Newtonian Results Research Articles

A new higher-order super compact finite difference scheme to study three-dimensional non-Newtonian flows

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed higher-order compact finite difference scheme to solve 3D non-Newtonian flow problems. The proposed scheme is fourth-order accurate in space and second-order accurate in time, utilizing only seven adjacent grid points at the (n+1)th time level for the finite difference discretization. A time-marching methodology is employed with pressure calculated via a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning (n = 0.5), shear-thickening (n = 1.5), and Newtonian (n = 1.0) fluids across different Reynolds numbers (Re=1,50,100,200). Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. It is found that for shear-thinning fluid (n = 0.5), u velocity is higher near the top moving wall than the case of Newtonian (n = 1.0) and shear-thickening fluid (n = 1.5) for all Re values. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

Dynamical evolution timescales for the triple supermassive black hole system in NGC 6240

Aims. Based on the available observational data from the literature, we analysed the dynamics of the NGC 6240 galaxy central supermassive black hole (SMBH) system. Methods. For the dynamical modelling of this triple SBMH system, we used the massively parallel and GPU accelerated φ-GPU direct summation N-body code. Following a long-timescale modelling of the triple system, we carried out a very detailed time output analysis of the von Zeipel–Lidov–Kozai (ZLK) oscillations for the black holes. Results. According to our Newtonian simulation results, for all models and randomisations, the bound system from S1+S2 components formed at ≈3.6 Myr. The formation of the bound hierarchical triple system S+N occurred at ≈18 Myr. Over the course of these Newtonian simulations of the evolution of the triple SMBH system and the surrounding environment in NGC 6240, ZLK oscillations were detected (in most cases) for the binary components. The inclination angle between the orbital angular momentum of binary components aptly coincides with the theoretical calculations of the ZLK mechanism. Conclusions. In our set of randomised 15 Newtonian N-body dynamical galaxy models in 13 systems, we were able to detect a ZLK mechanism. In contrast, our extra few-body post-Newtonian runs (for one randomisation case) show it is only for the large inner binary initial eccentricity (in our case ≳0.9) that we are able to observe the possibility of the inner binary merging, due to the post-Newtonian energy radiation effects. For the lower eccentricity cases, the test runs show no sign of possible merging or any ZLK oscillations in the system.

Precession of planets' orbits between Newtonian gravity and Einstein's general relativity

The recent result that, contrary to a longstanding conviction older than 160 years, the precession of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury's mass is confirmed. Orbit's precession does not occur in an inertial (in Newtonian sense) frame of reference, but it occurs in the non-inertial frame of reference of the Sun because in Newtonian theory, the distance which is travelled by a body depends on the frame of reference in which the motion of the body is analyzed. After reviewing a previous solution, the precession is directly obtained from the orbit equation in the non-inertial frame of reference of the Sun. The Newtonian formula of the precession of planets' perihelion breaks down for the other planets because the predicted Newtonian result is indeed too large for Venus and Earth. In a previous paper, it was shown that corrections due to gravitational and rotational time dilation, in an intermediate framework (a particular post-Newtonian approximation of general relativity) which analyzes gravity between Newton and Einstein, solve the problem in accordance with some other results in the literature. By adding such corrections, a result consistent with the one of general relativity was indeed obtained. Those corrections also are re-analyzed in this paper by stressing the difference between general relativity and Newtonian physics by evoking the Einstein Equivalence Principle, and the third postulate of relativity. This framework of gravity between Newton and Einstein seems consistent with global covariance. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a better understanding of the famous Dark Matter and Dark Energy problems.

Computational study on interaction between rotating non-spherical particles and shear-thinning fluids

In this paper, the drag coefficient (Cd), lift coefficient (Cl), and torque coefficient (Ct) of rotating non-spherical particles in shear-thinning non-Newtonian fluids are investigated based on particle-resolved direct numerical simulation. The Carreau model is used to describe the rheological behavior of non-Newtonian fluids, and the numerical model is validated against previously published data. Then, the effects of aspect ratio (Ar), spin number (Spa), flow index (n), and Carreau number (Cu) on Cd, Cl, and Ct of rotating non-spherical particles are investigated at different Reynolds numbers (Re). The numerical results show that the closer the particles are to the spherical shape, the smaller the fluctuations of Cd, Cl, and Ct curves. The peaks and valleys of Cd, Cl, and Ct of oblate and prolate ellipsoidal particles are reversely distributed. The fluctuations of Cd and Cl curves increase with increasing Spa. Cd decreases with increasing Spa at low Re, contrary to Newtonian fluids' results. Cd and Ct decrease with increasing shear-thinning properties, Cl increases with increasing shear-thinning properties, and the effect of shear-thinning properties decreases with increasing Re. The variation of viscosity and pressure is the main reason for the variation of Cd, Cl, and Ct under different variables. Predictive correlations of Cd and Ct are established based on Re, Spa, n, Cu, and α. The findings indicate that particle rotation and shear-thinning properties must be considered when evaluating particle-fluid interactions, which provide important guidance for predicting and controlling the orientation and distribution of non-spherical particles in non-Newtonian fluids.

Modelling Neutron-Star Ocean Dynamics

We revisit the calculation of mode oscillations in the ocean of a rotating neutron star, which may be excited during thermonuclear X-ray bursts. Our present theoretical understanding of ocean modes relies heavily on the traditional approximation commonly employed in geophysics. The approximation elegantly decouples the radial and angular sectors of the perturbation problem by neglecting the vertical contribution from the Coriolis force. However, as the implicit assumptions underlying it are not as well understood as they ought to be, we examine the traditional approximation and discuss the associated mode solutions. The results demonstrate that, while the approximation may be appropriate in certain contexts, it may not be accurate for rapidly rotating neutron stars. In addition, using the shallow-water approximation, we show analytically how the solutions that resemble r-modes change their nature in neutron-star oceans to behave like gravity waves. We also outline a simple prescription for lifting Newtonian results in a shallow ocean to general relativity, making the result more realistic.

Fatty acid profile and rheological behavior of annatto seed oil (Bixa orellana), cupuassu seed fat (Theobroma grandiflorum), and their blends

Annatto seed oil (ASO) and cupuassu seed fat (CSF) were combined at the ratios: 30:70, 50:50, and 70:30 (% w/w). Their fatty acid profile, nutritional quality, FTIR (Fourier Transform Infrared) spectra, and rheological behavior were evaluated. ASO increased the content of polyunsaturated fatty acids in the blends; whereas CSF conferred higher contents of monounsaturated fatty acids. The blends exhibited low atherogenicity and thrombogenicity indices, suggesting nutritional advantages. The Newtonian fluid behavior and FTIR results suggested that mixing ASO and CSF at different proportions did not affect the functional groups. ASO showed an activation energy value which indicated that this fat viscosity was more sensitive to temperature changes. The Newtonian model proved to be suitable to describe the behavior of samples, according to statistical fit parameters R2, χ2, and RSS. The resulting blends presented improved physicochemical properties and nutritional attributes, indicating their feasibility for the development of new products.

New avenue for accurate analytical waveforms and fluxes for eccentric compact binaries

We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\leq \hat{a}\leq +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.

Non-Newtonian Endothelial Shear Stress Simulation: Does It Matter?

Patient-specific coronary endothelial shear stress (ESS) calculations using Newtonian and non-Newtonian rheological models were performed to assess whether the common assumption of Newtonian blood behavior offers similar results to a more realistic but computationally expensive non-Newtonian model. 16 coronary arteries (from 16 patients) were reconstructed from optical coherence tomographic (OCT) imaging. Pulsatile CFD simulations using Newtonian and the Quemada non-Newtonian model were performed. Endothelial shear stress (ESS) and other indices were compared. Exploratory indices including local blood viscosity (LBV) were calculated from non-Newtonian simulation data. Compared to the Newtonian results, the non-Newtonian model estimates significantly higher time-averaged ESS (1.69 (IQR 1.36)Pa versus 1.28 (1.16)Pa, p < 0.001) and ESS gradient (0.90 (1.20)Pa/mm versus 0.74 (1.03)Pa/mm, p < 0.001) throughout the cardiac cycle, under-estimating the low ESS (<1Pa) area (37.20 ± 13.57% versus 50.43 ± 14.16%, 95% CI 11.28–15.18, p < 0.001). Similar results were also found in the idealized artery simulations with non-Newtonian median ESS being higher than the Newtonian median ESS (healthy segments: 0.8238Pa versus 0.6618Pa, p < 0.001 proximal; 0.8179Pa versus 0.6610Pa, p < 0.001 distal; stenotic segments: 0.8196Pa versus 0.6611Pa, p < 0.001 proximal; 0.2546Pa versus 0.2245Pa, p < 0.001 distal) On average, the non-Newtonian model has a LBV of 1.45 times above the Newtonian model with an average peak LBV of 40-fold. Non-Newtonian blood model estimates higher quantitative ESS values than the Newtonian model. Incorporation of non-Newtonian blood behavior may improve the accuracy of ESS measurements. The non-Newtonian model also allows calculation of exploratory viscosity-based hemodynamic indices, such as local blood viscosity, which may offer additional information to detect underlying atherosclerosis.

Moment analysis of unsteady bi-component species (drug) transport with coupled chemical reaction in non-Newtonian blood flow

Motivated by exploring the fluid dynamics of dual drug delivery systems in biomedicine, a mathematical analysis of the bi-component species transport (convective-diffusion) in rheological blood flow with bulk chemical reaction through a two-dimensional rigid vessel is presented. Two different bulk degradation reaction rates are included for the dual species (pharmacological agents, A, B). An analytical expression for axial velocity is derived using a perturbation method. The decoupled convection-diffusion equations are then analyzed with the Aris – Barton approach. The mean concentration of the species is estimated using the first five concentration moments with the aid of fourth order Hermite polynomials. A finite difference technique based on the Crank Nicholson implicit scheme is employed to handle the pth order moment of the general concentration. The analysis reveals that increasing reversible transfer rate and irreversible bulk degradation result in a reduction in the total mass of the species over time. The mass of both species decreases with an increase in reversible transfer rate, even though the mass of species A depletes faster than the mass of species B. The skewness of the concentration distribution decreases as yield stress increases and the distributions in all scenarios are positively skewed and tend to zero over time, implying that the distribution tends to symmetry over time. The kurtosis decreases over time from positive to negative values and eventually approaches zero. Mean concentration peaks for both species A and B are elevated with increasing yield stress, although magnitudes are significantly higher for species A. With increasing values of the distribution coefficient between two species, mean concentration peaks are elevated for species (component) A whereas they are depleted for species B, although substantially greater magnitudes are computed for species B. Good correlation of the skewness with earlier Newtonian results is achieved. The results provide some useful insight into the bi-component drug transport in smaller vessel pharmacodynamics where hemorheology is important.

Influence of the diameter of the magnetic core and surfactant thickness on water carrying iron (iii) oxide ferrofluid flow over a rotating disk

Analysis of ferrofluid over a rotating plate is very important in the field of biomedical sciences, electronic devices, and aerodynamics. This work investigates the influence of the diameter of the magnetic core and thickness of the surfactant layer on water-carrying iron(iii) oxide ferrofluid flow and heat transfer over a rotating disk in the presence of a stationary magnetic field. The nonlinear differential equations for velocity and temperature are solved numerically using the finite element procedure. The validation of the present numerical solution is also demonstrated. The non-Newtonian results under the influence of stationary magnetic field for velocity and temperature profiles are compared with the Newtonian results of velocity and temperature profiles in the absence of the magnetic field. Increasing the diameter size of the iron(iii) oxide nanoparticles reduces the velocity and temperature in the flow. However, the thickness of the surfactant layer enhances the velocity and temperature. However, the magnetic field produces the shear thickening in the flow. Enhancement in the diameter of the iron (iii) oxide nanoparticles increases the stress on the disk and local heat transfer, and enhancement in the thickness of the surfactant layer of the nanoparticles reduces the stress and local heat transfer.

Heat Transfer of Casson Fluid over a Vertical Plate with Arbitrary Shear Stress and Exponential Heating

The basic objective of this work is to study the heat transfer of Casson fluid of non-Newtonian nature. The fluid is considered over a vertical plate such that the plate exhibits arbitrary wall shear stress at the boundary. Heat transfers due to exponential plate heating and natural convection are due to buoyancy force. Magnetohydrodynamic (MHD) analysis in the occurrence of a uniform magnetic field is also considered. The medium over the plate is porous and hence Darcy’s law is applied. The governing equations are established for the velocity and temperature fields by the usual Boussinesq approximation. The problem is first written in dimensionless form using some useful non-dimensional quantities and then solved. The exact analysis is performed and hence solutions via integral transform are established. The analysis of various pertinent parameters on temperature distribution and velocity field are reported graphically. It is found that pours medium permeability parameter retards the fluid motion whereas, velocity decreases with increasing magnetic parameter. Velocity and temperature decrease with increasing Prandtl number whereas the Grashof number enhances the fluid motion. Further, it is concluded from this study that the results obtained here are more general and in a limiting sense several other solutions can be recovered. The Newtonian fluid results can be easily established by taking the Casson parameter infinitely large i.e., when .

The secret of planets’ perihelion between Newton and Einstein

Abstract Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury’s perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury’s mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets’ perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: (i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets’ orbit. The real problem is instead that a pure Newtonian prediction is too large. (ii) Perihelion’s precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a subsequent better understanding of the famous Dark Matter and Dark Energy problems.

Modulated gravity effects on nonlinear convection in viscoelastic ferromagnetic fluids between two horizontal parallel plates

AbstractIn this study, the analysis of nonlinear stability with viscoelastic ferromagnetic fluids as working media is performed by finite‐amplitude perturbations. The solution of the resulting nonautonomous system of the Lorenz model (generalized Khayat–Lorenz model of four modes) is obtained numerically to measure the amount of heat transport. The effects of elastic parameters, Prandtl number, modulation parameters, buoyancy magnetic parameter, and nonbuoyancy magnetic parameter on heat transport are studied. Heat transport is quantified through the average Nusselt number, which is determined by solving the scaled Lorenz model. As limiting cases of the study, the results of Newtonian, Maxwell, Rivlin–Ericksen fluids are determined. The results obtained have been presented graphically.

Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design

In post-operative scenarios of arterial graft surgeries to bypass coronary artery stenosis, fluid dynamics plays a crucial role. Problems such as intimal hyperplasia have been related to fluid dynamics and wall shear stresses near the graft junction. This study focused on the question of the use of Newtonian and non-Newtonian models to represent blood in this type of problem in order to capture important flow features, as well as an analysis of the performance of geometry from the view of Constructive Theory. The objective of this study was to investigate the effects rheology on the steady-state flow and on the performance of a system consisting of an idealized version of a partially obstructed coronary artery and bypass graft. The Constructal Design Method was employed with two degrees of freedom: the ratio between bypass and artery diameters and the junction angle at the bypass inlet. The flow problem was solved numerically using the Finite Volume Method with blood modeled employing the Carreau equation for viscosity. The Computational Fluid Dynamics model associated with the Sparse Grid method generated eighteen response surfaces, each representing a severe stenosis degree of 75% for specific combinations of rheological parameters, dimensionless viscosity ratio, Carreau number and flow index at two distinct Reynolds numbers of 150 and 250. There was a considerable dependence of the pressure drop on rheological parameters. For the two Reynolds numbers studied, the Newtonian case presented the lowest value of the dimensionless pressure drop, suggesting that the choice of applying Newtonian blood may underestimate the value of pressure drop in the system by about 12.4% (Re =150) and 7.8% (Re = 250). Even so, results demonstrated that non-Newtonian rheological parameters did not influence either the shape of the response surfaces or the optimum bypass geometry, which consisted of a diameter ratio of 1 and junction angle of 30°. However, the viscosity ratio and the flow index had the greatest impact on pressure drop, recirculation zones and wall shear stress. Rheological parameters also affected the recirculation zones downstream of stenosis, where intimal hyperplasia is more prevalent. Newtonian and most non-Newtonian results had similar wall shear stresses, except for the non-Newtonian case with high viscosity ratio. In the view of Constructal Design, the geometry of best performance was independent of the rheological model. However, rheology played an important role on pressure drop and flow dynamics, allowing the prediction of recirculation zones that were not captured by a Newtonian model.

A Cartesian grid generation technique for 2-D non-Newtonian blood flow through a bileaflet mechanical heart valve

Non-Newtonian blood flow through an aortic bileaflet mechanical heart valve is investigated numerically using the Casson model for the shear thinning behavior of the blood. The objective of this study is to deal with the influence of the non-Newtonian property of blood as well as of geometry of the prosthesis on flow phenomena and wall shear stress during the peak systolic phase. A comparison of non-Newtonian and Newtonian results is also presented. A nonuniform Cartesian grid generation technique is presented to generate a two-dimensional grid for the irregular geometry of the Butterfly valve. The governing Navier–Stokes equations of the flow, written in a stream function-vorticity formulation, are solved by the finite difference method with hybrid differencing of the convective terms. The results obtained with the model show that the blood non-Newtonian behavior induces a flow deceleration with the existence recirculation and consequently stagnation causing thrombus formation, as well as an increase of the shear stress along the wall which contributes the hemolytic blood damage; this is in agreement with the clinical observations concerning thromboembolic problems.

Large-scale peculiar velocity fields: Newtonian vs relativistic treatment

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within the framework of Newtonian gravity and then compare our results to those of the corresponding relativistic treatment. In so doing, we use the same mathematical formalism and apply the same physical approach. This facilitates a direct and transparent comparison between the two treatments. Our study recovers and extends the familiar Newtonian results on the one hand, while on the other it shows that the Newtonian analysis leads to substantially weaker growth-rates for the peculiar velocity field, compared to the relativistic approach. This implies that, by using Newton's rather than Einstein's theory, one could seriously underestimate the overall kinematic evolution of cosmological peculiar motions. We are also in the position to identify the reason the two theories arrive at such considerably different results and conclusions.

Radio and high-energy emission of pulsars revealed by general relativity

Context. According to current pulsar emission models, photons are produced within their magnetosphere and current sheet, along their separatrix, which is located inside and outside the light cylinder. Radio emission is favoured in the vicinity of the polar caps, whereas the high-energy counterpart is presumably enhanced in regions around the light cylinder, whether this is the magnetosphere and/or the wind. However, the gravitational effect on their light curves and spectral properties has only been sparsely researched. Aims. We present a method for simulating the influence that the gravitational field of the neutron star has on its emission properties according to the solution of a rotating dipole evolving in a slowly rotating neutron star metric described by general relativity. Methods. We numerically computed photon trajectories assuming a background Schwarzschild metric, applying our method to neutron star radiation mechanisms such as thermal emission from hot spots and non-thermal magnetospheric emission by curvature radiation. We detail the general-relativistic effects onto observations made by a distant observer. Results. Sky maps are computed using the vacuum electromagnetic field of a general-relativistic rotating dipole, extending previous works obtained for the Deutsch solution. We compare Newtonian results to their general-relativistic counterpart. For magnetospheric emission, we show that aberration and curvature of photon trajectories as well as Shapiro time delay significantly affect the phase delay between radio and high-energy light curves, although the characteristic pulse profile that defines pulsar emission is kept.

Relativistic geoid: Gravity potential and relativistic effects

The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of (post-)Newtonian notions. This potential exists in any stationary configuration with rigidly co-rotating observers, and it is the same as realized by local plumb lines. In a second step, we employ the gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limit, the framework allows to recover well-known (post-) Newtonian results. For a better illustration and proper interpretation of the general relativistic gravity potential and geoid, some particular examples are considered. Explicit results are derived for exact vacuum solutions to Einstein's field equation as well as a parametrized post-Newtonian model. Comparing the Earth's Newtonian geoid to its relativistic generalization is a very subtle problem, but of high interest. An isometric embedding into Euclidean three-dimensional space is an appropriate solution and allows a genuinely intrinsic comparison. With this method, the leading-order differences are determined, which are at the mm-level.

Viscoelastic fluid flow simulations in the e-VROCTM geometry

Microfluidic contraction devices have been proposed for extensional rheometry measurements, in particular as a useful method for determining the extensional viscosity of low elasticity solutions. The first commercially available “Extensional Viscometer-Rheometer-On-a-Chip” (e-VROCTM), developed by Rheosense, is a hyperbolically-shaped contraction/expansion geometry which incorporates pressure-drop measurement capabilities. To better understand the underlying flow kinematics within this geometry we have conducted a numerical study performing three-dimensional numerical simulations for both Newtonian and viscoelastic fluids. For the viscoelastic fluids the simplified Phan-Thien and Tanner (sPTT) and the Finitely Extensible Nonlinear Elastic models (FENE-P) are employed, in order to investigate the efficiency of this configuration in terms of increasing Weissenberg numbers and to understand the effects of various model parameters on the flow field. Our Newtonian fluid results suggest that the e-VROCTM geometry produces only a small region of extensional flow and is mainly shear-dominated, potentially suggesting any pressure-drop measurements from this device may be related to viscoelastic first normal-stress differences developed via a combination of shear and extension, rather than solely pure extension. By a careful selection of the sPTT and FENE-P model parameters, such that steady-state viscometric properties in homogeneous flows are matched, we are able to show that a small enhanced pressure-drop is seen for both models, which is larger for the FENE-P model.

P858High endothelial shear stress and local Reynolds number are associated with lipid growth of coronary plaques

Abstract Background Local haemodynamic disturbances in coronary blood flow are associated with abnormal endothelial shear stress (ESS) and progressive atherosclerosis. However, standard techniques to estimate ESS lack the diagnostic specificity necessary for future clinical utility. Possible improvements include use of a more realistic non-Newtonian model of blood, which may provide more accurate ESS measurements and is further able to detect local variations in blood viscosity. Purpose To compare accuracy of ESS generated by Newtonian versus non-Newtonian rheological models to detect coronary plaque progression. To investigate local Reynolds number (ReL), a viscosity-based haemodynamic metric calculated by the non-Newtonian model, as an independent marker of plaque progression. Methods Sixteen patients with non-culprit plaques completely visualised in serial optical coherence tomography (OCT) imaging were identified. Plaques were analysed in 0.2mm intervals at each timepoint for lipid and calcium arc. Computational fluid dynamic simulations were performed using Newtonian and non-Newtonian models to calculate ESS, whereas ReL was calculated by the non-Newtonian simulations. Each haemodynamic index was compared to interval changes in lipid and calcium using multivariate regression. Results In total, 894 matched arterial segments from baseline and follow up imaging were analysed. In the Newtonian results, baseline segments exposed to ESS&gt;1.7Pa had a 12.5° increase in lipid arc (95% CI 2.2° to 22.8°, p=0.018) while segments exposed to ESS&lt;1.1Pa had an 8.1° decrease in calcium (95% CI −14.0° to −2.2°, p=0.007). In the non-Newtonian results, baseline regions exposed to ESS&gt;2.2Pa had a 14.4° increase in lipid (95% CI 4.2° to 24.7°, p=0.006) while areas with ESS&lt;1.4Pa had an 8.7° decrease in calcium (95% CI −14.6° to −2.8°, p=0.004). Baseline regions exposed to ReL&lt;34 showed an average 11.9° increase in lipid arc (95% CI 0.6° to 23.2°, p=0.039). Regions exposed to ReL&gt;55 had an average increase in lipid arc of 26.6° (95% CI 14.5° to 38.6°, p&lt;0.001). Conclusions Both Newtonian and non-Newtonian rheological models show that high ESS is associated with increased lipid while low ESS is associated with decreased calcium. ReL is independently associated with interval increases in lipid arc, suggesting a mechanistic role of local blood viscosity in lipid accumulation. ReL may serve as a novel haemodynamic marker of plaque progression.