Formulation of the settling velocity of small particles initially situated inside a vortex

2008 ◽  
pp. 764-764
Author(s):  
U. Sánchez ◽  
M.J. Moreno-López
Keyword(s):  
Settling Velocity ◽  
Small Particles

scholarly journals Formulation of the Settling Velocity of Small Particles Initially Situated inside an Inclined Vortex

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Urbano Sánchez
Keyword(s):  
Settling Velocity ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Particle Separation ◽  
Small Particles ◽  
Theoretical Formulation ◽  
Heavy Particles ◽  
Elapsed Time ◽  
Escape Process ◽  
Separation Devices

Both the estimation of the time that small heavy particles remain inside a 3D vortex and the estimation of the average settling velocity of those particles are some important features in many practical situations. Previous works focused on the case of a horizontal 2D vortex. In this paper, we simulate the dynamics of heavy particles initially situated inside a three-dimensional vortex obtaining a formula for their average settling velocity. In a previous paper we obtained the trajectories of the particles and a formula that provides the time that they need to escape,Te⁎. This work simulates and analyses the escape process, and its main result is the obtaining, from numerical simulation, of a theoretical formulation of the average settling velocityVz⁎and its relationship with the elapsed time. We prove that the permanence time is of the order ofdp⁎-10(withdp⁎particle diameter) and that the average settling velocity is of the order ofTe⁎-1/5for sufficiently small particles. Some applications of the settling velocity formula developed in this work would be the design of mixture devices, the design of particle separation devices, and the prediction of the settling of pollutant particles, seeds, and pollen.

scholarly journals Study of impact of sonic energy waves on the rate of precipitation of particles in liquid

2021 ◽  
Author(s):  
Abdisamed Sheik-Qasim
Keyword(s):  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Hydroxypropyl Cellulose ◽  
Fluid Viscosity ◽  
Small Particles ◽  
Particle Settling ◽  
Sonic Energy ◽  
Different Diameters ◽  
Good Agreement

The effects of sonic energy waves on the settling velocity of small particles in water were studied. A design of experiment (DOE) with five variables (frequency, amplitude, particle diameter, particle density and fluid viscosity) at two or three levels was conducted to obtain the particle settling velocity as the response. The DOE data were analyzed both experimentally and by a statistical multiple regression software. It was concluded that when sound frequency and amplitude in the range of 0 to 500 Hz and 2 to 3 Vrms (root mean square) respectively were applied to plastic particles of three different diameters (2,381 μm, 3,175 μm, and 4,763 μm) and two different densities ... their effects on the particle settling velocity in hydroxypropyl cellulose (HPC) solutions of three different viscosities ... were insignificant. The regression analysis gave an equation that is in good agreement with the experimental data.

Stokesian motion of a spherical particle near a right corner made by tangentially moving walls

2021 ◽  
Vol 927 ◽  
Author(s):  
Francesco Romanò ◽  
Pierre-Emmanuel des Boscs ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Buoyancy Force ◽  
Settling Velocity ◽  
Slow Motion ◽  
Creeping Flow ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Small Particles ◽  
Gravitational Settling ◽  
Dynamical Regimes ◽  
The Impact

The slow motion of a small buoyant sphere near a right dihedral corner made by tangentially sliding walls is investigated. Under creeping-flow conditions the force and torque on the sphere can be decomposed into eleven elementary types of motion involving simple particle translations, particle rotations and wall movements. Force and torque balances are employed to find the velocity and rotation of the particle as functions of its location. Depending on the ratio of the wall velocities and the gravitational settling velocity of the sphere, different dynamical regimes are identified. In particular, a non-trivial line attractor/repeller for the particle motion exists at a location detached from both the walls. The existence, location and stability of the corresponding two-dimensional fixed point are studied depending on the wall velocities and the buoyancy force. The impact of the line attractors/repellers on the motion of small particles in cavities and its relevance for corner cleaning applications are discussed.

Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling

2006 ◽  
Vol 18 (2) ◽  
pp. 027102 ◽  
Author(s):  
Thorsten Bosse ◽  
Leonhard Kleiser ◽  
Eckart Meiburg
Keyword(s):  
Settling Velocity ◽  
Homogeneous Turbulence ◽  
Small Particles ◽  
Velocity Enhancement

scholarly journals Study of impact of sonic energy waves on the rate of precipitation of particles in liquid

2021 ◽  
Author(s):  
Abdisamed Sheik-Qasim
Keyword(s):  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Hydroxypropyl Cellulose ◽  
Fluid Viscosity ◽  
Small Particles ◽  
Particle Settling ◽  
Sonic Energy ◽  
Different Diameters ◽  
Good Agreement

The effects of sonic energy waves on the settling velocity of small particles in water were studied. A design of experiment (DOE) with five variables (frequency, amplitude, particle diameter, particle density and fluid viscosity) at two or three levels was conducted to obtain the particle settling velocity as the response. The DOE data were analyzed both experimentally and by a statistical multiple regression software. It was concluded that when sound frequency and amplitude in the range of 0 to 500 Hz and 2 to 3 Vrms (root mean square) respectively were applied to plastic particles of three different diameters (2,381 μm, 3,175 μm, and 4,763 μm) and two different densities ... their effects on the particle settling velocity in hydroxypropyl cellulose (HPC) solutions of three different viscosities ... were insignificant. The regression analysis gave an equation that is in good agreement with the experimental data.

Analytical expression for predicting the reduced settling velocity of small particles in turbulence

2020 ◽  
Vol 20 (4) ◽  
pp. 905-922 ◽  
Author(s):  
Xiao Chen ◽  
Zhaowei Liu ◽  
Yongcan Chen ◽  
Haoran Wang
Keyword(s):  
Settling Velocity ◽  
Small Particles ◽  
Analytical Expression

Suspended particles in wastewater: their optical, sedimentation and acoustical characterization and modeling

2011 ◽  
Vol 63 (2) ◽  
pp. 240-247 ◽  
Author(s):  
A. Pallarès ◽  
P. François ◽  
M.-N. Pons ◽  
P. Schmitt
Keyword(s):  
Real Time ◽  
Suspended Solids ◽  
Settling Velocity ◽  
Suspended Particles ◽  
Small Particles ◽  
Time Data ◽  
Good Comparison ◽  
Real Wastewater ◽  
The Individual ◽  
Good Agreement

Wastewater regulation and treatment is still a major concern in planetary pollution management. Some pollutants, referred to as particulate matter, consist of very small particles just suspended in the water. Various techniques are used for the suspended particles survey. Few of them are able to provide real-time data. The development of new, real time instruments needs the confrontation with real wastewater. Due its instability, the modeling of wastewater in terms of suspended solids was explored. Knowing the description of real wastewater, we tried to produce a synthetic mixture made of basic organic ingredients. A good agreement in terms of turbidity and settling velocity was observed between the artificial wastewater matrix and the real one. The investigation of the individual contribution of the different compounds to the acoustical signal showed a more complex dependance. Thus the modeling of wastewater with reference to turbidity and settling velocity is not sufficient to describe it acoustically. Further studies should lead to a good comparison of the acoustical and turbidity behavior of wastewater.

scholarly journals Settling of Particles beneath Water Waves

2008 ◽  
Vol 38 (12) ◽  
pp. 2846-2853 ◽  
Author(s):  
Ian Eames
Keyword(s):  
Water Waves ◽  
Settling Velocity ◽  
Added Mass ◽  
Stokes Drift ◽  
Inertial Forces ◽  
Leading Order ◽  
Small Particles ◽  
Fall Velocity ◽  
Finite Distance ◽  
The Mean

Abstract Considered here is the motion of small particles beneath irrotational water waves. The added mass and inertial forces are shown to be an important role in the mean transport of particles. To leading order, particles are transported with a mean horizontal Stokes drift velocity and sediment with their terminal fall velocity. The combination of a settling velocity and a mean drift transports particles a finite distance forward from their point of release.

Stereo Electron Microscopy Applied to High Resolution Freeze-Etch Replicas

1970 ◽  
Vol 28 ◽  
pp. 306-307
Author(s):  
L. Andrew Staehelin
Keyword(s):  
Electron Microscopy ◽  
Plastic Deformation ◽  
High Resolution ◽  
Smooth Surfaces ◽  
Small Particles ◽  
Membrane Surfaces ◽  
Wide Acceptance ◽  
New Information ◽  
Number Of Particles ◽  
Small Holes

Freeze-etched membranes usually appear as relatively smooth surfaces covered with numerous small particles and a few small holes (Fig. 1). In 1966 Branton (1“) suggested that these surfaces represent split inner mem¬brane faces and not true external membrane surfaces. His theory has now gained wide acceptance partly due to new information obtained from double replicas of freeze-cleaved specimens (2,3) and from freeze-etch experi¬ments with surface labeled membranes (4). While theses studies have fur¬ther substantiated the basic idea of membrane splitting and have shown clearly which membrane faces are complementary to each other, they have left the question open, why the replicated membrane faces usually exhibit con¬siderably fewer holes than particles. According to Branton's theory the number of holes should on the average equal the number of particles. The absence of these holes can be explained in either of two ways: a) it is possible that no holes are formed during the cleaving process e.g. due to plastic deformation (5); b) holes may arise during the cleaving process but remain undetected because of inadequate replication and microscope techniques.

Dynamic Scanning Electron Microscopy of Small Particles

1975 ◽  
Vol 33 ◽  
pp. 280-281
Author(s):  
W. Krakow ◽  
W. C. Nixon
Keyword(s):  
Electron Microscopy ◽  
Low Noise ◽  
Time Sequence ◽  
Field Of View ◽  
Video Tape ◽  
Small Particles ◽  
Polystyrene Spheres ◽  
Field Distributions ◽  
Dynamic Scanning ◽  
Scanning Electron

The scanning electron microscope (SEM) can be run at television scanning rates and used with a video tape recorder to observe dynamic specimen changes. With a conventional tungsten source, a low noise TV image is obtained with a field of view sufficient to cover the area of the specimen to be recorded. Contrast and resolution considerations have been elucidated and many changing specimens have been studied at TV rates.To extend the work on measuring the magnitude of charge and field distributions of small particles in the SEM, we have investigated their motion and electrostatic interaction at TV rates. Fig. 1 shows a time sequence of polystyrene spheres on a conducting grating surface inclined to the microscope axis. In (la) there are four particles present in the field of view, while in (lb) a fifth particle has moved into view.

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