scholarly journals Rheology of sheared suspensions of rough frictional particles

2014 ◽  
Vol 757 ◽  
pp. 514-549 ◽  
Author(s):  
Stany Gallier ◽  
Elisabeth Lemaire ◽  
François Peters ◽  
Laurent Lobry
Keyword(s):  
Normal Stress ◽  
Three Dimensional ◽  
Normal Stress Difference ◽  
Normal Stresses ◽  
Fictitious Domain Method ◽  
Concentrated Suspensions ◽  
Physical Description ◽  
Normal Stress Differences ◽  
Sheared Suspensions ◽  
Effective Friction

AbstractThis paper presents three-dimensional numerical simulations of non-Brownian concentrated suspensions in a Couette flow at zero Reynolds number using a fictitious domain method. Contacts between particles are modelled using a discrete element method (DEM)-like approach, which allows for a more physical description, including roughness and friction. This work emphasizes the effect of friction between particles and its role on rheological properties, especially on normal stress differences. Friction is shown to notably increase viscosity and second normal stress difference $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}|N_2|$ and decrease $|N_1|$, in better agreement with experiments. The hydrodynamic and contact contributions to the overall particle stress are particularly investigated. This shows that the effect of friction is mostly due to the additional contact stress since the hydrodynamic stress remains unaffected by friction. Simulation results are also compared with experiments, such as normal stresses or effective friction coefficient $\mu (I_v)$, and the agreement is improved when friction is accounted for. This suggests that friction is operative in actual suspensions.

Normal stress differences in suspensions of rigid  fibres

2014 ◽  
Vol 758 ◽  
pp. 486-507 ◽  
Author(s):  
Braden Snook ◽  
Levi M. Davidson ◽  
Jason E. Butler ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Normal Stress ◽  
Fibre Length ◽  
Normal Stress Difference ◽  
Contact Forces ◽  
Stress Difference ◽  
Normal Stresses ◽  
First Normal Stress Difference ◽  
Second Normal Stress Difference ◽  
Aspect Ratios ◽  
Normal Stress Differences

AbstractMeasurements of normal stress differences are reported for suspensions of rigid, non-Brownian fibres for concentrations of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}nL^2d=1.5\text {--}3$ and aspect ratios of $L/d=11\text {--}32$, where $n$ is the number of fibres per unit volume, $L$ is the fibre length and $d$ is the diameter. The first and second normal stress differences are determined experimentally from measuring the deformation in the free surface in a tilted trough and in a Weissenberg rheometer. Simulations are performed as well, and the hydrodynamic and contact contributions to the normal stresses are calculated. The experiments and simulations indicate that the second normal stress difference is negative and that its magnitude increases as the concentration is raised and the aspect ratio is lowered. The first normal stress difference is positive and its magnitude is approximately twice that of the second normal stress difference. Simulation results indicate that, for the concentrations and aspect ratios studied, contact forces between fibres form the dominant contribution to the normal stress differences.

Normal stresses and microstructure in bounded sheared suspensions via Stokesian Dynamics simulations

2000 ◽  
Vol 412 ◽  
pp. 279-301 ◽  
Author(s):  
ANUGRAH SINGH ◽  
PRABHU R. NOTT
Keyword(s):  
Normal Stress ◽  
Couette Flow ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Normal Stresses ◽  
Plane Couette Flow ◽  
Stokesian Dynamics ◽  
First Normal Stress Difference ◽  
Particle Pressure ◽  
Dynamics Simulations

We report the normal stresses in a non-Brownian suspension in plane Couette flow determined from Stokesian Dynamics simulations. The presence of normal stresses that are linear in the shear rate in a viscometric flow indicates a non-Newtonian character of the suspension, which is otherwise Newtonian. While in itself of interest, this phenomenon is also important because it is believed that normal stresses determine the migration of particles in flows with inhomogeneous shear fields. We simulate plane Couette flow by placing a layer of clear fluid adjacent to one wall in the master cell, which is then replicated periodically. From a combination of the traceless hydrodynamic stresslet on the suspended particles, the stresslet due to (non-hydrodynamic) inter-particle forces, and the total normal force on the walls, we determine the hydrodynamic and inter-particle force contributions to the isotropic ‘particle pressure’ and the first normal stress difference. We determine the stresses for a range of the particle concentration and the Couette gap. The particle pressure and the first normal stress difference exhibit a monotonic increase with the mean particle volume fraction ϕ. The ratio of normal to shear stresses on the walls also increases with ϕ, substantiating the result of Nott & Brady (1994) that this condition is required for stability to concentration fluctuations. We also study the microstructure by extracting the pair distribution function from our simulations; our results are in agreement with previous studies showing anisotropy in the pair distribution, which is the cause of normal stresses.

scholarly journals Normal Stress Effects in the Creep of Ice

1985 ◽  
Vol 31 (108) ◽  
pp. 120-126 ◽  
Author(s):  
David F. McTigue ◽  
Stephen L. Passman ◽  
Stephen J. Jones
Keyword(s):  
Normal Stress ◽  
Principal Stress ◽  
Exact Analytical Solution ◽  
Secondary Creep ◽  
Normal Stresses ◽  
Stress Effects ◽  
Polycrystalline Ice ◽  
Biaxial Creep ◽  
Normal Stress Differences ◽  
Steep Slopes

AbstractMost non-linear fluids for which the appropriate measurements have been made exhibit non-zero and unequal normal stress differences in shearing flows. Power-law models such as Glen’s law cannot represent this phenomenon. The simplest constitutive equation that does embody normal stress effects defines the second-order fluid. An exact analytical solution for biaxial creep of such a fluid is fit to data from four tests on polycrystalline ice. The model gives an excellent representation of both primary and secondary creep. The fits provide values for the three material constants. These coefficients indicate positive first and second normal stress differences. One consequence is the prediction that a steady open-channel flow will exhibit a longitudinal free-surface depression of up to several meters for sufficiently thick ice on steep slopes. In addition, the compressive principal stress at the channel margin is decreased and the tensile principal stress is increased in magnitude over those predicted by models without normal stresses. The normal stresses thus favor the formation of crevasses. Furthermore, the angle these crevasses form with the channel margin is decreased.

Thermohydrodynamic Analysis of Journal Bearings Lubricated by Non-Newtonian Fluids—Theory and Experiments

1994 ◽  
Vol 208 (3) ◽  
pp. 173-181 ◽  
Author(s):  
O Sheeja ◽  
B S Prabhu
Keyword(s):  
Film Thickness ◽  
Normal Stress ◽  
Journal Bearing ◽  
Fluid Model ◽  
Normal Stress Difference ◽  
Fluid Film ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Cubic Law ◽  
Normal Stress Differences

Viscosity index improvers cause the lubricants to exhibit non-Newtonian flow behaviour and display shear thinning and normal stress differences. Shear thinning behaviour is studied by using a rotary shear viscometer. Owing to the non-availability of a rheogoniometer (for the measurement of normal stress differences), the first normal stress difference is calculated from the viscometric data using the Carreau viscosity function. The influence of the first normal stress difference on the hydrodynamic lubrication is analysed and shows that most of the commercial oils are inelasticoviscous in nature. Regression analysis shows that a large number of commercial lubricants follow the inelasticoviscous cubic law fluid model. Hence the cubic law fluid model is considered for the theoretical analysis. An experimental programme is developed to measure the effect of test parameters on the performance of a journal bearing lubricated with different types of non-Newtonian fluids. The experiments mainly include the measurements of the steady state characteristics like film thickness and fluid film friction. The experimental film thickness values are compared with the respective theoretical ones and are in good agreement. The theoretical performance characteristics are obtained through the simultaneous solution of the modified Reynolds equation using the cubic law fluid model and energy equation. The fluid film friction in a hydrodynamic journal bearing is experimentally determined through coastdown analysis. The results are presented in the form of an apparent Stribeck diagram of friction and are compared with the respective theoretical values.

Free Surface Effects on Normal Stress Measurements in Cone and Plate Flow

2007 ◽  
Vol 17 (3) ◽  
pp. 36494-1-36494-6 ◽  
Author(s):  
David C. Venerus
Keyword(s):  
Free Surface ◽  
Stress Field ◽  
Normal Stress ◽  
Spherical Shape ◽  
Normal Stress Difference ◽  
Surface Shape ◽  
Stress Difference ◽  
Stress Measurements ◽  
Free Surface Shape ◽  
Normal Stress Differences

Abstract The effects of free surface shape on normal stress difference measurements in cone and plate flow are investigated. The analysis shows that the stress field is significantly altered by deviations of the free surface from an ideal (spherical) shape. For the cone and partitioned plate technique, it is shown how modest deviation from a spherical free surface shape can lead to errors of roughly 10% in the measured normal stress differences.

The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions

2008 ◽  
Vol 603 ◽  
pp. 207-243 ◽  
Author(s):  
ARUN RAMACHANDRAN ◽  
DAVID T. LEIGHTON
Keyword(s):  
Normal Stress ◽  
Secondary Flow ◽  
Cross Section ◽  
Concentration Distribution ◽  
Normal Stress Difference ◽  
Secondary Flows ◽  
Stress Difference ◽  
Second Normal Stress Difference ◽  
Normal Stress Differences ◽  
The Cross

It was first demonstrated experimentally by H. Giesekus in 1965 that the second normal stress difference in polymers can induce a secondary flow within the cross-section of a non-axisymmetric conduit. In this paper, we show through simulations that the same may be true for suspensions of rigid non-colloidal particles that are known to exhibit a strong negative second normal stress difference. Typically, the magnitudes of the transverse velocity components are small compared to the average axial velocity of the suspension; but the ratio of this transverse convective velocity to the shear-induced migration velocity is characterized by the shear-induced migration Péclet number χ which scales as B2/a2, B being the characteristic length scale of the cross-section and a being the particle radius. Since this Péclet number is kept high in suspension experiments (typically 100 to 2500), the influence of the weak circulation currents on the concentration profile can be very strong, a result that has not been appreciated in previous work. The principal effect of secondary flows on the concentration distribution as determined from simulations using the suspension balance model of Nott & Brady (J. Fluid Mech. vol. 275, 1994, p. 157) and the constitutive equations of Zarraga et al. (J. Rheol. vol. 44, 2000, p. 185) is three-fold. First, the steady-state particle concentration distribution is no longer independent of particle size; rather, it depends on the aspect ratio B/a. Secondly, the direction of the secondary flow is such that particles are swept out of regions of high streamsurface curvature, e.g. particle concentrations in corners reach a minimum rather than the local maximum predicted in the absence of such flows. Finally, the second normal stress differences lead to instabilities even in such simple geometries as plane-Poiseuille flow.

scholarly journals Normal Stress Effects in the Creep of Ice

1985 ◽  
Vol 31 (108) ◽  
pp. 120-126 ◽  
Author(s):  
David F. McTigue ◽  
Stephen L. Passman ◽  
Stephen J. Jones
Keyword(s):  
Normal Stress ◽  
Principal Stress ◽  
Exact Analytical Solution ◽  
Secondary Creep ◽  
Normal Stresses ◽  
Stress Effects ◽  
Polycrystalline Ice ◽  
Biaxial Creep ◽  
Normal Stress Differences ◽  
Steep Slopes

AbstractMost non-linear fluids for which the appropriate measurements have been made exhibit non-zero and unequal normal stress differences in shearing flows. Power-law models such as Glen’s law cannot represent this phenomenon. The simplest constitutive equation that does embody normal stress effects defines the second-order fluid. An exact analytical solution for biaxial creep of such a fluid is fit to data from four tests on polycrystalline ice. The model gives an excellent representation of both primary and secondary creep. The fits provide values for the three material constants. These coefficients indicate positive first and second normal stress differences. One consequence is the prediction that a steady open-channel flow will exhibit a longitudinal free-surface depression of up to several meters for sufficiently thick ice on steep slopes. In addition, the compressive principal stress at the channel margin is decreased and the tensile principal stress is increased in magnitude over those predicted by models without normal stresses. The normal stresses thus favor the formation of crevasses. Furthermore, the angle these crevasses form with the channel margin is decreased.

The rheology and microstructure of concentrated non-colloidal suspensions of deformable capsules

2011 ◽  
Vol 685 ◽  
pp. 202-234 ◽  
Author(s):  
Jonathan R. Clausen ◽  
Daniel A. Reasor ◽  
Cyrus K. Aidun
Keyword(s):  
Normal Stress ◽  
Three Dimensional ◽  
Colloidal Suspensions ◽  
Elastic Membrane ◽  
Normal Stresses ◽  
Particle Deformation ◽  
Self Diffusion ◽  
Sign Change ◽  
Stress Changes ◽  
Particle Level

AbstractA detailed study into the rheology and microstructure of dense suspensions of initially spherical capsules is presented, where capsules are composed of a fluid-filled interior surrounded by an elastic membrane. This study couples a lattice-Boltzmann fluid solver to a finite-element membrane model creating a robust and scalable method for the simulation of these suspensions. A Lees–Edwards boundary condition is used to simulate periodic simple shear to obtain bulk rheological properties, and three-dimensional results are presented for capsules in the regime of negligible inertia, Brownian motion and colloidal interparticle forces. The simulation results focus on describing the suspension rheology as a function of the particle concentration and deformability, and relating these macroscopic rheological findings to changes at the particle level, i.e. the suspension microstructure. Several important findings are made: suspensions of deformable capsules are found to be shear thinning, and the initially compressive normal stresses associated with rigid spherical suspensions undergo rapid changes with moderate levels of particle deformation. These normal stress changes are particularly evident in the first normal stress difference, which undergoes a sign change at fairly minor levels of deformation, and the particle pressure, which decreases rapidly with increasing particle deformability. Changes in the microstructure as quantified by the single-body microstructure and the pair distribution function are reported. Also, results calculating particle self-diffusion are presented and related to changes in the normal stresses.

scholarly journals Effect of confinement in wall-bounded non-colloidal suspensions

2016 ◽  
Vol 799 ◽  
pp. 100-127 ◽  
Author(s):  
Stany Gallier ◽  
Elisabeth Lemaire ◽  
Laurent Lobry ◽  
Francois Peters
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Colloidal Suspensions ◽  
Wall Slip ◽  
Hexagonal Structure ◽  
Normal Stress Difference ◽  
Contact Forces ◽  
Wall Region ◽  
Stress Difference

This paper presents three-dimensional numerical simulations of non-colloidal dense suspensions in a wall-bounded shear flow at zero Reynolds number. Simulations rely on a fictitious domain method with a detailed modelling of particle–particle and wall–particle lubrication forces, as well as contact forces including particle roughness and friction. This study emphasizes the effect of walls on the structure, velocity and rheology of a moderately confined suspension (channel gap to particle radius ratio of 20) for a volume fraction range $0.1\leqslant {\it\phi}\leqslant 0.5$. The wall region shows particle layers with a hexagonal structure. The size of this layered zone depends on volume fraction and is only weakly affected by friction. This structure implies a wall slip which is in good accordance with empirical models. Simulations show that this wall slip can be mitigated by reducing particle roughness. For ${\it\phi}\lessapprox 0.4$, wall-induced layering has a moderate impact on the viscosity and second normal stress difference $N_{2}$. Conversely, it significantly alters the first normal stress difference $N_{1}$ and can result in positive $N_{1}$, in better agreement with some experiments. Friction enhances this effect, which is shown to be due to a substantial decrease in the contact normal stress $|{\it\Sigma}_{xx}^{c}|$ (where $x$ is the velocity direction) because of particle layering in the wall region.

Normal Stress Differences of Human Blood in Unidirectional Large-Amplitude Oscillatory Shear Flow

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Chaimongkol Saengow ◽  
Alan Jeffrey Giacomin ◽  
Andrea Stephanie Dimitrov
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Human Blood ◽  
Stress Responses ◽  
Large Amplitude ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Large Amplitude Oscillatory Shear ◽  
Oscillatory Shear Flow ◽  
Normal Stress Differences

Abstract This work analyzes normal stress difference responses in blood tested in unidirectional large-amplitude oscillatory shear flow (udLAOS), a novel rheological test, designed for human blood. udLAOS mimics the pulsatile flow in veins and arteries, in the sense that it never reverses, and yet also nearly stops once per heartbeat. As for our continuum fluid model, we choose the Oldroyd 8-constant framework for its rich diversity of popular constitutive equations, including the corotational Jeffreys fluid. This work arrives at exact solutions for normal stress differences from the corotational Jeffreys fluid in udLAOS. We discover fractional harmonics comprising the transient part of the normal stress difference responses, and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. More generally, predictions from the Oldroyd 8-constant framework are explored by means of the finite difference method. Finally, the generalized versions of both the Oldroyd 8-constant framework and the corotational Jeffreys fluid are employed to predict the nonlinear normal stress responses for the model parameters fitted to udLAOS measurements from three very different donors, all healthy. From our predictions, we are led to expect less variation in normal stress differences in udLAOS from healthy donor to donor, than for the corresponding measured shear stress responses.

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