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• The flow development of power-law fluids in pipe and channel flows is studied by means of finite element simulations. • In addition to the centreline definition of the entrance length, the global velocity and the wall shear stress entrance lengths are considered. • Results have been obtained for values of the power-law exponent n ranging from 0.2 to 1.5 and for Reynolds numbers (Re) up to 1000. • In pipes, centreline and global entrance lengths coincide for moderately shear thinning fluids (n >0.7). • In channels, the classical entrance length is lower than the other two lengths and the differences are relatively reduced as Re and n are increased. The entrance length needed for pipe and channel flows to re-adjust from a uniform to a fully-developed velocity profile is typically defined as the length required for the centreline velocity to reach 99% of its fully-developed value. This definition may be quite inaccurate in non-Newtonian flows with almost flat fully-developed velocity distributions near the centreline. Shear-thinning and viscoplasticity may cause the flow close to the centreline to evolve faster than that closer to the walls. Thus, alternative definitions of the entrance length have been proposed, e.g., for viscoplastic flows. In the present work, we numerically solve the flow development of power-law fluids in pipes and channels and calculate the entrance length as a function of the transverse coordinate, determining the global entrance length, L g , along with the standard centreline estimate, L c. We also consider an alternative definition, L t , based on the evolution of the wall shear stress. Results have been obtained for values of the power-law exponent n ranging from 0.2 to 1.5 and for Reynolds numbers (Re) up to 1000. In pipes, centreline and global entrance lengths coincide for n >0.7, i.e., the flow indeed develops more slowly at the symmetry axis. This is not the case, however, with fluids that are more shear-thinning. Big differences are observed, which are more pronounced at lower Re. The stress entrance length is smaller than the classical centreline entrance length except for n <0.4 and n >1.45. More dramatic are the differences in channel flow. For n <1 (shear thinning fluids), L c is smaller than both L t and L g. The differences are relatively reduced as Re and n are increased. [ABSTRACT FROM AUTHOR]

The development of Bingham plastic flow in tubes and channels is investigated numerically using the Papanastasiou regularization and finite element simulations. It is assumed that slip occurs along the wall following Navier's law, according to which the slip velocity varies linearly with the wall shear stress. Alternative definitions of the development length are discussed and the combined effects of slip and yield stress at low and moderate Reynolds numbers are investigated. It is demonstrated that even for the Newtonian channel flow using the conventional centerline development length is not a good choice when slip is present. Similarly, the development length definition proposed by Ookawara et al. (2000) for viscoplastic flows results in misleading conclusions regarding the effect of yield stress on flow development. To avoid such inconsistencies a global development length is employed. In general, the global development length is monotonically increasing with the Reynolds and Bingham numbers. As slip is increased, the latter length initially increases exhibiting a global maximum before vanishing rapidly slightly above the critical point corresponding to sliding flow. [ABSTRACT FROM AUTHOR]

We solve numerically the cessation of the pressure-driven Poiseuille flow of a Bingham plastic under the assumption that slip occurs along the wall following a generalized Navier-slip law involving a non-zero slip yield stress. In order to avoid the numerical difficulties caused by their inherent discontinuities, both the constitutive and the slip equations are regularized by means of exponential (Papanastasiou-type) regularizations. As with one-dimensional Poiseuille flows, in the case of Navier slip (zero slip yield stress), the fluid slips at all times, the velocity becomes and remains plug before complete cessation, and the theoretical stopping time is infinite. The cessation of the plug flow is calculated analytically. No stagnant regions appear at the corners when Navier slip is applied. In the case of slip with non-zero slip yield stress, the fluid may slip everywhere or partially at the wall only in the initial stages of cessation depending on the initial condition. Slip ceases at a critical time after which the flow decays exponentially and the stopping times are finite in agreement with theory. The combined effects of viscoplasticity and slip are investigated for wide ranges of the Bingham and slip numbers and results showing the evolution of the yielded and unyielded regions are presented. The numerical results also showed that the use of regularized equations may become problematic near complete cessation or when the velocity profile becomes almost plug. [ABSTRACT FROM AUTHOR]

The singular function boundary integral method (SFBIM) is applied for the numerical solution of a 2-D Laplace model problem of a perfectly elastic wedge beam under plane stress conditions. The beam has a point boundary singularity, it includes a curved boundary part and is subjected to non-trivial distributed external loading. The implemented solution method converges for this special model problem extremely fast. The numerical estimates attained for the leading singular coefficients of the local asymptotic expansion and the stress and strain fields are highly accurate, as verified by comparison with the available analytical solution. [ABSTRACT FROM AUTHOR]

Abstract: A standard method used to determine material properties of semi-solid slurries is the squeeze flow experiment; a fixed amount of material is squeezed under constant force or velocity and the relation between the force and the displacement of the sample provides information about the rheology of the slurry. The objective of this work is to contribute to the further development of the squeeze flow methodology in order to accurately determine material properties. This is achieved by a model that accounts for the finite yield stress and the thixotropy of the slurry. More specifically a structural viscoplastic model based on the Bingham plastic constitutive equation is proposed. The yield stress is assumed to vary linearly with the structural parameter which follows a first-order rate equation accounting for the material structure break-down and build-up. Numerical experiments of squeeze flow under either constant load or constant velocity are presented and discussed. Comparisons with their non-thixotropic counterparts are made in the case of compression under constant load. The development of the yielded/unyielded regions in relation to material structural changes is analyzed. The numerical results show that initially thixotropy does not affect the flow. However, once the structure is destroyed, the unyielded regions grow slower than the non-thixotropic case allowing for longer compression of the sample. Under constant force the structure may be destroyed at the early stages of the compression but at a later time it re-builds steadily till the cessation of the flow experiment. Under constant velocity, however, the structure is destroyed steadily. Depending then on the case, the final internal structure of the squeezed material can vary significantly. This is an important issue that needs to be taken into consideration in the evaluation of the material parameters. [Copyright &y& Elsevier]

In this study, we have carried out experiments to characterize the wall slip of colloidal suspensions of kaolinites. To demonstrate slip, the rheological measurements were carried out with parallel-plate geometry with smooth and rough plates. The asperities of the rough surface penetrated the slip layer and created a nearly no-slip region, whereas the smooth plate showed significantly higher slip, a conclusion drawn by comparing the macroscopic flow curves in both cases. Two slip regimes were identified, namely, (i) an elastic slip regime below the yield stress of the suspension where the material slips like a solid and (ii) a slip regime above the yield stress where the material yields and flows. The slip velocity was quantified using a simple phenomenological slip model that seems to capture slip in both flow regimes. The transition from the first slip regime to the other has been resolved numerically as the material starts yielding first at the edge of the parallel-plate geometry with the yield point propagating inwards as the rotational speed is increased. The numerical method also establishes uniquely the yield stress value, which was found to agree with data obtained from parallel-plate, cone-and-plate, and concentric cylinder geometries. [ABSTRACT FROM AUTHOR]

Marine pollution impacts coastal nations around the world, and more so: (a) in confined maritime areas with significant marine traffic, (b) where exploitation of natural and mineral resources is taking place, or (c) in regions witnessing pressure from tourism, local population growth, and industry. In this work, Digital Elevation Models, hydrographic, and climatic data are used together with computer simulations to understand the control of climate change on marine pollution. The results show that different climate change signals can potentially alter the flow and concentration of pollution in the European Seas, when compared to the present day. Ultimately, this work identifies the main sources of marine pollution as: (1) rivers and streams near cities and industrialised areas, (2) coastal areas experiencing sudden demographic pressures, (3) offshore shipping lanes in which oil and other marine debris are released, and (4) areas of rugged seafloor where industrial fishing takes place. This paper finishes by describing new educational material prepared to teach school children around the world. It explains why how a new training curriculum and e-game developed by Sea4All can be crucial in future Environmental Education and Education for a Sustainable Development. [ABSTRACT FROM AUTHOR]

• The poiseuille flow of a bingham plastic in a tube of variable radius is considered. • A lubrication solution is derived at zero order. • The lubrication paradox is avoided at zero order. • The lubrication solution is validated against an approximate analytical solution. • It is demonstrated that the perturbation solution exists only for small variations of the tube radius. We extend a method developed by Fusi and Farina (Appl. Math. Comp. 320, 1–15, 2018) to obtain semi-analytical lubrication-approximation solutions for the flow of a Bingham-plastic in a tube of variable radius. The proposed method is applicable provided that the unyielded core extends continuously from the inlet to the outlet. It turns out that the variable radius of the latter core obeys a stiff integral-algebraic equation which is solved both numerically and asymptotically. The pressure distribution is then obtained integrating a 1st-order ODE and the velocity components are computed using analytical expressions. Converging or diverging either linearly or exponentially, undulating and stenosed tubes are considered. The effects of the shape of the wall on the yield surface which separates the yielded region from the unyielded core and on the pressure difference required to drive the flow are investigated and discussed. The results show that the effect of the wall variation amplitude is greatly amplified as the volumetric flow rate (or, equivalently, the imposed pressure difference driving the flow) increases. It is also demonstrated that the pressure difference needed to achieve a given volumetric flow rate in a converging pipe is always higher than that for a diverging one. [ABSTRACT FROM AUTHOR]

We consider both the axisymmetric and planar steady-state Poiseuille flows of weakly compressible Newtonian fluids, under the assumption that both the density and the shear viscosity vary linearly with pressure. The primary flow variables, i.e. the two non-zero velocity components and the pressure, as well as the mass density and viscosity of the fluid are represented as double asymptotic expansions in which the isothermal compressibility and the viscosity–pressure-dependence coefficient are taken as small parameters. A standard perturbation analysis is performed and asymptotic, analytical solutions for all the variables are obtained up to second order. These results extend the solutions of the weakly compressible flow with constant viscosity and those of the incompressible flow with pressure-dependent viscosity. The combined effects of compressibility and the pressure dependence of the viscosity are analyzed and discussed. [ABSTRACT FROM AUTHOR]

Highlights: [•] A regularized slip equation with slip yield stress is proposed. [•] The cessation of the axisymmetric Poiseuille flow of Herschel-Bulkley fluids is solved numerically. [•] Different steady-state flow regimes are identified depending on relative values of the slip parameters. [•] In the case of zero slip yield stress, the velocity of viscoplastic fluids becomes and remains flat till complete cessation. [•] The stopping time of viscoplastic flow is finite only if the slip exponent is less than unity. [ABSTRACT FROM AUTHOR]

The geometric and hemodynamic characteristics of the left and right vertebral arteries (LVA, RVA) of six healthy volunteers were investigated for the supine (S) and the prone position (P) a common sleeping posture with head rotation. MRI images were used to reconstruct the subject specific three-dimensional solid models of the LVA and RVA from the level of the carotid bifurcation to the vertebrobasilar junction (VJ). Geometric parameters such as cross sectional area ratio, curvature, tortuosity and branch angle were estimated. MR-PCA was used to obtain the blood flow waveforms for the two positions and computational fluid dynamics (CFD) were used to assess the flow field in terms of wall shear stress (WSS) relative residence times (RRT) and localized normalized helicity (LNH). Significant geometric changes but moderate flow changes were observed for both vertebral arteries with head rotation. The CFD results at the VJ show that head rotation causes changes in the WSS distribution, RRT and LNH. Further studies are warranted to assess the clinical significance of the results in terms of atherosclerosis development at the VJ and how the observed geometric changes may affect blood flow to the brain in healthy subjects and vertebral artery stenosis patients, and in terms of increased rapture susceptibility in vertebrobasilar aneurysm patients.

Head and neck postures may cause morphology changes to the geometry of the carotid bifurcation (CB) that alter the low and oscillating wall shear stress (WSS) regions previously reported as important in the development of atherosclerosis. Here the right and left CB were imaged by MRI in two healthy subjects in the neutral head posture with the subject in the supine position and in two other head postures with the subject in the prone position: (1) rightward rotation up to 80°, and (2) leftward rotation up to 80°. Image-based computational models were constructed to investigate the effect of posture on arterial geometry and local hemodynamics. The area exposure to unfavorable hemodynamics, based on thresholds set for oscillatory shear index (OSI), WSS and relative residence time, was used to quantify the hemodynamic impact on the wall. Torsion of the head was found to: (1) cause notable changes in the bifurcation and internal carotid artery angles and, in most cases, on cross-sectional area ratios for common, internal and external carotid artery, (2) change the spatial distribution of wall regions exposed to unfavorable hemodynamics, and (3) cause a marked change in the hemodynamic burden on the wall when the OSI was considered. These findings suggest that head posture may be associated with the genesis and development of atherosclerotic disease as well as complications in stenotic and stented vessels.