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.

Numerical Simulation of a First Normal Stress Difference-Based Model for Shear-Induced Crystallization of Polyethylene

2011 ◽  
Vol 266 ◽  
pp. 130-134
Author(s):  
Jin Yan Wang ◽  
Jing Bo Chen ◽  
Chang Yu Shen
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Normal Stress ◽  
Viscoelastic Model ◽  
Normal Stress Difference ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Avrami Model ◽  
First Normal Stress Difference ◽  
Induced Crystallization

The paper presents a numerical simulation for the isothermal flow-induced crystallization of polyethylene under a simple shear flow. The effect of flow on crystllization is considered through the simple mathematical relationship between the additional number of nuclei induced by shear treatment and the first normal stress difference. Leonov viscoelastic model and Avrami model are used to describe the normal stress difference and the crystallization kinetics, respectively. It is found that the short-term shear treatment has a large effect on the crystallization dynamics of polyethylene , but the effect of the intensity of the shear flow is not infinite ,which shows a saturation phenomenon, namely, the accelerated degree of crystallization tending to level off when the shear rate or shear time is large enough.

Numerical Simulation of Two-Dimensional Drops Suspended in Simple Shear Flow at Nonzero Reynolds Numbers

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
S. Mortazavi ◽  
Y. Afshar ◽  
H. Abbaspour
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Normal Stress ◽  
Reynolds Numbers ◽  
Normal Stress Difference ◽  
Two Dimensions ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Areal Fraction ◽  
Small Reynolds Numbers

The motion of deformable drops suspended in a linear shear flow at nonzero Reynolds numbers is studied by numerical simulations in two dimensions. It is found that a deformable drop migrates toward the center of the channel in agreement with experimental findings at small Reynolds numbers. However, at relatively high Reynolds numbers (Re=80) and small deformation, the drop migrates to an equilibrium position off the centerline. Suspension of drops at a moderate areal fraction (φ=0.44) is studied by simulations of 36 drops. The flow is studied as a function of the Reynolds number and a shear thinning behavior is observed. The results for the normal stress difference show oscillations around a mean value at small Reynolds numbers, and it increases as the Reynolds number is raised. Simulations of drops at high areal fraction (φ=0.66) show that if the Capillary number is kept constant, the effective viscosity does not change in the range of considered Reynolds numbers (0.8–80). The normal stress difference is also a weak function of the Reynolds number. It is also found that similar to flows of granular materials, suspension of drops at finite Reynolds numbers shows the same trend for the density and fluctuation energy distribution across the channel.

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.

The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region

Soft Matter ◽  
2020 ◽  
Vol 16 (43) ◽  
pp. 9864-9875
Author(s):  
Young Ki Lee ◽  
Kyu Hyun ◽  
Kyung Hyun Ahn
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Hard Sphere ◽  
Normal Stress Difference ◽  
Oscillatory Shear ◽  
Stress Difference ◽  
Large Amplitude Oscillatory Shear ◽  
First Normal Stress Difference ◽  
Oscillatory Shear Flow ◽  
Sphere Suspensions

The first normal stress difference (N1) as well as shear stress of non-Brownian hard-sphere suspensions in small to large amplitude oscillatory shear flow is investigated.

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).

Shear flow of highly concentrated emulsions of deformable drops by numerical simulations

2002 ◽  
Vol 455 ◽  
pp. 21-61 ◽  
Author(s):  
ALEXANDER Z. ZINCHENKO ◽  
ROBERT H. DAVIS
Keyword(s):  
Phase Transition ◽  
Shear Flow ◽  
Normal Stress ◽  
Normal Stress Difference ◽  
Boundary Integral ◽  
Stress Difference ◽  
Time Step ◽  
Strong Function ◽  
Good Convergence ◽  
The Matrix

An efficient algorithm for hydrodynamical interaction of many deformable drops subject to shear flow at small Reynolds numbers with triply periodic boundaries is developed. The algorithm, at each time step, is a hybrid of boundary-integral and economical multipole techniques, and scales practically linearly with the number of drops N in the range N < 1000, for NΔ ∼ 103 boundary elements per drop. A new near-singularity subtraction in the double layer overcomes the divergence of velocity iterations at high drop volume fractions c and substantial viscosity ratio γ. Extensive long-time simulations for N = 100–200 and NΔ = 1000–2000 are performed up to c = 0.55 and drop-to-medium viscosity ratios up to λ = 5, to calculate the non-dimensional emulsion viscosity μ* = Σ12/(μeγ˙), and the first N1 = (Σ11−Σ22)/(μe[mid ]γ˙[mid ]) and second N2 = (Σ22−Σ33)/(μe[mid ]γ˙[mid ]) normal stress differences, where γ˙ is the shear rate, μe is the matrix viscosity, and Σij is the average stress tensor. For c = 0.45 and 0.5, μ* is a strong function of the capillary number Ca = μe[mid ]γ˙[mid ]a/σ (where a is the non-deformed drop radius, and σ is the interfacial tension) for Ca [Lt ] 1, so that most of the shear thinning occurs for nearly non-deformed drops. For c = 0.55 and λ = 1, however, the results suggest phase transition to a partially ordered state at Ca [les ] 0.05, and μ* becomes a weaker function of c and Ca; using λ = 3 delays phase transition to smaller Ca. A positive first normal stress difference, N1, is a strong function of Ca; the second normal stress difference, N2, is always negative and is a relatively weak function of Ca. It is found at c = 0.5 that small systems (N ∼ 10) fail to predict the correct behaviour of the viscosity and can give particularly large errors for N1, while larger systems N [ges ] O(102)show very good convergence. For N ∼ 102 and NΔ ∼ 103, the present algorithm is two orders of magnitude faster than a standard boundary-integral code, which has made the calculations feasible.

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 Flow of a Dense Suspension Modeled as a Modified Second Grade Fluid

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 55 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
James Antaki ◽  
Mehrdad Massoudi
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Simple Shear Flow ◽  
Second Grade Fluid ◽  
Dense Suspension ◽  
Grade Fluid

In this paper, a simple shear flow of a dense suspension is studied. We propose a new constitutive relationship based on the second grade fluid model for the suspension, capable of exhibiting non-linear effects, where the normal stress coefficients are assumed to depend on the volume fraction of the particles and the shear viscosity depends on the shear rate and the volume fraction. After non-dimensionalizing the equations, we perform a parametric study looking at the effects of the normal stress coefficients and the variable viscosity. The numerical results show that for a certain range of parameters, the particles tend to form a region of high and uniform volume fraction, near the lower half of the flow.

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