scholarly journals Parabolic velocity profile causes shape-selective drift of inertial ellipsoids

2021 ◽  
Vol 926 ◽  
Author(s):  
J. Bagge ◽  
T. Rosén ◽  
F. Lundell ◽  
A.-K. Tornberg
Keyword(s):  
Velocity Profile ◽  
Rotational Inertia ◽  
Fluid Inertia ◽  
Magnus Force ◽  
Heavy Particles ◽  
Viscous Forces ◽  
Oblate Spheroids ◽  
Parabolic Velocity Profile ◽  
Order Of Magnitude ◽  
Shape Selective

Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the Magnus force, Saffman force and Segré–Silberberg effect all arise only due to inertia of the fluid, with similar effects on all non-spherical particle shapes. In this work, we present a new shape-selective lateral drift mechanism, arising from particle inertia rather than fluid inertia, for ellipsoidal particles in a parabolic velocity profile. We show that the new drift is caused by an intermittent tumbling rotational motion in the local shear flow together with translational inertia of the particle, while rotational inertia is negligible. We find that the drift is maximal when particle inertial forces are of approximately the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. Furthermore, since tumbling motion is not a stable rotational state for inertial oblate spheroids (nor for spheres), this new drift only applies to prolate spheroids or tri-axial ellipsoids. Finally, the drift is compared with the effect of gravity acting in the directions parallel and normal to the flow. The new drift mechanism is stronger than gravitational effects as long as gravity is less than a critical value. The critical gravity is highest (i.e. the new drift mechanism dominates over gravitationally induced drift mechanisms) when gravity acts parallel to the flow and the particles are small.

scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

Über die Abhängigkeit der relativen biologischen Wirksamkeit hochenergetischer Bremsstrahlen von der durchstrahlten Materieschicht / Dependence of the Relative Biological Efficiency of High Energy Bremssstrahlen on the Depth in a Phantom

1969 ◽  
Vol 24 (12) ◽  
pp. 1633-1640 ◽  
Author(s):  
F. Stähler ◽  
F. Zywietz ◽  
W. Ewert ◽  
H. A. Künkel
Keyword(s):  
Energy Transfer ◽  
Vicia Faba ◽  
Linear Energy Transfer ◽  
Experimental Error ◽  
Nuclear Reactions ◽  
High Energy ◽  
Biological Efficiency ◽  
Heavy Particles ◽  
Order Of Magnitude

The Relative Biological Efficiency (RBE) of 6-GeV-bremsstrahlung on 3-days-old seedlings of Vicia faba was investigated with the Deutsches ElektronenSynchrotron. Dosimetry was carried out by means of the butanol-sensitized FeII/FeIII-reaction. In a Lucite-phantom we observed an increase of the RBE from 0,65 at the surface to values of about 2 at a depth of 40 cm. As changes of that order of magnitude are doubtless beyond the limits of the maximum experimental error we suppose that production of heavy particles by nuclear reactions such as (γ, n) or (γ, p) in deeper layers of matter might cause an increase of the linear energy transfer of the beam.

scholarly journals Circulation and formation number of laminar vortex rings

1998 ◽  
Vol 376 ◽  
pp. 297-318 ◽  
Author(s):  
MOSHE ROSENFELD ◽  
EDMOND RAMBOD ◽  
MORTEZA GHARIB
Keyword(s):  
Velocity Profile ◽  
Time Scale ◽  
Vortex Generator ◽  
Formation Time ◽  
Vortex Rings ◽  
Axisymmetric Vortex ◽  
Parabolic Velocity Profile ◽  
Formation Number ◽  
Experimental Findings ◽  
Good Agreement

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.

Jet Formation in Micro Post Arrays

2014 ◽  
Vol 553 ◽  
pp. 367-372
Author(s):  
Ryan S. Pawell ◽  
Robert A. Taylor ◽  
David W. Inglis ◽  
Tracie J. Barber
Keyword(s):  
Velocity Profile ◽  
Metastatic Cancer ◽  
Streamwise Velocity ◽  
Transitional Region ◽  
Jet Formation ◽  
Jet Length ◽  
Viscous Forces ◽  
Cancer Management ◽  
And Performance ◽  
Reynolds Number Flows

Micropost arrays serve as a plaform for the next generation of diagnostic devices. These arrays are found in microfluidic devices for peripheral blood-based diagnostics and metastatic cancer management. The function and performance of these devices is determined by the underlying micro-scale fluid mechanics. Typically, these devices operate in the creeping regime (Re << 1) where the viscous forces of the fluids dominate. Recent advances in manufacturing allow for higher Reynolds number flows (Re >> 1) where the inertial forces dominate. In this work, we use computational simulations to show there is a transitional region (1 < Re < 20) in between the laminar and creeping regimes for two different micropost array geometries. Numerical analysis is employed to investigate jet formation both within the array and at the array exit. The peak-to-peak amplitude of the streamwise normalized velocity profile is used to quantify jet formation within the array; the streamwise velocity profile at the end of the array exit is used to determine jet length at the exit of the array. Above the transitional region (Re > 20) significant jets form downstream of the posts, amplitude scales exponentially and jet length scales with Re according to power law.

A simple expression for fluid inertia force acting on micro-plates undergoing squeeze film damping

2010 ◽  
Vol 467 (2126) ◽  
pp. 522-536 ◽  
Author(s):  
Shujuan Huang ◽  
Diana-Andra Borca-Tasciuc ◽  
John A. Tichy
Keyword(s):  
Separation Distance ◽  
Simple Expression ◽  
Squeeze Film ◽  
Inertia Force ◽  
Viscous Damping ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Viscous Forces ◽  
Squeeze Film Damping ◽  
Micro Plates

Squeeze film damping in systems employing micro-plates parallel to a substrate and undergoing small normal vibrations is theoretically investigated. In high-density fluids, inertia forces may play a significant role affecting the dynamic response of such systems. Previous models of squeeze film damping taking inertia into account do not clearly isolate this effect from viscous damping. Therefore, currently, there is no simple way to distinguish between these two hydrodynamic effects. This paper presents a simple solution for the hydrodynamic force acting on a plate vibrating in an incompressible fluid, with distinctive terms describing inertia and viscous damping. Similar to the damping constant describing viscous losses, an inertia constant, given by ρL 3 W / h (where ρ is fluid density, L and W are plate length and width, respectively, and h is separation distance), may be used to accurately calculate fluid inertia for small oscillation Reynolds numbers. In contrast with viscous forces that suppress the amplitude of the oscillation, it is found that fluid inertia acts as an added mass, shifting the natural frequency of the system to a lower range while having little effect on the amplitude. Dimensionless parameters describing the relative importance of viscous and inertia effects also emerge from the analysis.

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