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

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

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

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

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

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

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

We investigate experimentally the effects of a pipe axial rotation on buoyant miscible displacement flows in an inclined pipe. The displacing Newtonian fluid (salt-water solution) is heavier than the displaced viscoplastic one (Carbopol solution). Via image processing techniques and ultrasound Doppler velocity measurements, we analyze the key flow features such as the flow patterns, the velocity and

This paper reports on the multiplicity of steady state solutions and the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a horizontal rectangular cavity filled with a power-law non-Newtonian fluid. The short vertical sides of the cavity are submitted to horizontal thermal and solutal flux densities, while its horizontal walls are impermeable and adiabatic. The problem

Fluid flow inside nano-channels coated with a polyelectrolyte brush layer (PEL) is dictated by the brush structure and its interaction with the counter-ion dominated electrical double layer (EDL) near the walls of the PEL channel. In this work, we bring out the confluence of spatial permittivity variation, the influence of proximity between ions in charged PEL channels and non-Newtonian constitutive

The relation between the drag reduction (DR) performance of several water-soluble polymers and their viscoelastic properties was investigated. Polymers with a flexible molecular structure including three grades of polyacrylamides (PAM), and a polyethylene oxide (PEO) were investigated. Xanthan gum (XG) and carboxymethyl cellulose (CMC), each with a rigid molecular structure, were also considered. The

In this paper, we present result from a direct numerical simulation (DNS) of turbulent flow in a converging T-junction for both Newtonian (water) and non-Newtonian inelastic fluid (dilute Xanthan Gum solution). Based on experimental data, the Bird-Carreau law is used to capture the inelastic shear thinning property of the solution. For the Xanthan solution, the viscosity at rest is about 100 times

Shear-thickening and thinning behaviors are often observed in the rheological measurements of dilute surfactant solutions with drag-reducing ability in wall-bounded turbulent flows. This study proposes a simple rheological modeling method based on combining constitutive equations, such as Giesekus and FENE-P models, with a fluidity equation to determine both thickening and thinning behaviors in simple

This work is concerned with time-dependent axisymmetric free surface flows of Oldroyd-B fluids for any value of , the ratio of solvent to total viscosities. The Oldroyd-B constitutive equation is dealt with by employing a novel technique to calculate the conformation tensor while an EVSS transformation allows the solution of the momentum equations coupled with the free surface stress conditions: this

The relevance of upstream contraction for extrudate swell behavior of polymer melts is numerically investigated for slit dies with an aspect ratio of 10 and a length-to-height ratio ranging from 2.5 to 40. Three-dimensional (3D) flow simulations are performed with ANSYS Polyflow software at different flow rates and a constant temperature of 200°C, selecting a differential multimode Phan-Thien-Tanner

We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described

Wall slip quantification using the classical Mooney slip analysis has produced physically unreasonable results for many complex fluids. Over the past decades, the assumption that the slip velocity is solely dependent on the wall shear stress has therefore been questioned. In this contribution, the influence of the radius of cylindrical dies on the wall slip velocity of highly concentrated non-Brownian

We consider the impact of periodical finite-amplitude perturbations induced by oscillations of the supporting plane on the natural instability of a falling film. The oscillations change the basic state of the flow from steady to periodical; for non-Newtonian liquids, the mean parameters of the basic state depend on the plane’s oscillations. We solve the eigenvalue problem for linearized generalized

A detailed numerical study on the flow and heat transfer phenomena from a rotating cylinder submerged in a streaming viscoelastic FENE-P fluid has been carried out. The governing equations, along with the FENE-P viscoelastic constitutive equation, have been solved using OpenFOAM over the following ranges of conditions: Reynolds number, 10 ≤ Re ≤ 100; Weissenberg number, 0 ≤ Wi ≤ 10; non-dimensional

Buoyant Marangoni convection of a power-law fluid confined in a shallow cavity heated from below is investigated. The free upper surface of the system is assumed to be flat and underformable. A simplified analytical model, valid for an infinite layer, is derived on the basis of the parallel flow approximation. The criteria, for the onset of convection, are predicted for both shear-thinning and shear

An analytical model capturing the effects of mean-field considerations on the orientation evolution of a plurality of rigid spheroids suspended in a Newtonian matrix is developed. Three approaches are taken with increasing sophistication: a mesoscale view involving the analysis of several distinct layers of material subjected to simple shear flow, a traditional micromechanics inspired approach involving

A 3D transient non-isothermal finite element code is developed to predict the extrudate shape of viscoelastic fluids emerging from an asymmetric keyhole shaped die. The corner-line method is used to model the movement of the free surfaces. The code is tested using two benchmark problems. First the corner-line method is tested using a trumpet shaped object in a 3D uniaxial extensional flow. Secondly

The present work studied the rheological properties of concentrated non-colloidal aqueous suspensions of graphite particles together with carboxymethyl cellulose (CMC) having various molecular weights, especially focusing on the applicability of the modified Cox-Merz rule. These suspensions were investigated as model slurries to produce anode electrodes of lithium ion batteries. In the case of suspensions

Systematic rheometric measurements are carried out to explore the nonlinear responses of carbon black-filled polyisoprene/squalene solutions with the polymer concentrations ϕ in the matrix ranging from the coil overlapping state (ϕ =ϕ*) to the melt state (ϕ =1). At the coil overlapping state, when ϕ <<1, the system typically shows the classic nonlinearity, where the storage modulus G’ decreases as

In this note, we investigate through scaling laws and direct numerical simulations the development of inertia-dominated coiling instabilities in power-law fluids. Our numerical results are based on an adaptive variational multi-scale method for multiphase flows. In short, when inertia is balanced by viscous forces in the coil, both the coiling frequency and the coil radius are given by a power-law

The squeeze flow of a viscoplastic material between two parallel coaxial disks with yield slip condition at the wall is examined. The governing equations are solved employing the accelerated augmented Lagrangian method for both the viscoplastic model and the yield slip equation. We compute the shape of the yield surface, the velocity and stress fields using the finite difference method. The effect

The performance of supercritical carbon dioxide (scCO2) foams in aquifer remediation and Enhanced Oil Recovery is negatively affected by the foam instability at underground conditions (elevated temperatures and pressures). In search of solutions, viscoelastic surfactants are considered as potential stabilizers beyond traditional surfactants. There are limited studies on the effect of viscoelasticity

In this paper, a Helmholtz-potential-based thermodynamic approach was developed for modelling fluids that exhibit both yielding and thixotropic behavior. The yielding behavior was captured using a framework of multiple natural configurations. The thixotropy was described using a structural parameter. The Helmholtz potential is made a function of a structural parameter and a stretch quantity, and the