Roll cells and disclinations in sheared nematic polymers

2001 ◽  
Vol 449 ◽  
pp. 179-200 ◽  
Author(s):  
J. J. FENG ◽  
J. TAO ◽  
L. G. LEAL
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Flow Direction ◽  
Flow Regimes ◽  
Flow Conditions ◽  
Break Up ◽  
Nematic Polymers ◽  
Defect Nucleation

We use the Leslie–Ericksen theory to simulate the shear flow of tumbling nematic polymers. The objectives are to explore the onset and evolution of the roll-cell instability and to uncover the flow scenario leading to the nucleation of disclinations. With increasing shear rate, four flow regimes are observed: stable simple shear, steady roll cells, oscillating roll cells and irregular patterns with disclinations. In the last regime, roll cells break up into an irregular and uctuating pattern of eddies. The director is swept into the flow direction in formations called ‘ridges’, which under favourable flow conditions split to form pairs of ± 1 disclinations with non-singular cores. The four regimes are generally consistent with experimental observations, but the mechanism for defect nucleation remains to be verified by more detailed measurements.

Effects of shear rate on rouleau formation in simple shear flow

Biorheology ◽  
1988 ◽  
Vol 25 (1-2) ◽  
pp. 113-122 ◽  
Author(s):  
T. Murata ◽  
T.W. Secomb
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Rouleau Formation

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

1998 ◽  
Vol 361 ◽  
pp. 117-143 ◽  
Author(s):  
S. RAMANUJAN ◽  
C. POZRIKIDIS
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Large Deformations ◽  
Viscosity Ratio ◽  
Curvilinear Coordinates ◽  
Triangular Element ◽  
Elastic Membrane ◽  
Simple Shear Flow ◽  
Liquid Drops

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Reynolds numbers using a boundary-element method. The surface of the capsule is discretized into quadratic triangular elements that form an evolving unstructured grid. The elastic membrane tensions are expressed in terms of the surface deformation gradient, which is evaluated from the position of the grid points. Compared to an earlier formulation that uses global curvilinear coordinates, the triangular-element formulation suppresses numerical instabilities due to uneven discretization and thus enables the study of large deformations and the investigation of the effect of fluid viscosities. Computations are performed for capsules with spherical, spheroidal, and discoidal unstressed shapes over an extended range of the dimensionless shear rate and for a broad range of the ratio of the internal to surrounding fluid viscosities. Results for small deformations of spherical capsules are in quantitative agreement with the predictions of perturbation theories. Results for large deformations of spherical capsules and deformations of non-spherical capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially spherical capsules deform into steady elongated shapes whose aspect ratios increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed for any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymmetric capsules subject to a stagnation-point flow. When the shear rate is sufficiently high and the viscosity ratio is sufficiently low, liquid drops exhibit continuous elongation leading to breakup. Axisymmetric capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of capsules in shear flow, large elastic tensions develop at large deformations and prevent continued elongation, stressing the importance of the vorticity of the incident flow. The long-time behaviour of deformed capsules depends strongly on the unstressed shape. Oblate capsules exhibit unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sphericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinning behaviour.

Evidence of magmatic flow by 2-D image analysis of 3-D shape preferred orientation distributions

2004 ◽  
Vol 175 (4) ◽  
pp. 331-350 ◽  
Author(s):  
Patrick Launeau
Keyword(s):  
Image Analysis ◽  
Shear Flow ◽  
Simple Shear ◽  
Flow Direction ◽  
Preferred Orientation ◽  
Simple Shear Flow ◽  
Shear Direction ◽  
Thin Sections ◽  
Passive Deformation ◽  
Shape Ratio

Abstract The 3-D Shape Preferred Orientation (SPO) ellipsoid can be obtained by image analysis on a minimum of three perpendicular sections, when the 2-D measurements can be assimilated to ellipses. As numerous phenomenons can modify the SPO in magma (boundary condition effects, crystal interactions, joint migrations, etc.), the ellipsoid calculation is first tested on a set of digital models of simple shear flow. Those models, made of scattered shape ratio distribution, show that a suspension of crystals in a simple shear flow of the magma produces SPO parallel to the shear direction with an intensity given by the average shape ratio of the crystals, without any link with the amount of shear flow. This steady state SPO along the flow direction is particularly useful to study magma emplacement even if it is also shown that a critical shear rate γ between 4 and 8, for crystal shape ratio between 2 and 5 respectively, is sufficient to completely reorient a SPO. Therefore the SPO does not record magmatic strain as may do an enclave, which is an interface between two magmas with low viscosity contrast, that can record the whole strain of the magma by its passive deformation along the flow. An infinite strain is necessary here to parallelize the enclave on the shear flow direction. The application to a natural case (gabbronorite of the Bushveld, South Africa) shows that we must take care of the mineral chosen to describe a flow in a magma and that a careful classical study of the structures observed in thin sections is always required. To allow anyone to test the quality of the 2-D/3-D conversions, a web site is associated to this publication with a free access to all the image analysis and ellipsoid programs presented below.

Observations of fibre orientation in simple shear flow of semi-dilute suspensions

1992 ◽  
Vol 238 ◽  
pp. 277-296 ◽  
Author(s):  
Carl A. Stover ◽  
Donald L. Koch ◽  
Claude Cohen
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Fibre Orientation ◽  
Flow Direction ◽  
Orientation Distribution ◽  
Index Of Refraction ◽  
Simple Shear Flow ◽  
Flow Gradient ◽  
Dilute Suspensions ◽  
Rotary Diffusion

The orientations of fibres in a semi-dilute, index-of-refraction-matched suspension in a Newtonian fluid were observed in a cylindrical Couette device. Even at the highest concentration (nL3 = 45), the particles rotated around the vorticity axis, spending most of their time nearly aligned in the flow direction as they would do in a Jeffery orbit. The measured orbit-constant distributions were quite different from the dilute orbit-constant distributions measured by Anczurowski & Mason (1967b) and were described well by an anisotropic, weak rotary diffusion. The measured ϕ-distributions were found to be similar to Jeffery's solution. Here, ϕ is the meridian angle in the flow-gradient plane. The shear viscosities measured by Bibbo (1987) compared well with the values predicted by Shaqfeh & Fredrickson's theory (1990) using moments of the orientation distribution measured here.

Flow of Granular Materials Modeled as a Generalized Reiner-Rivlin Type Fluid

2012 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
Mehrdad Massoudi
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Constitutive Model ◽  
Granular Materials ◽  
Simple Shear ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Lower Plate ◽  
Simple Shear Flow ◽  
Rate Dependent

In this paper we use a non-linear constitutive model for flowing granular materials developed by Massoudi [1] which not only considers the effect of volume fraction but also has a viscosity which is shear rate dependent. This model is a generalization of Reiner’s model [2] derived for wet sand. Specifically we study the simple shear flow of granular materials between two horizontal plates, with the lower plate fixed and the upper plate moving at a constant speed. Numerical solutions are presented for various dimensionless parameters.

Negative Viscosity Due to Magnetic Properties of a Semi-Dense Colloidal Dispersion Composed of Ferromagnetic Rod-Like Particles With Magnetic Moment Normal to the Particle Axis

2007 ◽  
Author(s):  
Yasuhiro Sakuda ◽  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Simple Shear ◽  
Magnetic Moment ◽  
Flow Direction ◽  
Colloidal Dispersion ◽  
Magnetic Interactions ◽  
Simple Shear Flow ◽  
Magnetic Field Direction ◽  
Negative Viscosity

We have investigated the negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rodlike particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.

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