation zone” is along the pipe’s radius from r/R = 0.475 to r/R = 1 at Re = 523, Bn = 411.16, Pr = 45, u1 = 0.10 m/s, t1 = 25 °C, and tw = 0 °C. The influence of the heat of phase transition of paraffinic oil on the development of flow and heat transfer characteristics along the pipe length is demonstrated.

A generalized method aiming at predicting the polymer melt flow field in the metering zone of large-scale single-screw extruders

Single-screw extruders (SSE) are commonly used in a wide variety of applications, ranging from polymer-extrusion to pellet additive manufacturing (PAM). Existing mathematical models focus on Newtonian and power-law rheologies to model melt flow in the last screw vanes. However, molten polymers usually follow more complex rheological patterns, and a generalized extrusion model is still lacking. Therefore, a semi-analytical model aiming at describing the flow of molten polymers in SSE is presented, to encompass a wide range of non-Newtonian fluids, including generalized non-Newtonian fluids (GNF). The aim is to evaluate the molten polymer flow field under the minimum set of dimensionless parameters. The effect of dimensionless extrusion temperature, flow rate, channel width, and height on the flow field has been investigated. A full factorial plane has been chosen, and it was found that the impact of dimensionless flow rate is the most prominent. The results were initially compared to numerical computations, revealing a strong agreement between the simulations and the proposed GNF method. However, significant deviations emerged when employing the traditional power-law model. This is particularly true at high values of flow rate and extrusion temperature: the mean error on overall flow speed is reduced from 12.91% (traditional power-law method) to 1.04% (proposed GNF method), while keeping a reasonable computational time (time reduction: 96.70%, if compared to fully numerical solutions). Then, the predicted pressure drop in the metering section was benchmarked against established literature data for industrial-scale extruders, to show the model’s accuracy and reliability. The relative errors of the traditional model range between 34.33 and 62%. The proposed method reduces this gap (errors ranging between 5.34% and 10.97%). The low computational time and high accuracy of the GNF method will pave the way for its integration in more complex mathematical models of large-scale additive manufacturing processes.

Two-layer gravity currents of generalized Newtonian fluids

We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.

Modelling blood flow in coronary arteries: Newtonian or shear-thinning non-Newtonian rheology?

BackgroundThe combination of medical imaging and computational hemodynamics is a promising technology to diagnose/prognose coronary artery disease (CAD). However, the clinical translation of in silico hemodynamic models is still hampered by assumptions/idealizations that must be introduced in model-based strategies and that necessarily imply uncertainty. This study aims to provide a definite answer to the open question of how to properly model blood rheological properties in computational fluid dynamics (CFD) simulations of coronary hemodynamics. MethodsThe geometry of the right coronary artery (RCA) of 144 hemodynamically stable patients with different stenosis degree were reconstructed from angiography. On them, unsteady-state CFD simulations were carried out. On each reconstructed RCA two different simulation strategies were applied to account for blood rheological properties, implementing (i) a Newtonian (N) and (ii) a shear-thinning non-Newtonian (non-N) rheological model. Their impact was evaluated in terms of wall shear stress (WSS magnitude, multidirectionality, topological skeleton) and helical flow (strength, topology) profiles. Additionally, luminal surface areas (SAs) exposed to shear disturbances were identified and the co-localization of paired N and non-N SAs was quantified in terms of similarity index (SI). ResultsThe comparison between paired N vs. shear-thinning non-N simulations revealed remarkably similar profiles of WSS-based and helicity-based quantities, independent of the adopted blood rheology model and of the degree of stenosis of the vessel. Statistically, for each paired N and non-N hemodynamic quantity emerged negligible bias from Bland-Altman plots, and strong positive linear correlation (r > 0.94 for almost all the WSS-based quantities, r > 0.99 for helicity-based quantities). Moreover, a remarkable co-localization of N vs. non-N luminal SAs exposed to disturbed shear clearly emerged (SI distribution 0.95 [0.93, 0.97]). Helical flow topology resulted to be unaffected by blood rheological properties. ConclusionsThis study, performed on 288 angio-based CFD simulations on 144 RCA models presenting with different degrees of stenosis, suggests that the assumptions on blood rheology have negligible impact both on WSS and helical flow profiles associated with CAD, thus definitively answering to the question “is Newtonian assumption for blood rheology adequate in coronary hemodynamics simulations?”.

Post-seismic gravity change modelling based on non-linear power-law upper mantle rheology

SUMMARY Post-seismic gravity change modelling is commonly based on earth model with Newtonian linear rheology. Here, we present a novel way of modelling post-seismic gravity change by using a non-linear power-law rheology earth model. The method is constructed based on the framework of spectral finite element method (SFEM). SFEM has been proven practical for the purpose of modelling gravity change occurring during megathrust earthquakes. Our method implements the strain rate expression of non-linear power-law rheology into the mathematical framework of SFEM. Using our method, simulations of geoid change caused by synthetic point source earthquakes were made. The results revealed the potential of using non-linear power-law rheology for the explanation of rapid gravity changes in the beginning of the post-seismic epoch. Further on, we computed the post-seismic gravity change of the 2011 M9.0 Tohoku-Oki earthquake based on Maxwell non-linear power-law rheology in the upper mantle. It demonstrated the potential of power-law upper mantle flow as a possible candidate for the explanation of post-seismic gravity change after the earthquake occurs. However, a Maxwell non-linear power-law rheology alone is insufficient for the explanation of the post-seismic gravity change occurred.

Numerical Analysis of Viscous Polymer Resin Mixing Processes in High-Speed Blade-Free Planetary Blender Using Smoothed Particle Hydrodynamics

High-speed planetary mixers can rapidly and efficiently combine rheological liquids, such as polymer resins and paste materials, because of the large centrifugal forces generated by the planetary motion of the mixing vessel. Only a few attempts have been made to computationally model and analyze the intricate mixing patterns of highly viscous substances. This paper presents meshless flow simulations of the planetary mixing of polymeric fluids. This research utilized the smoothed particle hydrodynamics (SPH) approach for numerical calculations. This method has advantages over the finite-volume method, which is a grid-based computational technique, when it comes to modeling interfacial and free surface flow problems. Newtonian rheology and interfacial surface force models were used to calculate the dissipative forces in the partial differential momentum equation of fluid motion. Simulations of the flow of an uncured polyurethane resin were carried out while it was mixed in a planetary mixer, under various operating conditions. Simulations using SPH were able to accurately reproduce the intricate flow and blending pattern, providing insight into mixing mechanics and mixing index evolution characteristics according to operating conditions for the planetary mixing of polymeric fluids. The simulation results showed that the spiral band, which promotes the mixing performance, is densely and distinctively formed under high-speed operation conditions.

Progressive weakening within the overriding plate during dual inward dipping subduction

The evolution of dual inward dipping subduction (DIDS) is crucial to understand multiple slab interaction. Yet, how DIDS influences the thermo-mechanical behaviour of the overriding plate remains unclear, as previous DIDS investigations all applied a compositional or Newtonian rheology that excludes temperature dependency. Here we apply a composite rheology, including temperature dependent creep deformation mechanisms, in 2-D thermo-mechanical numerical modelling to investigate how DIDS modifies the rheological structure of the overriding plate. Three variables on plate sizes are investigated to understand what may control the maximum degree of plate weakening. We find that reducing the initial length or initial thickness of the overriding plate and increasing the initial thickness of the subducting plate can enhance the viscosity reduction within the overriding plate. The progressive weakening can result in a variety of stretching states ranging from 1) little or no lithosphere thinning and extension (<5% accumulation of strain), to 2) limited thermal lithosphere thinning (<30% accumulation of strain), and 3) localised rifting followed by spreading extension. Compared with single sided subduction, DIDS further reduces the magnitude of viscosity in the overriding plate. It does this by creating a dynamic fixed boundary condition for the overriding plate and forming a stronger upwelling mantle flow, both of which promote the progressive weakening in the overriding plate. The result implies that these generic DIDS effects are important aspects to consider to understand extension developed in natural DIDS cases. We also demonstrate that both temperature dependent creep rheologies and yielding deformation mechanism contribute significantly to the continuous viscosity reduction. The finding may also have a broader implication for more general processes that involve plate scale weakening, strain localisation and the formation of new plate boundaries.

PHYSICAL CHARACTERIZATION AND SUNSCREEN ACTIVITY OF NUTMEG OIL NANOEMULSION WITH ISOPROPYL MYRISTATE VARIATIONS

The nutmeg seed oil contains myristicin which can absorb UV rays. Nanoemulsion with isopropyl myristate can be used to increase the activity of sunscreen. This study aimed to determine the physical characteristics and effectivity of nutmeg oil (NMO) nanoemulsion with isopropyl myristate as an enhancer. The nanoemulsion was made with 6.4% NMO and variations of isopropyl myristate 1% (FI), 3% (FII), and 5% (FIII). The nanoemulsions were evaluated for physical characteristics such as appearance, pH, viscosity, transmittance percentage, particle size, and polydispersity index (PI). The in vitro SPF value was tested using a spectrophotometer, and sunscreen effectivity was determined by the Minimum Erythemal Dose (MED) value. Data obtained were analyzed using one-way ANOVA. This study showed that the colour of the NMO nanoemulsion was light yellow and clear, with a transmittance percentage of 97.5-97.9%. The pH FI, FII, and FIII results were 6.79±0.03, 6.84±0.04, and 7.02±0.03. The viscosity was 1.63 ± 0.81 to 1.82 ± 0.85 d.Pas with Newtonian rheology. The particle size was 14.3 ± 1.41 nm to 16.0 ± 2.13 nm, with PI less than 0.5. SPF value were 16.34 ± 5.50 (FI); 16.70 ± 5.20 (FII) and 17.80 ± 3.20 (FIII). MED values were 220.5 ± 6.34 (FI), 225.4 ±5.41 (FII), and 240.2 ±3.45 (FIII) minutes. The MED value showed that FIII was significantly different from FI and FII. Isopropyl myristate at 5% in nanoemulsion increases the effectivity of sunscreen.

Temperature gradient focusing of bio-analyte in a microfluidic channel dealing with non-Newtonian electrolyte considering temperature-dependent zeta potential.

Temperature gradient focusing (TGF) relies on establishing a precise balance between the electrophoretic motility of a target analyte and the advective flow of the background electrolyte (BGE) to locally concentrate the analyte in a microfluidic configuration. This paper presents a finite-element-based numerical analysis where the coupled electric field and the transport equations are solved to describe the effects of the shear-dependent apparent viscosity of a non-Newtonian BGE on the localized concentration buildup of a charged bio-sample inside a microchannel by TGF via Joule heating. Effects of the temperature-dependent nature of the wall zeta potential and the flow behavior index (n) of BGE on the flow, thermal, and species concentration profiles inside the microchannel have been investigated. Study using a fluorescein-Na analyte sample shows that the maximum normalized analyte concentration (Cmax /C0 ) reduces as the zeta potential increases linearly with temperature. The maximum concentration enhancement is achieved when the BGE displays the Newtonian rheology. For example, Cmax /C0 increases 134- to 280-fold when n is increased from 0.8 to 1 (pseudoplastic regime) and again reduces to 190-fold when n increases further from 1 to 1.2 (dilatant regime).

Permeation grouting in soils: numerical discussion of a simplified analytical approach

Permeation grouting – injections at low-pressure values of either microfine cements or chemical products – is frequently adopted to increase the mechanical/hydraulic properties of soils, and standard design approaches are currently either empirical or based on simplified analytical solutions. In this paper, some fundamental hypotheses of these analytical solutions are discussed by carrying out a campaign of finite-element numerical analyses, in which the injection phase in a water-saturated soil is analysed, a Newtonian rheology for the grout is implemented and the hypothesis of immiscibility for the two liquids is assumed. The effect of injection source geometry is discussed, as well as the role of gravity and capillarity. The authors analyse the conditions, in terms of injection flow rate, grout viscosity, soil intrinsic permeability and retention curve, under which the analytical solutions provide reliable results. The numerical results have been compared with the simplified analytical solution herein derived for a one-dimensional spherical geometry, in terms of the ‘characteristic curves’ for the system: the relationship between injection pressure/grout front advancement and injection time.

The Interaction Between Frictional Slip and Viscous Fault Root Produces Slow Slip Events

AbstractWe consider a model where an unstable frictional region, governed by rate and state friction, interacts with a viscous zone with Newtonian rheology. The system is loaded at distance with a constant velocity. Pore pressure variations are considered and we show that the model of Segall and Rice (1995, https://doi.org/10.1029/95jb02403) relating porosity changes to variations of the state variable could be derived considering viscoplastic deformation of a population of identical asperities. We perform a linear stability analysis in the case of a constant pore pressure in agreement with the full numerical results. For a given value of the viscosity of the viscous region, stable slip is promoted at low normal stress and unstable slip at high normal stress. Near the transition from stable to unstable slip, modest acceleration of slip, resembling slow slip events (SSE) are observed. We show that our model can reproduce real SSE sequences in the Guerrero subduction zone which are the largest worldwide. The best fit parameters suggest that SSEs happen in areas of low effective normal stress (for the frictional region) and low viscosity (for the viscous region). In our model, SSEs happen in a regime where the viscous region is able to counteract the instability of the frictional one. We show that considering a rate strengthening rheology or a non newtonian one leads to the same linear stability results. Our work shows that a simple model with homogeneous spatial properties can lead to complex dynamics, covering a wide range of observed sliding modes, from steady‐state creep to seismic slip and SSEs.

Proper orthogonal decomposition modal analysis in a baffled stirred tank: a base tool for the study of structures

Proper orthogonal decomposition (POD) is applied to three-dimensional (3-D) velocity fields collected from large-eddy simulations (LES) of a baffled stirred tank. In the LES, the tank operates with a Rushton-type impeller under turbulent conditions (at least in the near-impeller region) and the working fluid exhibits either Newtonian or shear-thinning rheology. The most energetic POD modes are analysed, and a POD reconstruction based on the higher modes is proposed to approximate the fluctuating component of the velocity field. Subsequently, the POD reconstruction is used to identify vortical structures and characterise them in terms of their shape. The structures are identified by considering a frame-invariant formulation of a popular, Eulerian, local-region-type method: the $Q$ -criterion. Statistics of shape-related parameters are then investigated to address the morphology of the structures. It is found that: (i) regardless of the working fluid rheology, it seems feasible to decompose the 3-D field into its mean, most energetic periodic and fluctuating components using POD, allowing, for instance, reduced-order modelling of the energetic periodic motions for mixing enhancement purposes, and (ii) vortical structures related to turbulence are mostly tubular. Finding (ii) implies that, as starting point, phenomenological models for the interaction between fluid particles (drops and bubbles) and vortices should consider the latter as cylindrical structures rather than of spherical shape, as classically assumed in these models.

Analysis of Helical Grafts in Steady and Unsteady Flow: Development of a Novel Bypass Graft

Abstract Helical secondary flow has been shown to be beneficial as it has improved bypass graft patency in revascularization through more uniform wall shear stress and improved mixing. An unfavorable by-product of generating helical flow is the proportional increase in pressure drop, which is a critical limiting factor as it constrains the amount of beneficial helicity that can be generated. A validated CFD methodology was used to simulate the development of secondary flow in multiple helical bypass grafts with Newtonian and non-Newtonian rheology. These simulations revealed that the secondary flow is fully developed by the second pitch of a helical geometry for physiologically realistic, unsteady flows, indicating the potential for maximizing secondary flows while at the same time minimizing the induced pressure drops through optimization studies. Building on this, a novel Hybrid Graft Geometry (HGG) was developed which resulted in a 390% increase in cycle-averaged helical intensity while maintaining a mere 2% increase in cycle-averaged pressure drop when compared to graft geometries in the literature. The helical effectiveness he, defined as the ratio of helical intensity to the induced pressure drop, is a newly created parameter designed to quantify the performance of the helical grafts. The cycle-averaged he clearly reveals the superior performance of the HGG, which is up to 3.6 times higher than other helical grafts tested. For the first time in the open literature, this study presents the proper basis for future optimization studies through he, which should be maximized to improve graft patency.

Monte Carlo Simulations of Shear‐Thinning Flow in Geological Fractures

AbstractThe hydraulic behavior of fractured rocks under shear‐thinning flow is a challenging topic of interest in several fields, related either to environmental remediation or to natural resources recovery. The compound effect of fluid rheology and medium heterogeneity strongly affects flow and transport in fractured geological formations. Here, a stochastic analysis is conducted via Monte Carlo simulations to investigate the flow of shear‐thinning fluids in fractures subjected to both natural and forced flow, considering different fracture dimensions, for a spatial correlation of the fracture that is an intrinsic parameter of the geological formation, independent of the fracture size. Considering the lubrication approximation, a generalized Reynolds equation for shear‐thinning fluids is solved using an ad hoc, finite volume‐based, numerical scheme. The influence of the rheology and aperture field heterogeneity on ensemble statistics of the velocity components and magnitude, as well as apparent fracture‐scale transmissivity, is quantified over 103 fracture realizations. The probability density functions (PDFs) and relative confidence intervals, obtained by averaging over the statistics, are analyzed to characterize the apparent transmissivity transition from Newtonian to shear‐thinning regime. The autocorrelation functions of velocity components are computed to understand the impact of rheology on spatial correlations the flow. Velocity components exhibit narrow PDFs with nearly exponential decay. More elevated pressure gradients emphasize the shear‐thinning behavior, inducing a more pronounced flow localization, under otherwise identical conditions. This translates at the scale of the fracture into a larger apparent transmissivity as compared to the same configuration with Newtonian rheology, by orders of magnitude.

A method to quantify time-dependent yield stress build-up in mineral slurries

Mineral slurries can have very complex rheology which may not be evident in bench-scale mixing tests. On scale-up to large industrial stirred tanks, an unexpected stagnant layer sometimes forms at the surface. We hypothesize that this occurs due to build-up of yield stress when the fluid is at rest. This behavior can cause problems on scale-up, where insufficiently mixed regions of the tank contain a much larger volume of fluid and the residence time in these regions can be much longer than at the bench scale. To study this effect, a method for continuous torque measurements was developed to quantify rest time effects at the bench scale. Nickel laterite slurries (NLS) with a broad range of solids concentration (25.2–71.8 wt%) were used to test this new method. Concentric cylinder viscometry and vane rheometry were also used to measure the behavior of the test sample. Evidence for a complex mechanism of network build-up for rest times of two minutes and longer was found. Moreover, it was found that 45 wt% is the upper limit for assuming behavior which approximates Newtonian rheology in this nickel laterite slurry sample. Solids concentration greater than 60 wt% showed rapid build-up of yield stress and thixotropic behavior. The rest time experiments validated the scale-up hypothesis. The slurry concentration at which non-Newtonian behavior appears is in accordance with other rheological investigations of nickel laterite slurries.

Viscous to Inertial Transition in Dense Granular Suspension.

Granular suspensions present a transition from a Newtonian rheology in the Stokes limit to a Bagnoldian rheology when inertia is increased. A custom rheometer that can be run in a pressure- or a volume-imposed mode is used to examine this transition in the dense regime close to jamming. By varying systematically the interstitial fluid, shear rate, and packing fraction in volume-imposed measurements, we show that the transition takes place at a Stokes number of 10 independent of the packing fraction. Using pressure-imposed rheometry, we investigate whether the inertial and viscous regimes can be unified as a function of a single dimensionless number based on stress additivity.

Non-Newtonian Rheology in Twist–Bend Nematic Liquid Crystals

A simple qualitative model has been presented to describe shear rheological behavior of the twist–bend nematic liquid crystals (NTB). It has been found that at relatively low shear rate (dot {gamma } leqslant {{dot {gamma }}_{{c1}}}) the stress tensor σ created by this shear strain, scales as sigma propto {{dot {gamma }}^{{1/2}}}. Thus, the effective viscosity decreases with the shear rate (eta propto {{dot {gamma }}^{{ - 1/2}}}) manifesting so-called shear-thinning phenomenon. At intermediate shear rate {{dot {gamma }}_{{c1}}} leqslant dot {gamma } leqslant {{dot {gamma }}_{{c2}}}, σ is almost independent of dot {gamma } (a sort of plateau), and at large shear rate (dot {gamma } geqslant {{dot {gamma }}_{{c2}}}), sigma propto dot {gamma }, and it looks like as Newtonian rheology. Within our theory the critical values of the shear rate scales as {{dot {gamma }}_{{c1}}} propto {{(tilde {eta }_{2}^{0}{text{/}}tilde {eta }_{3}^{0})}^{2}}, and {{dot {gamma }}_{{c2}}} propto {{(tilde {eta }_{2}^{0}{text{/}}tilde {eta }_{3}^{0})}^{4}}, respectively. Here tilde {eta }_{2}^{0} and tilde {eta }_{3}^{0} are bare coarse grained shear viscosity coefficients of the effective smectics equivalent to the NTB phase at large scales. The results of our work are in the agreement with recent experimental studies.

Post-seismic motion after 3 Chilean megathrust earthquakes: a clue for a linear asthenospheric viscosity

SUMMARYOver the last decade, three major subduction earthquakes, Maule Mw 8.8 (2010), Illapel Mw 8.3 (2015) and Iquique Mw 8.1 (2014), occurred in Chile and generated significant post-seismic deformations. These large scale and long lasting deformations can be quantified with modern GNSS precise positioning and highlight viscoelastic processes in the asthenosphere. Here, we calculate the ratios of cumulative post-seismic displacements after 5 yr over the coseismic offsets. We find that at any distance from the trench, ratios are similar for the three earthquakes despite their different magnitudes which imply induced stresses that are more than one order of magnitude apart. This observation suggests that the post-seismic deformation is related to the same effective viscosity for the three earthquakes, indicating Newtonian rheology, rather than power-law rheology in the asthenosphere.

A comparison of Newtonian and non-Newtonian pulsatile blood rheology in carotid bifurcation through fluid–solid interaction hemodynamic assessment based on experimental data

Endothelial cells play a crucial role in the arterial homeostasis. In addition to physiological risk factors, abnormal levels of hemodynamic parameters induced by the pulsatile flow contribute to atherosclerotic plaque formation and development. In this study, we used an experimental setup to study the hemodynamics of Newtonian and non-Newtonian blood flow on a deformable model of human carotid bifurcation. The flow/pressure pulses of the experimental model were fed into a fluid–structure interaction numerical model, and respective hemodynamic parameters were obtained and compared between the two flow regimes. Results revealed noticeable differences among the two flow regimes when the pulsatile nature of blood flow and pressure were considered, with more distinct differences near junction sites. Velocity profiles of the non-Newtonian model were more flattened with higher back flow during the diastole. The shear stress waves as well as shear-dependent parameters, such as oscillatory shear index, relative residence time, and vorticity, as well as wall stress and strain, also indicated significant differences among the two models. Regardless of flow regime, results showed a good agreement with clinical outcomes in human carotid bifurcation, especially the carotid sinus. Near the bifurcation, marked fluctuations of shear stress are evident. Around the junction site, wall pulsation experienced variations up to five times of the normal pulse span. The quantified hemodynamic parameters obtained from proposed accurate model of carotid bifurcation may help to achieve technological solutions to adjust the out of biological ranges of these parameters, and avoid atheroma formation or treat the diseased artery.

A Hydrodynamic Thrust Bearing Lubricated By A Non-Newtonian Giesekus Fluid

There exists a huge volume of studies of hydrodynamic and elastohydrodynamic lubrication problems for lubricants with Newtonian rheology. Lubricants with Newtonian rheology do not exhibit the usually observed experimentally behavior of having relatively high viscosity for low stresses and relatively low viscosity for high stresses. In this paper we extend the earlier conducted analysis of lubricants with a non-Newtonian Giesekus behavior for the case of thrust bearing modeling. The main goal of the paper is to obtain an analytical solution for a hydrodynamically thrust bearing lubricated by a fluid with the Giesekus rheology. This goal is achieved by careful application of perturbation methods. A three-term approximate analytical solution is obtained and its dependence on the problem input parameters is analyzed.