Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

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On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

Aeronautical Quarterly ◽

10.1017/s0001925900009859 ◽

1955 ◽

Vol 6 (1) ◽

pp. 31-45

Author(s):

H. K. Zienkiewicz

Keyword(s):

Method Of Characteristics ◽

Order Theory ◽

Stagnation Pressure ◽

Slender Body Theory ◽

Pressure Losses ◽

The Method Of Characteristics ◽

Curvature Approximation ◽

Body Theory ◽

Theory And Experiment ◽

Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

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Slender-body theory for steady sheared plumes in very viscous fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112008002887 ◽

2008 ◽

Vol 612 ◽

pp. 21-44 ◽

Cited By ~ 3

Author(s):

ROBERT J. WHITTAKER ◽

JOHN R. LISTER

Keyword(s):

Simple Model ◽

Shear Flow ◽

Viscous Fluid ◽

Experimental Studies ◽

Slender Body ◽

Slender Body Theory ◽

Dimensionless Parameters ◽

Dynamical Regimes ◽

Body Theory ◽

Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

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The deformation of a nearly straight thread in a shearing flow with weak Brownian motions

Journal of Fluid Mechanics ◽

10.1017/s0022112076000529 ◽

1976 ◽

Vol 75 (4) ◽

pp. 765-775 ◽

Cited By ~ 11

Author(s):

E. J. Hinch

Keyword(s):

Degrees Of Freedom ◽

Hydrodynamic Resistance ◽

Simple Shear Flow ◽

Transverse Displacement ◽

Slender Body Theory ◽

Brownian Motions ◽

Shearing Flow ◽

Projected Length ◽

Body Theory ◽

Resistance Coefficients

As a model of an almost fully extended macromolecule, a small, flexible, inextensible, nearly straight thread in a shearing flow with weak Brownian motions is considered. The hydrodynamic resistance to motion is included using the slenderbody theory for Stokes flow. The variation of the small transverse displacements along the thread is expressed as a truncated sum of Fourier components, with appropriately chosen modal functions. A diffusion equation is derived in the Fourier space and solved. The expected deformation of the thread is then given for axisymmetric and two-dimensional straining flows. The transverse displacement of the ends and the small shortening of the projected length of the thread are both found to be sensitive to the truncation of the Fourier representation, although it becomes clear on physical grounds that the ratio of the shortening to the typical transverse distortion should increase with the number of degrees of freedom. In simple shear flow the deformation increases as the thread aligns with the flow, until the analysis breaks down when the entire thread is no longer in the extensional quadrants. The influence of the 2:1 ratio of the resistance coefficients from the slender-body theory is found to be a small numerical factor.

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A hydrodynamical analysis of fish turning manoeuvres

Proceedings of the Royal Society of London Series B Biological Sciences ◽

10.1098/rspb.1972.0066 ◽

1972 ◽

Vol 182 (1066) ◽

pp. 59-72 ◽

Cited By ~ 76

Keyword(s):

Present Theory ◽

Inviscid Fluid ◽

Centre Of Mass ◽

Turning Process ◽

Slender Body Theory ◽

Turning Mechanism ◽

Three Stages ◽

Straight Lines ◽

Body Theory ◽

Good Agreement

Slender body theory, adapted here to the study of unsteady, curvilinear large amplitude movements in an inviscid fluid, is applied to the study of the turning mechanism in fishes. The vortex wake is represented by the circulation shed from the fins in the present theory. Examination of filmed sequences of turning fish show that the turning process includes three stages, distinguished by different movements of the centre of mass. In the first and third stages the centre of mass moves in straight lines in the initial and final directions of swimming while in the middle period it moves along an approximately circular connecting arc. The forces and moments acting on the fish, calculated by the present method are found to be in good agreement with these experimental observations.

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Software development for subsonic aircraft’s unsteady longitudinal stability derivatives calculation

Theoretical and Applied Mechanics ◽

10.2298/tam0504319m ◽

2005 ◽

Vol 32 (4) ◽

pp. 319-340 ◽

Cited By ~ 1

Author(s):

Nikola Maricic

Keyword(s):

Method Of Images ◽

Lattice Method ◽

Aerodynamic Stability ◽

Slender Body Theory ◽

Stability Derivatives ◽

Doublet Lattice Method ◽

Body Theory ◽

General Configuration ◽

Finite Element Methodology ◽

Good Agreement

Subsonic general configuration aircrafts? unsteady longitudinal aerodynamic stability derivatives can be estimated using finite element methodology based on the Doublet Lattice Method (DLM), the Slender Body Theory (SBT) and the Method of Images (MI). Applying this methodology, software DERIV is developed. The obtained results from DERIV are compared to NASTRAN examples HA21A and HA75H. A good agreement is achieved.

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The distortion of a flexible inextensible thread in a shearing flow

Journal of Fluid Mechanics ◽

10.1017/s002211207600181x ◽

1976 ◽

Vol 74 (2) ◽

pp. 317-333 ◽

Cited By ~ 47

Author(s):

E. J. Hinch

Keyword(s):

Shear Flow ◽

Simple Shear ◽

Stokes Flow ◽

Equations Of Motion ◽

Simple Shear Flow ◽

Qualitative Behaviour ◽

Slender Body Theory ◽

Shearing Flow ◽

Numerical Studies ◽

Body Theory

Using the slender-body theory for Stokes flow, the equations of motion are developed for a small flexible inextensible thread. The nearly straight thread is examined analytically, and is shown to straighten rapidly. In a simple shear flow the distortions decay less rapidly, but rapidly enough not to rotate the thread through the plane of flow. Numerical studies of simple shear with more substantially distorted threads show the same qualitative behaviour. Additionally some differences are revealed in the nonlinear regime between the buckling and stretching processes which occur in the compressive and tensile quadrants of the flow.

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The effect of shear-thinning behaviour on rod orientation in filled fluids

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.323 ◽

2016 ◽

Vol 798 ◽

pp. 350-370 ◽

Cited By ~ 14

Author(s):

Julien Férec ◽

Erwan Bertevas ◽

Boo Cheong Khoo ◽

Gilles Ausias ◽

Nhan Phan-Thien

Keyword(s):

Cell Model ◽

Rheological Behaviour ◽

Shear Thinning ◽

Shear Rates ◽

High Shear Rates ◽

Model Predictions ◽

The Matrix ◽

The One ◽

Good Agreement ◽

Low Shear

In the present article, the cell model (or self-consistent scheme) is used to derive constitutive equations for rod suspensions in non-Newtonian viscous matrices such as power-law, Ellis and Carreau fluids. It is found that the shear-thinning character of the matrix influences considerably the rod contribution to the stress tensor, but has no impact on the rod orientation dynamics: the same microstructure evolution as the one encountered in Newtonian fluids is obtained. The rod suspension behaves differently than the unfilled matrix in the sense that, depending on rod orientation, the onset of shear thinning in the composite occurs at lower or higher shear rates. Our analysis also provides a semi-analytical model for rod suspensions in an Ellis fluid, which appears to be suitable for predicting a Newtonian plateau at low shear rates and a shear-thinning behaviour at high shear rates. In addition, the model predictions are in good agreement with the shear viscosity measurements of glass-fibre-filled polystyrene melts (Chan et al., J. Rheol., vol. 22 (5), 1978, pp. 507–524), demonstrating its ability to describe the rheological behaviour of such polymer composites. Finally, the proposed approach is extended to a Carreau fluid although its solution requires the numerical solution of a set of partial differential equations.

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Asialo von Willebrand Factor Enhances Platelet Adhesion to Vessel Subendothelium

Thrombosis and Haemostasis ◽

10.1055/s-0038-1647629 ◽

1988 ◽

Vol 60 (01) ◽

pp. 030-034 ◽

Cited By ~ 9

Author(s):

Eva Bastida ◽

Juan Monteagudo ◽

Antonio Ordinas ◽

Luigi De Marco ◽

Ricardo Castillo

Keyword(s):

Von Willebrand Factor ◽

Platelet Adhesion ◽

Human Albumin ◽

Membrane Receptors ◽

Shear Rates ◽

High Shear Rates ◽

Platelet Deposition ◽

Platelet Spreading ◽

Von Willebrand ◽

Willebrand Factor

SummaryNative von Willebrand factor (N-vWF) binds to platelets activated by thrombin, ADP or ristocetin. Asialo vWF (As-vWF) induces platelet aggregation in absence of platelet activators. N-vWF mediates platelet adhesion to vessel subendothelium at high shear rates. We have investigated the role of As-vWF in supporting platelet deposition to rabbit vessel subendothelium at a shear rate of 2,000 sec-1, using the Baumgartner perfusion system. We have studied the effects of the addition of As-vWF (from 2 to 12 μg/ml) to perfusates consisting of washed red blood cells, 4% human albumin and washed platelets. Our results show a significant increase in platelet deposition on subendothelium (p <0.01) in perfusions to which As-vWF had been added. Blockage of the platelet glycoproteins Ib and IIb/IIIa (GPIb and GPIIb/IIIa) by specific monoclonal antibodies (LJIb1 and LJCP8, respectively) resulted in a decrease of platelet deposition in both types of perfusates prepared with N-vWF and As-vWF. Our results indicate that As-vWF enhances platelet deposition to vessel subendothelium under flow conditions. Furthermore, they suggest that this effect is mediated by the binding of As-vWF to platelet membrane receptors, which in turn, promote platelet spreading and adhesion to the subendothelium.

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