Ensemble-Average Equations of a Particulate Mixture

1997 ◽  
Vol 119 (2) ◽  
pp. 428-434 ◽  
Author(s):  
L. M. Liljegren
Keyword(s):  
Fluid Transport ◽  
Transport Equations ◽  
Ensemble Average ◽  
Spherical Particles ◽  
Particle Phase ◽  
Virtual Mass ◽  
The Third ◽  
Continuity Equations ◽  
Two Phases ◽  
Drag Term

A method of evaluating the transfer terms appearing in the ensemble-average fluid transport equation is developed and applied to obtain the transport equations describing flow of a dilute particulate mixture containing solid spherical particles. The equations apply in the limit where interactions between phases are both quasi-steady and viscous, which is defined as flows that meet the three criterion Ref(a/ℒ)2 ≪ 1, vfτ/a2 ≫ 1, and Rep ≪ 1. In this limit, the terms describing transfer of momentum between the two phases of the mixture are evaluated to O(1) in the particle radius and O(γp) in the particle phase density. The continuity equations and consistency principle are exact. When the first two conditions are not met, the transport equations require the terms that describe virtual mass forces; when the third is not met, the transport equations require terms that describe Oseen corrections to the drag term.

The Free Responsible Action of the Individual

2018 ◽  
Author(s):  
Michael P. DeJonge
Keyword(s):  
The Novel ◽  
Extreme Situation ◽  
The Third ◽  
Third Phase ◽  
Responsible Action ◽  
Action Type ◽  
Two Phases ◽  
The Individual ◽  
The Church

If, as Chapter 12 argues, much of Bonhoeffer’s resistance thinking remains stable even as he undertakes the novel conspiratorial resistance, what is new in his resistance thinking in the third phase? What receives new theological elaboration is the resistance activity of the individual, which in the first two phases was overshadowed by the resistance role played by the church. Indeed, as this chapter shows, Bonhoeffer’s conspiratorial activity is associated with what he calls free responsible action (type 6), and this is the action of the individual, not the church, in the exercise of vocation. As such, the conspiratorial activity is most closely related to the previously developed type 1 resistance, which includes individual vocational action in response to state injustice. But the conspiratorial activity differs from type 1 resistance as individual vocational action in the extreme situation.

scholarly journals Effect of hydrodynamic forces on mineral particles trajectories in gravimetric concentrator type JIG

2018 ◽  
Vol 14 (27) ◽  
pp. 68-79
Author(s):  
Manuel Alejandro Ospina ◽  
Liliana María Usuga Manco
Keyword(s):  
Pressure Gradient ◽  
Density Distribution ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
Solid Particles ◽  
Lagrangian Model ◽  
High Yield ◽  
Virtual Mass ◽  
Particle Trajectories ◽  
Continuity Equations

Hydrodynamic interaction is a sensitive process for gravity concentration equipment. Because of the nonlinearity and complexity of interaction dynamics due the solid particles and water, reliable mathematical models are needed to perform plant width design (PWD)-oriented tasks. To this end, in this paper we present a study of particle motion in a water oscillating flow subjected to a sinusoidal profile on a jig device, which is a high yield and high recovery gravimetric concentrator device widely used in minerals processing. A mathematical Eulerian-Lagrangian model (ELM) is used where fluid motion is calculated by solving the Navier-Stokes and continuity equations by a widely used numerical procedure call Semi-Implicit Method for Pressure Linked Equations algorithm (SIMPLE). The motion of individual particles is obtained by a forces balance applying the Newton’s second law of motion through the action of forces imposed by the water and gravity. Liquid-solid interactions forces are calculated by the mathematical Eulerian-Lagrangian model extended to a particle suspension having a wide size and density distribution. The calculation and comparison of Basset, pressure gradient and virtual mass forces with other forces (drag and buoyancy) acting on particle trajectories in water oscillating flows were carried out under turbulent regimen flow. It was found that Basset, pressure gradient and virtual mass forces have a significant effect on the particle’s trajectories affecting their subsequent stratification. Furthermore, the conditions under which these forces can be neglected in the jig’s hydrodynamic model were studied. The study demonstrates significant differences in the particle trajectories for various size and density distribution.

Human pituitary chronoendocrinology: repetitive stimulation with LRH/TRH at different times of the day

1983 ◽  
Vol 102 (3) ◽  
pp. 327-331 ◽  
Author(s):  
F. R. Pérez-López ◽  
A. Legido ◽  
M. D. Abós ◽  
L. Lafarga
Keyword(s):  
Healthy Subjects ◽  
Repetitive Stimulation ◽  
Hormonal Changes ◽  
Human Pituitary ◽  
Single Bolus ◽  
The Third ◽  
Hypothalamic Hormones ◽  
The Mean ◽  
Two Phases ◽  
Tsh Levels

Abstract. To determine whether human pituitary is characterized by a circadian periodicity in response to repetitive injection of hypothalamic hormones, 8 healthy subjects were challenged iv with a triple stimulation with 50 μg of LRH and 100 μg of TRH in a single bolus at 0, 90 and 180 min, receiving the first pulse of hypothalamic hormones either at 02.00 h (02.00 h test) or at 09.00 h (09.00 h test). In addition, a placebo was injected instead of LRH/TRH to evaluate the spontaneous hormonal changes during the 02.00 h test. The LH, FSH, Prl and TSH basal levels were similar in the two phases studied. The mean LH, FSH and TSH peaks after each injection of LRH/TRH were similar among them. The mean Prl peak responses to the third pulse of LRH/TRH, in both the 02.00 h and the 09.00 h tests, were lower (P < 0.05) than those after the first pulse of LRH/TRH. Placebo did not significantly change circulating LH, FSH, Prl or TSH during nocturnal sampling. The mean LH, FSH and Prl levels after LRH/TRH during the 02.00 h test were similar to those during the 09.00 h test. The mean TSH levels 15 min after the second and third pulses of LRH/TRH during the 02.00 h test were higher (P < 0.05) than those of the 09.00 h test. Thus, thyrotropes responsiveness to pulsatile stimulation with LRH/TRH is greater during the night than in the morning, while LH, FSH and Prl responses remain constant at the two phases studied.

The Roman Road-Station at Thenadassa (Ain Wif)

1982 ◽  
Vol 13 ◽  
pp. 73-80 ◽  
Author(s):  
D. J. Mattingly
Keyword(s):  
Initial Phase ◽  
Indigenous Population ◽  
Second Century ◽  
Third Century ◽  
Second Phase ◽  
The Third ◽  
Military Presence ◽  
Two Phases ◽  
The Military ◽  
New Evidence

AbstractA reappraisal of the Roman period ruins at Ain Wif has been made following the identification there of traces of defensive walls. These walls are interpreted as being the robbed-out remains of a Roman fortlet and possibly also a tort on the same site. Two phases of military occupation were also evident in modern drain trenches being cut across the site and are attested epigraphically for the military bath-house by the spring. Ceramic evidence from the site suggests that the initial phase lies within the second century, whilst the Severan occupation, known from an inscription to begin early in the third century, represents a second phase. The previous view of the site as an undefended road-station, with a military presence only under the Severan emperors is no longer tenable. Moreover, the new evidence indicates that there was some measure of military organisation in the hinterland of the Emporia prior to the accession of Septimius Severus at the very end of the second century AD. The importance of the site also lies in its large civilian and indigenous population who continued to occupy the site long after the military had departed.

scholarly journals Direct numerical simulations of dense suspensions: wave instabilities in liquid-fluidized beds

2007 ◽  
Vol 587 ◽  
pp. 303-336 ◽  
Author(s):  
J. J. DERKSEN ◽  
S. SUNDARESAN
Keyword(s):  
Numerical Simulations ◽  
Bulk Viscosity ◽  
Fluid Model ◽  
Travelling Waves ◽  
System Size ◽  
Direct Numerical Simulations ◽  
Fluid Particle ◽  
Spherical Particles ◽  
Particle Phase ◽  
Viscosity Term

We present results of direct numerical simulations of travelling waves in dense assemblies of monodisperse spherical particles fluidized by a liquid. The cases we study have been derived from the experimental work of others. In these simulations, the flow of interstitial fluid is solved by the lattice-Boltzmann method (LBM) and the particles move under the influence of gravity, hydrodynamic forces stemming from the LBM, subgrid-scale lubrication forces and hard-sphere collisions. We first show that the propagating inhomogeneous structures seen in the simulations are in agreement with those observed experimentally. We then use the detailed information contained in the simulation results to assess aspects of two-fluid model closures, namely, fluid–particle drag, and the various contributions to the effective stresses. We show that the rates of compaction and dilation of the particle phase in the travelling waves are comparable to the rate at which the microstructure relaxes, and that there is a pronounced effect of the rate of compaction on the average collisional normal stress. Although this effect can be expressed as an effective bulk viscosity term, this approach would require the use of a path-dependent bulk viscosity. We also find that the effective fluid–particle drag coefficient can be described well with the often-used closure motivated by the experiments of Richardson & Zaki (Trans. Inst. Chem. Engng vol. 32, 1954, p. 35). In this respect, the effect of the system size for determining the drag requires specific care. The shear viscosity of the particle phase manifests small, but clearly noticeable dependence on the rate of compaction/dilation of the particle phase. Our observations point to the need for higher-order closures that recognize the slow evolution of the microstructure in these flows and account for the effects of non-equilibrium microstructure on the stresses.

Heat Transfer to Pneumatically Conveyed Glass Particles of Fixed Size

1963 ◽  
Vol 85 (2) ◽  
pp. 164-171 ◽  
Author(s):  
C. A. Depew ◽  
L. Farbar
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Constant Heat Flux ◽  
Vertical Tube ◽  
Spherical Particles ◽  
Analytical Treatment ◽  
Radial Temperature ◽  
Air Stream ◽  
The Difference ◽  
Two Phases

The phenomenon of heat transfer to an air stream laden with solid spherical particles flowing up a vertical tube with constant heat flux was investigated experimentally and analytically. Two particle sizes, 30 and 200 microns in diameter, were employed. The air flow conditions were held constant at Reynolds numbers of 13,500 and 27,400 while solids were added up to gravimetric ratios of seven. The analytical treatment parallels available solutions for single-phase flow. An approximate solution was obtained under the assumption that the difference in the temperature of the two phases is small, and that the radial temperature profiles of the two phases in the fully developed region are similar. Qualitative agreement with the experimental results is obtained. Large changes in the local Nusselt number were obtained in the experiments using 30-micron particles, in contrast to small effects due to 200-micron particles.

scholarly journals Physiological and structural maturation of a polarised epithelium: the Malpighian tubules of a blood-sucking insect, Rhodnius prolixus

1990 ◽  
Vol 96 (3) ◽  
pp. 537-547
Author(s):  
H. LE B. SKAER ◽  
J. B. HARRISON ◽  
S. H. P. MADDRELL
Keyword(s):  
Fluid Transport ◽  
Physiological Function ◽  
Fluid Secretion ◽  
Malpighian Tubules ◽  
Second Phase ◽  
Structural Development ◽  
Blood Sucking ◽  
Late Embryogenesis ◽  
Intercellular Contacts ◽  
Two Phases

The development of polarity in a simple epithelium, the Malpighian tubules of Rhodnius, is analysed both ultrastructurally and physiologically. The onset of physiological function, including fluid secretion and the transport of solutes, is determined in late embryos and young hatchling insects and compared with structural development in tubules over a similar period. Two phases of maturation, separated by several days, are detected. The first, during late embryogenesis, involves the development of mature intercellular contacts and the dilation of the lumen, and is associated with the ability to transport specific solutes. The second phase involves the elaboration of the apical and basal membranes and the generation of mitochondria, and is associated with the onset of fluid transport in the tubules and with feeding in 4-day-old hatchlings.

scholarly journals Practicing one thing at a time: the secret to reward-based learning?

2019 ◽  
Author(s):  
Katinka van der Kooij ◽  
Nina M van Mastrigt ◽  
Jeroen BJ Smeets
Keyword(s):  
Critical Conditions ◽  
Matching Task ◽  
Second Phase ◽  
The Third ◽  
Conditions For Learning ◽  
Third Phase ◽  
Number Of Factors ◽  
Two Factors ◽  
Two Phases ◽  
Giving Feedback

AbstractBinary reward feedback on movement success is sufficient for learning in some simple reaching tasks, but not in some more complex ones. It is unclear what the critical conditions for learning are. Here, we ask how reward-based sensorimotor learning depends on the number of factors that are task-relevant. In a task that involves two factors, we test whether learning improves by giving feedback on each factor in a separate phase of the learning. Participants learned to perform a 3D trajectory matching task on the basis of binary reward-feedback in three phases. In the first and second phase, the reward could be based on the produced slant, the produced length or the combination of the two. In the third phase, the feedback was always based on the combination of the two factors. The results showed that reward-based learning did not depend on the number of factors that were task-relevant. Consistently, providing feedback on a single factor in the first two phases did not improve motor learning in the third phase.

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