The influence of inertia on the rheology of a periodic suspension of neutrally buoyant rigid ellipsoids

2015 ◽  
Vol 781 ◽  
pp. 506-549 ◽  
Author(s):  
Mohsen Daghooghi ◽  
Iman Borazjani
Keyword(s):  
Normal Stress ◽  
Reynolds Stress ◽  
Intrinsic Viscosity ◽  
Volume Fraction ◽  
Normal Stress Difference ◽  
Numerical Results ◽  
Spherical Particles ◽  
Stress Difference ◽  
Neutrally Buoyant ◽  
Normal Difference

We investigate the rheological properties of a suspension of neutrally buoyant rigid ellipsoids by fluid–structure interaction simulations of a particle in a periodic domain under simple shear using the curvilinear immersed-boundary (CURVIB) method along with a quaternion–angular velocity technique to calculate the dynamics of the particle’s motion. We calculate all the different terms of particle stress for the first time for non-spherical particles, i.e. in addition to the stresslet, we calculate the acceleration and Reynolds stress, which are typically ignored in previous similar works. Furthermore, we derive analytical expressions for all these terms to verify the numerical results and deduce the effect of inertia by comparing our numerical results with the analytical solution. The effect of particle Reynolds number ($\mathit{Re}$), volume fraction (${\it\phi}$), and the shape of particles has been studied on all mechanisms of stress generation, the intrinsic viscosity, and normal stress differences of the suspension for the range$0.008\leqslant {\it\phi}\leqslant 0.112$and$0.01\leqslant \mathit{Re}\leqslant 10.0$. We found that inertia increases the shear and the second normal difference of the stresslet (dominant term of the particle stress), and decreases the first normal difference that is generated due to the strain field. The contribution of acceleration stress to the total stress is found to be important in the second normal stress difference, with a cycle-average comparable to the stresslet component. We also discovered that the contribution of Reynolds stress in the first normal stress difference becomes important even when inertia is as low as$\mathit{Re}\sim O(0.1)$, and its value can be even greater than the stresslet when inertia increases, i.e. Reynolds stresses cannot be ignored for non-spherical particles. For concentrations in the range from dilute to semi-dilute, the effect of inertia on the intrinsic viscosity of a suspension is found to be comparable to the volume fraction. Furthermore, our calculations show that for a dilute concentration and the low-inertia regime ($\mathit{Re}<1.0$), the intrinsic viscosity of a suspension consisting of ellipsoids with an aspect ratio of five can be 20 % higher than its Stokesian analytical value.

Suspensions in a tilted trough: second normal stress difference

2011 ◽  
Vol 686 ◽  
pp. 26-39 ◽  
Author(s):  
Étienne Couturier ◽  
François Boyer ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Volume Fraction ◽  
Behavioural Change ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Rigid Spheres ◽  
First Normal Stress Difference ◽  
Second Normal Stress Difference ◽  
Neutrally Buoyant

AbstractWe measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by Wineman & Pipkin (Acta Mechanica, vol. 2, 1966, pp. 104–115) and Tanner (Trans. Soc. Rheol., vol. 14, 1970, pp. 483–507), which relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen & Guazzeli (J. Fluid Mech., 2011, doi:10.1017/jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small.

scholarly journals Vliv smykové viskozity a elasticity na senzorickou viskozitu modelových kapalných potravin

1999 ◽  
Vol 17 (No. 1) ◽  
pp. 23-30 ◽  
Author(s):  
P. Novotna ◽  
M. Houska ◽  
V. Sopr ◽  
H. Valentova ◽  
P. Stern
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Shear Viscosity ◽  
Normal Stress Difference ◽  
Rheological Parameters ◽  
Cellulose Derivatives ◽  
Moderate Increase ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Normal Difference

The shear flow rheological properties of sugar solutions (70% w/w concentration) modified by different cellulose derivatives have been measured. Thickeners  were expected to cause the viscoelastic behaviour of the resulting sol ution. Therefore, the elastic rheological parameters were measured by oscillatory shear technique (phase angle, elastic modulus) and also the first normal stress difference N<sub>1</sub>. The increase of thickener concen tration caused a moderate increase of non-Newtonian behaviour in the shear flow. The sensory viscosity (ra nged between 0 and 100%) was evaluated by five different methods - as an effort for stirring with teaspoon, time for flowing down the spoon, slurping from spoon, compression between tongue and palate and swallowing. The influence of shear viscosity and first normal difference on sensory viscosity was tested. Correlation procedu re between change of sensory viscosity .tlSE and change of shear viscosity .tlJ.Iz showed that only for swallowing there is a statistically evident de­pendence. The correlation between change of sensory viscosity t.SE and first normal stress difference N<sub>1</sub> is not statistically   evident. For all the methods of sensory evaluation the dependence between these parameters is only weak and indirect (with increasing normal stress difference the sensory viscosity is decreasing).

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.

scholarly journals Structure, diffusion and rheology of Brownian suspensions by Stokesian Dynamics simulation

2000 ◽  
Vol 407 ◽  
pp. 167-200 ◽  
Author(s):  
DAVID R. FOSS ◽  
JOHN F. BRADY
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Normal Stress Difference ◽  
Dynamics Simulation ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Stokesian Dynamics ◽  
First Normal Stress Difference ◽  
Monodisperse Suspension

The non-equilibrium behaviour of concentrated colloidal dispersions is studied using Stokesian Dynamics, a molecular-dynamics-like simulation technique for analysing suspensions of particles immersed in a Newtonian fluid. The simulations are of a monodisperse suspension of Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of hydrodynamic and Brownian forces, over a range of volume fraction 0.316 [les ] ϕ [les ] 0.49. For Pe < 10, Brownian motion dominates the behaviour, the suspension remains well-dispersed, and the viscosity shear thins. The first normal stress difference is positive and the second negative. At higher Pe, hydrodynamics dominate resulting in an increase in the long-time self-diffusivity and the viscosity. The first normal stress difference changes sign when hydrodynamics dominate. Simulation results are shown to agree well with both theory and experiment.

Rheology of a dense suspension of spherical capsules under simple shear flow

2015 ◽  
Vol 786 ◽  
pp. 110-127 ◽  
Author(s):  
D. Matsunaga ◽  
Y. Imai ◽  
T. Yamaguchi ◽  
T. Ishikawa
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Simple Shear ◽  
Volume Fraction ◽  
Orientation Angle ◽  
Normal Stress Difference ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Specific Viscosity ◽  
Dense Suspension

We present a numerical analysis of the rheology of a dense suspension of spherical capsules in simple shear flow in the Stokes flow regime. The behaviour of neo-Hookean capsules is simulated for a volume fraction up to${\it\phi}=0.4$by graphics processing unit computing based on the boundary element method with a multipole expansion. To describe the specific viscosity using a polynomial equation of the volume fraction, the coefficients of the equation are calculated by least-squares fitting. The results suggest that the effect of higher-order terms is much smaller for capsule suspensions than rigid sphere suspensions; for example,$O({\it\phi}^{3})$terms account for only 8 % of the specific viscosity even at${\it\phi}=0.4$for capillary numbers$Ca\geqslant 0.1$. We also investigate the relationship between the deformation and orientation of the capsules and the suspension rheology. When the volume fraction increases, the deformation of the capsules increases while the orientation angle of the capsules with respect to the flow direction decreases. Therefore, both the specific viscosity and the normal stress difference increase with volume fraction due to the increased deformation, whereas the decreased orientation angle suppresses the specific viscosity, but amplifies the normal stress difference.

Measurements of the viscometric functions for a fluid in steady shear flows

1971 ◽  
Vol 270 (1208) ◽  
pp. 507-556 ◽  
Keyword(s):  
Normal Stress ◽  
Couette Flow ◽  
Direct Method ◽  
Normal Stress Difference ◽  
Optical Measurements ◽  
Measuring Error ◽  
Stress Difference ◽  
Concentric Cylinders ◽  
Plate Apparatus ◽  
Good Agreement

This paper describes a series of experiments in which the three material functions of steady viscometric flows were measured for a given polyisobutene solution. A number of instruments and measuring techniques were used in order to check the experimental method. The shear stress was determined from the torque transmitted by the fluid in a cone-and-plate apparatus and in Couette flow between concentric cylinders. The results obtained from these measurements were in good agreement with each other. The primary normal-stress difference was determined from the normal force acting on the plate of a cone-and-plate apparatus, and from stress-optical measurements on Couette flow between concentric cylinders. These results are in good agreement with each other. Detailed measurements of the distribution f Permanent address: Fluid Mechanics Research Institute, University of Essex, Colchester, Essex. of the normal stress acting on the plate of the cone-and-plate apparatus were made for three cone angles and for two boundary configurations at the rim of the apparatus: from these results a combination of the primary and the secondary normal-stress differences was deduced, thereby making possible the computation of the secondary normal-stress difference. When the normal stress acting on a rigid surface is measured by means of a hole leading to a pressure transducer the results are in error by an amount roughly proportional to the primary normal-stress difference of the fluid (cf. Kaye, Lodge & Vale 1968). In the present experiments this error was determined from measurements of the distribution of the normal stress acting on the plates of a plate-and-plate apparatus, together with the assumption that the error is a function only of the shear rate at the position o the hole in the undisturbed viscometric flow. The values of the measuring error thus obtained are in goo agreement with measurements made in Gouette flow between concentric cylinders. The secondary normal-stress difference, P2, was measured in a number of different ways. From the results it is suggested that the methods of Jackson & Kaye and of Marsh & Pearson may be imprecise and, in particular, may yield incorrect values for P2- A new, direct, method of estimating P2, suggested by Higashitani & Pritchard (1971) and outlined in appendix A, may provide a more convenient means of determining P2.

Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

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