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.

Comparison Study on the Effect of Traction Speed on the GAE and Traditional Extrusion Forming of Four-Lumen Plastic Micro-Catheter

2021 ◽  
Vol 881 ◽  
pp. 39-44
Author(s):  
Zhong Ren
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Axial Flow ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Micro Catheter ◽  
Flow Velocities

In this paper, the effect of traction speed on the four-lumen plastic micro-catheter (FLPMC) was numerically studied. Moreover, the numerical simulations of FLPMC based on two kinds of extrusions, i.e., traditional extrusion and gas-assisted extrusion were performed and compared. Numerical results show that with the increase of traction speed, the sizes of FLPMC for both extrusions all decrease. The sizes of FLPMC based on gas-assisted extrusion are sightly larger than those of the traditional extrusion. To ascertain the reasons, the flow velocities, pressure, shear stress and first normal stress difference distributions of melt based on both extrusions under two different traction speeds were obtained and compared. Results show that with the increase of traction speed under the fixed volume inlet flow rate, the radial flow velocities of melt at the outlet of die decrease but the axial flow velocities increase, which results in the decrease of the die swell at the outlet of die and the size shrinkage of exit face for the FLPMC based on both extrusions. However, for the gas-assisted extrusion, the axial velocities are larger, and the pressure, shear stress and first normal stress difference are far less than those of traditional extrusion, which results in the larger unit volume flow rate, then the sizes of cross-section face are larger than those of the traditional extrusion.

Viscoelastic Behavior of Disperse Systems with Silicone Oil and Different Fillers

2002 ◽  
Vol 12 (6) ◽  
pp. 297-302 ◽  
Author(s):  
Dimiter Hadjistamov
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Normal Stress ◽  
Silicone Oil ◽  
Flow Behavior ◽  
Normal Stress Difference ◽  
Filler Concentration ◽  
Stress Difference ◽  
Disperse Systems ◽  
First Normal Stress Difference

Abstract The rheological behavior of model suspensions with the silicone oil M20000 and different concentrations of Cab-o-sil TS 720 resp. Durcal 5 are compared. The increase of the Cab-o-sil concentration changes the flow behavior of the suspension from shear-thinning, to pseudoplastic, and to plastic flow behavior. The first normal stress difference rises at the same time at certain shear rate. The disperse systems with Durcal 5 keep the structural viscous behavior of the silicone oil even with a filler concentration of 40.5 wt%. The dependence of the first normal stress difference on shear rate represents for suspensions with Durcal 5 only one straight line with a slope of n = 2. The normal stress has double the amount of the silicone oil M20000 at given shear rate and is independent of the used Durcal 5 concentration. It was established that suspensions with the silicone oil M20000 have a first normal stress difference that can, depending on the filler type, either increase (with Cab-o-sil TS 720) or decrease (with Durcal 5) at certain shear stress with increasing filler concentration. It is to be supposed that the decrease of the normal stress at a given shear stress, with increasing Durcal concentration, is a softening effect, caused by the filler.

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.

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.

Numerical simulation of the rheological properties of fiber suspensions in turbulent pipe flows

2015 ◽  
Vol 25 (3) ◽  
pp. 639-650
Author(s):  
Xiaoyu Liang ◽  
Wei Yang ◽  
Lingxin Zhang
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Orientation Distribution ◽  
Normal Stress Difference ◽  
Fiber Suspensions ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Content Type ◽  
Fiber Orientation Distribution ◽  
The Mean

Purpose – The purpose of this paper is to study numerically the rheological properties of fiber suspensions flowing through turbulent pipe flows. Design/methodology/approach – The work presented in this paper is derived the fluctuating equation for fiber orientation distribution function (FODF) in turbulent flows and solved using the method of characteristics. The FODF is predicted numerically. The numerical results of root-mean-square velocities generated by kinetic simulation sweeping model and are compared with the experimental data. Findings – The fiber orientation distribution becomes wider with increasing Re. The components of the fourth-order orientation tensor increase with the increase of Re, and also increase along the radial direction and reach the maximum at the center line. The first normal stress difference is much less than the shear stress. For different Re the shear stress increases rapidly in the region far from the pipe center, and reaches its maximums at center, while the first normal stress difference decreases rapidly in the region far from the pipe center, and reaches its minimum at center finally. Originality/value – By solving numerically the equation in a turbulent pipe flow with Reynolds number ranging from 2,500 to 1,000, the authors obtain the mean FODF which is in agreement with the experimental one qualitatively. Then the shear stress and first normal stress difference of suspensions are calculated based on the mean FODF.

Rheology of LCP/PET Blends at Solid and Molten States of LCP

2006 ◽  
Vol 16 (3) ◽  
pp. 152-160 ◽  
Author(s):  
S.A.R. Hashmi ◽  
Takeshi Kitano
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Shear Viscosity ◽  
Liquid Crystalline ◽  
High Sensitivity ◽  
Crystalline Polymer ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Different Temperatures

Abstract Liquid crystalline polymer (LCP) and polyethylene terephthalate (PET) were blended in an elastic melt extruder to make samples having different volume fractions of constituent polymers. Shear stress, shear viscosity, first normal stress difference at different shear rates under steady state conditions of these blends were evaluated at two different temperatures 265 and 285˚C. The LCP was in solid state at 265˚C and in melt state at 285˚C and was dispersed in molten matrix of PET at both temperatures. Shear viscosity of blend increased with addition of LCP in PET matrix. A maxima was observed in viscosity versus composition plot. Blends containing more than 50 vol. % of LCP in the blend show higher viscosity as compared to the constituent polymers. First normal stress difference, N1, increased with LCP content in the blend at 285˚C when ploted against shear stress whereas at 265˚C this trend was opposite. The increased value of N1 with shear rate was explained assuming a tendency of asymmetric particles to rotate under velocity gradient of suspending medium. At 285˚C N1 varied with shear stress in two stages. First stage was characterized with high sensitivity of N1 with shear stress, which reduced in second stage on plastic deformation of LCP droplets.

Sign in / Sign up

Export Citation Format

Share Document