scholarly journals Negative normal stress differences N1–N2 in a low concentration capillary suspension

Soft Matter ◽  
2018 ◽  
Vol 14 (17) ◽  
pp. 3254-3264 ◽  
Author(s):  
Irene Natalia ◽  
Nicole Zeiler ◽  
Moritz Weiß ◽  
Erin Koos
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Solid Concentration ◽  
Particle Suspensions ◽  
Fluid System ◽  
Low Concentration ◽  
Capillary Suspensions ◽  
Normal Stress Differences ◽  
Capillary Attraction ◽  
Two Fluid

Negative normal stress differences are reported in capillary suspensions, i.e. particle suspensions in a two-fluid system that creates strong capillary attraction, at a solid concentration of 25%. This volume fraction has heretofore been too low to show such normal stress differences.

Microstructural theory and the rheology of concentrated colloidal suspensions

2012 ◽  
Vol 713 ◽  
pp. 420-452 ◽  
Author(s):  
Ehssan Nazockdast ◽  
Jeffrey F. Morris
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Perturbation Expansion ◽  
Colloidal Suspensions ◽  
Simple Shear Flow ◽  
Fluid Viscosity ◽  
Analytical Prediction ◽  
Regular Perturbation ◽  
Normal Stress Differences

AbstractA theory for the analytical prediction of microstructure of concentrated Brownian suspensions of spheres in simple-shear flow is developed. The computed microstructure is used in a prediction of the suspension rheology. A near-hard-sphere suspension is studied for solid volume fraction $\phi \leq 0. 55$ and Péclet number $Pe= 6\lrm{\pi} \eta \dot {\gamma } {a}^{3} / {k}_{b} T\leq 100$; $a$ is the particle radius, $\eta $ is the suspending Newtonian fluid viscosity, $\dot {\gamma } $ is the shear rate, ${k}_{b} $ is the Boltzmann constant and $T$ is absolute temperature. The method developed determines the steady pair distribution function $g(\mathbi{r})$, where $\mathbi{r}$ is the pair separation vector, from a solution of the Smoluchowski equation (SE) reduced to pair level. To account for the influence of the surrounding bath of particles on the interaction of a pair, an integro-differential form of the pair SE is developed; the integral portion represents the forces due to the bath which drive the pair interaction. Hydrodynamic interactions are accounted for in a pairwise fashion, based on the dominant influence of pair lubrication interactions for concentrated suspensions. The SE is modified to include the influence of shear-induced relative diffusion, and this is found to be crucial for success of the theory; a simple model based on understanding of the shear-induced self-diffusivity is used for this property. The computation of the microstructure is split into two parts, one specific to near-equilibrium ($Pe\ll 1$), where a regular perturbation expansion of $g$ in $Pe$ is applied, and a general-$Pe$ solution of the full SE. The predicted microstructure at low $Pe$ agrees with prior theory for dilute conditions, and becomes increasingly distorted from the equilibrium isotropic state as $\phi $ increases at fixed $Pe\lt 1$. Normal stress differences are predicted and the zero-shear viscosity predicted agrees with simulation results obtained using a Green–Kubo formulation (Foss & Brady, J. Fluid Mech., vol. 407, 2000, pp. 167–200). At $Pe\geq O(1)$, the influence of convection results in a progressively more anisotropic microstructure, with the contact values increasing with $Pe$ to yield a boundary layer and a wake. Agreement of the predicted microstructure with observations from simulations is generally good and discrepancies are clearly noted. The predicted rheology captures shear thinning and shear thickening as well as normal stress differences in good agreement with simulation; quantitative agreement is best at large $\phi $.

scholarly journals Normal stress differences in dense suspensions

2018 ◽  
Vol 857 ◽  
pp. 200-215 ◽  
Author(s):  
Ryohei Seto ◽  
Giulio G. Giusteri
Keyword(s):  
Normal Stress ◽  
Simple Shear ◽  
Volume Fraction ◽  
Hydrodynamic Lubrication ◽  
Contact Forces ◽  
Simple Shear Flow ◽  
First Normal Stress Difference ◽  
Dense Suspensions ◽  
Normal Stress Differences ◽  
Dynamics Simulations

The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_{1}$ , whereas positive values of $N_{1}$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.

Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences

2016 ◽  
Vol 805 ◽  
pp. 494-522 ◽  
Author(s):  
Priyesh Srivastava ◽  
Abhilash Reddy Malipeddi ◽  
Kausik Sarkar
Keyword(s):  
Reynolds Number ◽  
Normal Stress ◽  
Capillary Number ◽  
Volume Fraction ◽  
Small Range ◽  
Sign Reversal ◽  
Interfacial Stresses ◽  
Number Range ◽  
Shear Rheology ◽  
Normal Stress Differences

The shear rheology of an emulsion of viscous drops in the presence of finite inertia is investigated using direct numerical simulation. In the absence of inertia, emulsions display a non-Newtonian rheology with positive first and negative second normal stress differences. However, recently it was discovered that a small amount of drop-level inertia alters their signs – the first normal stress difference becomes negative and the second one becomes positive, each in a small range of capillary numbers (Li & Sarkar,J. Rheol., vol. 49, 2005, pp. 1377–1394). Sign reversal was shown numerically and analytically, but only in the limit of a dilute emulsion where drop–drop interactions were neglected. Here, we compute the rheology of a density- and viscosity-matched emulsion, accounting for the interactions in the volume fraction range of 5 %–27 % and Reynolds number range of 0.1–10. The computed rheological properties (effective shear viscosity and first and second normal stress differences) in the Stokes limit match well with previous theoretical (Choi–Schowalter in the dilute limit) and simulated results (for concentrated systems) using the boundary element method. The two distinct components of the rheology arising from the interfacial stresses at the drop surface and the perturbative Reynolds stresses are investigated as functions of the drop Reynolds number, capillary number and volume fraction. The sign change is caused by the increasing drop inclination in the presence of inertia, which in turn directly affects the interfacial stresses. Increase of the volume fraction or capillary number increases the critical Reynolds number for sign reversals due to enhanced alignment of the drops with the flow directions. The effect of increasing the volume fraction on the rheology is explained by relating it to interactions and specifically to the contact pair-distribution function computed from the simulation. The excess stresses are seen to show an approximately linear behaviour with the Reynolds number in the range of 0.1–5, while with the capillary number and volume fraction, the variation is weakly quadratic.

Normal stresses in concentrated non-Brownian suspensions

2013 ◽  
Vol 715 ◽  
pp. 239-272 ◽  
Author(s):  
T. Dbouk ◽  
L. Lobry ◽  
E. Lemaire
Keyword(s):  
Normal Stress ◽  
Pore Pressure ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Particle Volume Fraction ◽  
Radial Profile ◽  
Normal Stresses ◽  
Particle Volume ◽  
Wide Range ◽  
Normal Stress Differences

AbstractWe present an experimental approach used to measure both normal stress differences and the particle phase contribution to the normal stresses in suspensions of non-Brownian hard spheres. The methodology consists of measuring the radial profile of the normal stress along the velocity gradient direction in a torsional flow between two parallel discs. The values of the first and the second normal stress differences, ${N}_{1} $ and ${N}_{2} $, are deduced from the measurement of the slope and of the origin ordinate. The measurements are carried out for a wide range of particle volume fractions (between 0.2 and 0.5). As expected, ${N}_{2} $ is measured to be negative but ${N}_{1} $ is found to be positive. We discuss the validity of the method and present numerous tests that have been carried out in order to validate our results. The experimental setup also allows the pore pressure to be measured. Then, subtracting the pore pressure from the total stress, ${\mbrm{\Sigma} }_{\mathbf{22} } $, the contribution of the particles to the normal stress ${ \mbrm{\Sigma} }_{\mathbf{22} }^{\mathbi{p}} $ is obtained. Most of our results compare well with the different experimental and numerical data present in the literature. In particular, our results show that the magnitude of the particle stress tensor component and their dependence on the particle volume fraction used in the suspension model balance proposed by Morris & Boulay (J. Rheol., vol. 43, 1999, p. 1213) are suitable.

Dense suspensions in rotating-rod flows: normal stresses and particle migration

2011 ◽  
Vol 686 ◽  
pp. 5-25 ◽  
Author(s):  
François Boyer ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Shear Rate ◽  
Normal Stress ◽  
Volume Fraction ◽  
Particle Migration ◽  
Balance Model ◽  
Normal Stresses ◽  
Dense Suspensions ◽  
Normal Stress Differences ◽  
Neutrally Buoyant ◽  
Dependent Behaviour

AbstractNormal stress differences are measured in dense suspensions of neutrally buoyant non-Brownian spheres dispersed in a Newtonian fluid. Rotating-rod rheometry is used to characterize the suspension normal stresses which are responsible for a rod-dipping phenomenon. These normal stress differences are seen to strongly increase above a volume fraction of approximately 22 %. During the course of the experiments, a new time-dependent behaviour is also observed: the dip is filled with increasing times. This time evolution is found to be related to particle migration from regions of high shear rate to regions of low shear rate. The behaviour is compared with the predictions of a suspension balance model in which the particle migration flux is related to the normal stresses of the suspension.

Investigation of stresses and normal stress differences behavior on symmetric and asymmetric polymeric fluid flow through planar gradual expansions

Meccanica ◽  
2016 ◽  
Vol 52 (8) ◽  
pp. 1889-1909 ◽  
Author(s):  
M. Norouzi ◽  
A. Shahbani Zahiri ◽  
M. M. Shahmardan ◽  
H. Hassanzadeh ◽  
M. Davoodi
Keyword(s):  
Fluid Flow ◽  
Normal Stress ◽  
Polymeric Fluid ◽  
Flow Through ◽  
Normal Stress Differences

LOW CONCENTRATION LIMIT FOR A FLUID FLOW THROUGH A FILTER

1998 ◽  
Vol 08 (04) ◽  
pp. 623-643 ◽  
Author(s):  
SANJA MARUŠIĆ
Keyword(s):  
Asymptotic Behavior ◽  
Fluid Flow ◽  
Volume Fraction ◽  
Periodic Array ◽  
Concentration Limit ◽  
Global Flow ◽  
Low Concentration ◽  
Flow Through ◽  
Low Volume ◽  
Filtration Law

A fluid flow through an ∊-periodic array of obstacles distributed on a hypersurface (filter) is considered. The study of the asymptotic behavior as ∊→0 for two critical sizes of obstacles ∊ and ∊2 gives two different laws describing a global flow. In this paper we study the case of an intermediate obstacle size ∊β, 1 < β < 2 and we prove the continuity of the filtration law in the low-volume fraction limit.

Manufacturing and Measuring Mechanical Properties of Continuous Functionally Graded Beam

2021 ◽  
Vol 21 (2) ◽  
pp. 7-11
Author(s):  
Ahmed Mansoor Abbood ◽  
Haider K. Mehbes ◽  
Abdulkareem. F. Hasan
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
High Concentration ◽  
Functionally Graded Beam ◽  
Low Concentration ◽  
Graded Material ◽  
Vertical Gravity

In this study, glass-filled epoxy functionally graded material (FGM) was prepared by adopting the hand lay-up method. The vertical gravity casting was used to produce a continuous variation in elastic properties. A 30 % volume fraction of glass ingredients that have mean diameter 90 μm was spread in epoxy resin (ρ = 1050 kg/m3). The mechanical properties of FGM were evaluated according to ASTM D638. Experimental results showed that a gradually relationship between Young’s modulus and volume fraction of glass particles, where the value of Young’s modulus at high concentration of glass particles was greater than that at low concentration, while the value of Poisson’s ratio at high concentration of glass particles was lower than that at low concentration. The manufacture of this FG beam is particularly important and useful in order to benefit from it in the field of various fracture tests under dynamic or cyclic loads.

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