Natural convection in a cavity with non-uniformly heated bottom wall, partly filled with a non-Newtonian nanofluid (Cu-water) layer and partly with air layer is studied numerically in this work. The mixture of water and copper nanoparticles shows a shear-thinning rheological behavior. The nanofluid's rheological parameters, i.e. consistency and flow index, are obtained according to the solid volume

We report a study on the micro-confined electroosmotic flow of an Oldroyd-B fluid over a surface having asymmetric charge modulation. We have employed a combination of regular and matched asymptotic expansion to obtain the analytical solution. We have also carried out a full numerical simulation of the physicochemical problem in order to assess the full parameter space of the problem. The analytical

The response of non-colloidal suspensions to sudden strains and sudden changes of strain rate is explored. The matrix fluids were silicone oil and glycerol/water. A Oldroyd-B model of the suspensions augmented by a friction element gives a description of the shear stresses which agrees with experiment. Friction becomes dominant for volume fractions greater than 0.3.

The present comment concerns a wrong comparison made in the above paper.

Electro-thermo-convection is a typical interdisciplinary problem, that has been widely studied in terms of its physical phenomena in Newtonian fluids. As an essential supplement to the study of electrohydrodynamics, electro-thermo-convection in power-law fluids within rectangular enclosures is investigated in this paper. Two geometrical configurations are considered, namely differentially heated vertical

The sedimentation of a spherical solid particle in viscoelastic fluids was studied using a Giesekus model by development of a direct numerical simulation solver based on fully-resolved and immersed boundary methods to understand the complex non-Newtonian fluid flow and spherical particle dynamics. Two benchmark problems were modeled to evaluate the accuracy of the developed solver and excellent agreement

In recent years, there has been controversy in the literature regarding the role of viscoelasticity in determining the onset of stability for a viscoelastic thread surrounded by another viscoelastic fluid. Whereas a number of authors have found that viscoelasticity serves to destabilize the system, Patrascu and Balan (2018) obtained very different results. They considered a very simple canonical system

In this work we present theoretical and experimental studies on the structure factor in micellar systems. Cetyl trimethyl ammonium tosilate (CTAT) solutions in absence of salts exhibit a flow behavior similar to polymer solutions, while upon an increase in the ionic strength with NaCl, their behavior changes to that of a kinetic-controlled breakage-reformation process. The relaxation mechanism thus

The temporal instability behavior of a non-Newtonian liquid jet in a compressible gas is investigated theoretically. A corotational Jeffreys model is used for describing the viscoelastic liquid state. The dispersion relation is solved by Chebyshev collocation method. Besides, the effects of compressibility of gas, Reynolds number, elasticity number, and the ratio of deformation retardation time to

Linear stability analysis is performed to study the electrohydrodynamic instability of viscoelastic jets subjected to axisymmetric (m=0) and first non-axisymmetric (m=1) perturbations in the creeping-flow limit. The viscoelastic liquid jet is under the influence of a radially applied electric field induced by a concentrically placed electrode located at a finite gap width from the jet. The leaky dielectric

We investigate the linear stability of a unidirectional flow of a suspension (blood) modeling the latter as a inhomogeneous non-Newtonian fluid in which viscosity depends on both the red blood cell concentration (RBCs) and the shear rate. We consider small vessels like arteries terminal branches, arterioles or venules, where the RBCs do not distribute uniformly on the cross section. The stability analysis

In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approach in a finite volume framework on general unstructured meshes. The numerical stabilization framework is extended to consider thermo-rheological properties

We present an assessment of viscosity regularization (VR) in predicting transient flows of viscoplastic fluids (VPF). Although VR has been the most popular approach for computational studies of VPF in the last decade, the understanding of its effects on the predicted flow behaviour has remained largely qualitative. To reveal the effects of VR, we present a systematic quantitative comparison of the

We consider forcespinning (FS) of nonlinear three-dimensional rotating viscoelastic jets of Boger fluids and in the presence of gravity effect. In FS process, a fluid jet is forced through an orifice of a rotating spinneret leading to the formation of a curved jet. Applying the upper-convected Maxwell constitutive model for the stress tensor part of the governing non-Newtonian jet system and using

Adopting the form of the dynamic μ(Fr,h) basal friction law and introducing a second-order viscous term into the Saint Venant-type equations, we simulated two-dimensional granular roll waves generated in a rectangular chute applying the second-order-accurate total-variation-diminishing MacCormack scheme. Consistent with previous findings, we found that the amplitude and wavelength of the wave increased

We analyse through numerical simulations, experiments, and scaling laws the dam-break problem for viscoplastic materials. Numerically, both two and three-dimensional (2D and 3D) scenarios are considered thanks to a proposed adaptive stabilized finite element framework able to compute efficiently free surface flows of highly viscoplastic materials. We choose to focus on the Bingham model. Momentum and

We present proof-of-concept experiments to illustrate the application of viscoplastic lubrication in transport of high-concentration suspensions. The proposed transport method appears robust for a wide range of suspension concentrations. We develop a theoretical description of the flow that incorporates the significant density difference between the suspension and the lubricating fluid. We explore

A steady-state laminar flow of a viscoplastic fluid through an axisymmetric sudden pipe contraction under non-isothermal conditions has been studied numerically. Mathematical formulation of the problem is given using stream function – vorticity – temperature variables. Rheological properties of the fluid are described by the Herschel–Bulkley model, which implies an unyielded region formation in the

In this paper, the novel Tensor Diffusion approach for the numerical simulation of viscoelastic fluids is introduced based on the idea, that the extra-stress tensor in the momentum equation of the flow model can be replaced by the product of the strain-rate tensor and a (nonsymmetric) tensor-valued viscosity. As potential advantage (which can be demonstrated for fully developed channel, resp., pipe

Complex fluid–fluid interfaces determine for a large part the macroscopic material properties of foams and emulsions that appear in applications such as food, materials processing and consumer care products. As a step towards predicting these properties, a 2D axisymmetric and a 3D finite element model have been developed for simulating the dynamics of a single Newtonian drop in a Newtonian matrix fluid

Oil recovery processes depend on many factors that can be altered in order to maximize the sweeping efficiency in porous media, and one of these is the rheology behavior of the displacing agent. Furthermore, scales in the recovery process should also be considered: from the macro- to microscale systems, in which capillary forces become predominant. It is also well-known the non-Newtonian behavior of

The fundamental understanding of pore scale flow mechanisms associated with the mobilization of trapped oil ganglia during the injection of polymer solutions in porous media requires detailed analysis of viscoelastic flow through pore throats, which can be modeled as constricted capillaries. Despite the vast literature on macroscale and, more recently, microscale viscoelastic flow through contraction–expansion

In this paper we study the flow of a Bingham fluid on a curved (rectangular) pipe. Flows in this kind of geometries present secondary flows due to presence of centripetal forces in the radial direction. This so called Dean Flow has been extensively studied for Newtonian fluids. In considering a yield stress fluid in similar geometries the picture is less clear. Unfortunately, there is not an analytical

Natural mud usually exhibits non-Newtonian rheological behaviors like viscoelasticity, thixotropy and yield stress. The history of each mud sample is also an important factor influencing the rheological behavior, as the state of the clay fabric – for a same composition – is dependent on the shear stresses experienced previously by the sample. Several rheological tests including stress ramp-up, oscillatory

Rayleigh–Bénard convection (RBC) is studied in an elasto-viscoplastic (EVP) gel, the widely used and studied Carbopol gel. The transition from conductive to convective regime is determined by the Schmidt–Milverton principle which leads to a critical value of the inverse of the Yield number 1∕Yc. However, an oscillatory motion in the gel is observed below 1∕Yc≈60 when smooth and untreated walls are

The flow classification developed by Thompson and Souza Mendes [Int. J. Engng. Sci. 43 (2005) 79-105] is applied to radial and squeeze flows between two parallel disks. Based on the lubrication approximation, explicit expressions of the flow classification parameter, namely ℛ, could be obtained for those flows, and the results for power-law and Bingham fluids are presented. It is shown that 0≤ℛ≤1 in

Analytical solutions involving hypergeometric functions are presented for the fully developed laminar flow of a Non-Newtonian fluid in an annulus with a stationary or a moving inner boundary. The solutions are valid for arbitrary values of the power law index in the Couette–Poiseuille flow under consideration, and consider scenarios with and without extrema in the velocity profile, in addition to flow

Uncured styrene-butadiene rubber (SBR) can be modelled as a viscoelastic material with at least two different relaxation mechanisms. In this paper we compare multi-mode constitutive models combining two viscoelastic modes (linear and/or nonlinear) in three possible ways. Our particular choice of the two modes was inspired by models originally developed to describe the response of asphalt binders. We

We investigate the interactions between a cantilevered flexible beam and cross-flow of a viscoelastic fluid. Unlike Newtonian fluids, viscoelastic fluids exhibit elastic flow instabilities even in the absence of inertia. These elastic flow instabilities drive the oscillations of flexible structures placed in their flow path. In this work, the fluid–structure interactions between the flow of viscoelastic

In the Lattice Boltzmann Method (LBM) the viscosity is inversely proportional to the relaxation frequency. Hence, it should be possible to represent the singularity of some viscoplastic models by setting the relaxation frequency to zero. In the present paper we take full advantage of the LBM capabilities to propose an efficient and stable numerical scheme for viscoplastic fluid flow simulations invoking

The orientation distribution of tiny Brownian oblate spheroidal particles suspended in a turbulent channel flow along with their generated non-Newtonian stresses are studied numerically. The direct numerical simulation of turbulent channel flow is coupled with a direct Monte-Carlo simulator for the particles conformation. The effects of particle shape factor and the intensity of rotary Brownian motion

Motivated by the recent developments in the research of untethered microrobots for performing minimally invasive procedures inside blood vessels, we have devised a novel microfluidic experiment for studying the haemodynamics around different types of cylinders confined inside a straight, long, 270×100μm channel. Two test sections are studied: flow past a confined circular cylinder and past a confined

Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of artificial diffusion (AD) for numerical stability in hyperbolic problems, which alters the physical nature of the system. This study presents a hybrid numerical procedure

Large eddy simulation (LES) of turbulent flow of concentrated fiber suspension or pulp is carried out to investigate the flow and turbulence structures in a channel. The simulations are carried out for the turbulent flow of Eucalyptus pulp suspension using OpenFOAM for three fiber concentrations (c = 1.5, 2.0 and 2.5) and six different Reynolds numbers (6 ≤Res≤ 16,600). It is observed that the variation

The rise of a deforming air bubble of fixed volume surrounded by viscoelastic liquids is investigated by an adaptive direct numerical technique coupled with the volume-of-fluid method. The effects of the Weissenberg number (characterizing the strength of elasticity in the flow) and the viscosity ratio on the three-dimensional bubble dynamics have been studied and identified in a wide range of Galilei

This paper addresses the rheometrical flow that combines squeezing and rotating between coaxial parallel discs. Experimental results obtained with this flow have been used as evidence that the von Mises criterion holds for the materials tested. In fact, these results are frequently referred to as a proof of the validity of the von Mises criterion. However, the detailed analysis described here shows

Waxy oils are thermal and shear dependent materials as the initial and final cooling temperatures, cooling rate, shear rate applied during the cooling and the aging time affect the rheological properties of the material. As reported in recent papers, the waxy oil equilibrium flow curve is not only a function of thermal and shear histories but also of the maximum shear rate imposed on the sample. In

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

A fast numerical scheme is proposed to determine the velocity field of an incompressible fluid in a concentric annulus under a constant pressure gradient. The idea behind the scheme is to find the radius R in the annulus where the shear stress becomes zero. In the region from the inner wall at R=κ to R, the shear rate is positive, while it is negative from this radius to the outer wall at r=1. Integrating

We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending

Rigid macromolecules or polymer chains with persistence length on the order of the contour length (or greater) have traditionally been modelled as rods or very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely extensible about a non-zero natural length with tunable harmonic stiffness, is one such model which has previously been shown to reproduce bead–rod behaviour in the absence

This work deals with the zero shear rate (maximum velocity) position parameter λ of a steady laminar axial annular flow of power-law fluids especially polymeric ones. λ is involved in the shear rate, velocity profile and the flow rate calculations, which are essential for studies such as viscous dissipation, convective heat transfer and pressure drop prediction in annuli. However, the analytical explicit

Micelles are formed by the self-assembly of surfactants in solutions. Wormlike micelles or living polymers are a particularly interesting fluids because their long flexible cylindrical geometry can lead to entanglement even at relatively low concentrations. The rheological response of the wormlike micelles is similar in many ways to polymer solutions. Entangled wormlike micelles provide a model fluid

An experimental study was performed to investigate the effects of the extensional rheological properties of polymer solutions on vortex deformation in turbulent flow and turbulent statistics. To focus on the extensional properties, a self-standing two-dimensional (2D) turbulent flow was used as an experimental setup, and the flow was observed through interference patterns and particle image velocimetry

A continuum model for the transport of red blood cells (RBC) inside arteries and capillaries of small diameters is proposed. The pressure and velocity fields are solved using the Navier-Stokes equations while the distribution of the RBC volume fraction, namely, hematocrit is obtained by solving the particle transport equation arising from the diffusive flux model. The momentum and hematocrit transport

This paper is devoted to the numerical solution of the non-isothermal instationary Bingham flow with temperature dependent parameters by semismooth Newton methods. We discuss the main theoretical aspects regarding this problem. Mainly, we discuss the existence of solutions for the problem, and focus on a multiplier formulation which leads us to a coupled system of PDEs involving a Navier–Stokes type

We study the dynamics of a neutrally buoyant rigid sphere carried by an elastoviscoplastic fluid in a pressure-driven channel flow numerically. The yielding to flow is marked by the yield stress which splits the flow into two main regions: the core unyielded region and two sheared yielded regions close to the walls. The particles which are initially in the plug region are observed to translate with

Calculating the yield limit Yc (the critical ratio of the yield stress to the driving stress), of a viscoplastic fluid flow is a challenging problem, often needing iteration in the rheological parameters to approach this limit, as well as accurate computations that account properly for the yield stress and potentially adaptive meshing. For particle settling flows, in recent years calculating Yc has

Restart of gelled waxy crude oil pipeline is one of the major flow assurance concern in petroleum production. Reliable representation of rheological behavior of gelled waxy crude oil serves as the basis for pipeline restart analysis and modeling. In this work, the Dullaert-Mewis elasto-viscoplastic thixotropic model was modified and applied to improve the representation of the rheology of gelled waxy

Numerical models are developed to examine fiber suspension flows through axisymmetric geometries, such as a circular pipe, a center-gated disk and a die exit. The fiber orientation micro-structure is fully described by using the entire probability distribution function (PDF) in 3D instead of the second and fourth moments of the PDF, which introduce errors due to the closure approximation when using

Vortices can have negative effects on the processing of various flows in industrial engineering. Thus, there have been many attempts to seek vortex-free operating conditions. This study explores the feasibility of applying the flow reversal condition in the Couette–Poiseuille (C–P) flow of power-law fluid to the prediction of vortex birth. In previous studies, flow reversal conditions are explicitly

We use numerical simulations to study the stretching and pinching of a viscoplastic material that is confined by two coaxial disks when they are pulled apart. The material initially forms a cylindrical bridge between the disks, follows the Heschel-Bulkley model and yields according to the von Mises criterion. We solve the governing equations numerically in their 2D, axisymmetric form using the PAL

We carry out a linear stability analysis of the generalised BMP model, which incorporates the shear-banding phenomenon into flows of thixotropic-viscoelasto-plastic fluids: common behaviours observed in wormlike micellar solutions. We introduce a new dimensionless parameter governing shear-banding, and find that when a flow is unstable in the absence of shear-banding, this parameter has a stabilising

In this work we discuss the implementation and the performance of an in-house viscoelastic two-phase solver, based on a diffuse interface approach. The Phase-Field method is considered and the Cahn-Hilliard equation is employed for describing the transport of a binary fluid system. The interface between the two fluids utilises a continuum approach, which is responsible for smoothing the inherent discontinuities

The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical

Retraction dynamics of viscous drops and sheets depend on the relative magnitude of the viscous force over the inertia-capillary force. The dynamics are more complicated in the case of viscoplastic drops/sheets because the yield stress of the fluid also comes into play. The retraction of slender viscoplastic drops and sheets depends on the relative magnitude of the yield stress over the capillary stress

We present an experimental study using mixtures of aqueous superabsorbent polymers (SAP) where we systematically investigate the influence of the size of grains that make up the fluid structure on the mixture effective rheology and its domain of validity. In water, SAP powder grains can swell up to 200 times and form gel grains, dg, whose sizes (typically between 1 and 8 mm) can be controlled by choosing