scholarly journals Errata to The slow motion of a sphere in a second-order fluid

1977 ◽  
Vol 16 (3) ◽  
pp. 324-325 ◽  
Author(s):  
P. Brunn
Keyword(s):  
Slow Motion ◽  
Second Order

The slow motion of a sphere in a second-order fluid

1976 ◽  
Vol 15 (3-4) ◽  
pp. 163-171 ◽  
Author(s):  
P. Brunn
Keyword(s):  
Slow Motion ◽  
Second Order

The slow motion of a rigid particle in a second-order fluid

1977 ◽  
Vol 82 (3) ◽  
pp. 529-547 ◽  
Author(s):  
P. Brunn
Keyword(s):  
Shear Flow ◽  
Hydrodynamic Force ◽  
Transversely Isotropic ◽  
Slow Motion ◽  
Second Order ◽  
Axis Ratio ◽  
Rigid Particles ◽  
Derivatives Of ◽  
Quiescent Fluid ◽  
Fluid Parameters

The purpose of the present paper is to reach some general conclusions on the motion of rigid particles in a homogeneous shear flow of a viscoelastic fluid. Under the basic assumption of nearly Newtonian slow flow, the creeping-motion equations for a second-order fluid with characteristic time constants κ0(2) and κ0(11) can be employed. It is shown that the κ0(2) contributions to the hydrodynamic force F and couple G depend upon the hydrodynamic force, couple and stresslet which act upon the particle in a Newtonian fluid (termed F(1), G(1) and S(1), respectively). Since this relation involves time derivatives of F(1) and G(1), a little reflexion is needed to realize that the modification of the classical Stokes law for steady translation in a quiescent fluid can have no κ0(2) term. Since no results of such generality are possible for the κ0(11) contributions we focus attention on transversely isotropic particles. Employing the concept of material tensors, the symmetry of such particles dictates the form these tensors adopt. This alone is sufficient to show that sedimentation in a quiescent fluid is accompanied by a change in orientation until a stable terminal orientation is attained. Depending upon the type of particle only one of the two orientations, axis of symmetry parallel or perpendicular to the external force, is stable. Another result concerns two-dimensional shear flow, for which we show that the symmetry axis has to drift through various Jeffery orbits until an equilibrium orientation is reached. While the orbits C = 0 and C = ∞ are equilibrium orbits for every transversely isotropic particle there may be a third such preferred orbit, which we denote by C*. In order for these orbits to be stable certain restrictions have to hold, showing that the orbits C = 0 and C* cannot both be stable. For the special case of a rigid tridumbbell of axis ratio s the orbit C* does not exist. If s > 1 the drift for this particle is into the orbit C = 0 while for s < 1 it is into the orbit C = ∞. This agrees qualitatively quite well with experimental results obtained for rods and disks. No quantitative comparison is possible; the particle shape influences the result quantitatively owing to its effect on the combination of the fluid parameters κ0(2) and κ0(11).

Full Scale Measurements and Theoretical Predictions of 2nd Order Pitch and Roll Slow Motions of a Semisubmersible Platform

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Vinicius L. F. Matos ◽  
Eric O. Ribeiro ◽  
Alexandre N. Simos ◽  
Sergio H. Sphaier
Keyword(s):  
Environmental Conditions ◽  
Scale Effects ◽  
Vertical Plane ◽  
Production Capacity ◽  
Slow Motion ◽  
Second Order ◽  
Full Scale ◽  
Wave Basin ◽  
Theoretical Predictions ◽  
Slow Motions

In Oct. 2007, the semisubmersible platform PETROBRAS 52 (P-52) was installed in Campos Basin (Roncador Field) offshore Brazil, in a depth around 1800 m through 16 lines in taut-leg con. The maximum production capacity is 180.000 bpd with a displacement of 80,986t at the operational draft of 27.5 m. Slow drift motions in the vertical plane (heave, roll, and pitch) were observed in a model test performed in a wave basin during the design phase. As resonant responses vary considerably with the damping loads, slow motion could be affected by scale effects. To observe the phenomena, by that time, it was a doubt if this phenomenon would happen during the platform operation. Since June 2008, PETROBRAS has been monitoring P-52 motions with the use of accelerometers and rate-gyros. Through spectral analysis of the measured signals, it was possible to verify the presence of slow motions with frequencies around the natural frequencies of roll and pitch during almost the whole monitoring period. Sometimes, the 2nd order amplitudes were even greater than the 1st order ones. Furthermore, the environmental conditions have also been monitored through wave radars, ADCPS (current) and meteorological stations (wind) in the vicinity of P-52 location, making the excitation loads identification possible. A comparative study confronting full-scale measurements and theoretical predictions was performed. First and second-order forces and responses were calculated using Wamit® second order module. This study permitted the estimation of the full scale damping values of this offshore system (hull plus mooring and riser lines) for one of the environmental conditions measured. The results indicate the importance of considering the resonant roll and pitch motions in the seakeeping analysis of large-volume semisubmersible platforms, contributing with an important feedback to future designs.

scholarly journals The slow motion of slender rod-like particles in a second-order fluid

1975 ◽  
Vol 69 (2) ◽  
pp. 305-337 ◽  
Author(s):  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Fluid Model ◽  
Slow Motion ◽  
Second Order ◽  
Reciprocal Theorem ◽  
Simple Shear Flow ◽  
Shear Rates ◽  
Stable Orientation ◽  
The Reciprocal Theorem

The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Current Issues: Advanced Digital Technology for Supervising Graduate Clinicians

2010 ◽  
Vol 20 (1) ◽  
pp. 9-13 ◽  
Author(s):  
Glenn Tellis ◽  
Lori Cimino ◽  
Jennifer Alberti
Keyword(s):  
Real Time ◽  
Digital Technology ◽  
Clinical Training ◽  
State Of The Art ◽  
Clinical Skills ◽  
Slow Motion ◽  
Video Capture ◽  
Microsoft Excel ◽  
Clinical Supervisors ◽  
Training And Supervision

Abstract The purpose of this article is to provide clinical supervisors with information pertaining to state-of-the-art clinic observation technology. We use a novel video-capture technology, the Landro Play Analyzer, to supervise clinical sessions as well as to train students to improve their clinical skills. We can observe four clinical sessions simultaneously from a central observation center. In addition, speech samples can be analyzed in real-time; saved on a CD, DVD, or flash/jump drive; viewed in slow motion; paused; and analyzed with Microsoft Excel. Procedures for applying the technology for clinical training and supervision will be discussed.

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