Flotation kinetics equations and transfer functions for flotation machines taking account of the effect of the froth layer

1984 ◽  
Vol 20 (4) ◽  
pp. 337-341
Author(s):  
A. G. D'yakov
Keyword(s):  
Transfer Functions ◽  
Flotation Kinetics ◽  
Froth Layer ◽  
Flotation Machines

A novel multistage kinetic modeling of flotation for wastewater treatment

2013 ◽  
Vol 68 (4) ◽  
pp. 807-812 ◽  
Author(s):  
B. S. Ksenofontov ◽  
M. V. Ivanov
Keyword(s):  
Wastewater Treatment ◽  
Air Bubbles ◽  
Flotation Kinetics ◽  
Flotation Process ◽  
Multistage Model ◽  
New Model ◽  
Accurate Design ◽  
Flotation Treatment ◽  
Froth Layer ◽  
Kinetics Of

This study develops a new model for description of flotation kinetics. It defines flotation as a process that consists of several stages: separated air bubbles and particles, air bubbles and particles forming an aggregate, aggregate rising to the froth layer. This description significantly differs from known models, which are much simplified. The multistage model gives a novel in-depth description and considers different aspects of flotation, i.e. aggregate formation, which is critically important for flotation to take place. Experimental approval of the new model resulted in its accuracy. The model is to be used for a description of kinetics of all flotation processes in wastewater treatment. It helps in accurate design of flotation treatment plants and may be used for further research of the flotation process.

VERIFICATION OF FLOTATION KINETICS MODEL FOR TRIANGULAR DISTRIBUTION OF DENSITY FUNCTION OF FLOTABILITY OF COAL PARTICLES / WERYFIKACJA MODELU KINETYKI FLOTACJI DLA TRÓJKĄTNEGO ROZKŁADU FUNKCJI GĘSTOŚCI FLOTOWALNOŚCI ZIAREN WĘGLA

2013 ◽  
Vol 58 (4) ◽  
pp. 1279-1287 ◽  
Author(s):  
Krystian Kalinowski ◽  
Roman Kaula
Keyword(s):  
Density Function ◽  
Kinetics Model ◽  
Distribution Model ◽  
Triangular Distribution ◽  
Flotation Kinetics ◽  
Coal Flotation ◽  
Coefficient Distribution ◽  
Coal Particles ◽  
Supervisory Control System ◽  
Flotation Machines

Abstract Parameters of flotation kinetics model with a gamma and a triangular distribution have been determined based on the batch coal flotation experiments. Analyses were carried out at different values of the intensity of aeration air. The results of example analyses are presented in tables and graphs form. It follows from the carried out study on the mathematical models of flotability coefficient distribution of particles of examined coal samples that the triangular distribution model is statistical equivalent to the gamma flotability distribution. The assumption of the triangular distribution enables determination of the density function of distribution of fraction in the industrial flotation machines. Knowledge of this function will allow better evaluation of the phenomena occurring in the process of enrichment. It may be one of the basic information used in the supervisory control system.

A simple way for producing holographic filters suitable for image improvement

1978 ◽  
Vol 36 (1) ◽  
pp. 226-227
Author(s):  
K.-H. Herrmann ◽  
E. Reuber ◽  
P. Schiske
Keyword(s):  
Transfer Functions ◽  
Diffraction Order ◽  
Lateral Position ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Resolution Electron ◽  
Wiener Filters ◽  
Image Improvement ◽  
Optical Reconstruction ◽  
Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Electron Holography Improving Transmission Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 208-209
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
Transfer Functions ◽  
Imaging System ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Wave Aberration

Generally, the electron object wave o(r) is modulated both in amplitude and phase. In the image plane of an ideal imaging system we would expect to find an image wave b(r) that is modulated in exactly the same way, i. e. b(r) =o(r). If, however, there are aberrations, the image wave instead reads as b(r) =o(r) * FT(WTF) i. e. the convolution of the object wave with the Fourier transform of the wave transfer function WTF . Taking into account chromatic aberration, illumination divergence and the wave aberration of the objective lens, one finds WTF(R) = Echrom(R)Ediv(R).exp(iX(R)) . The envelope functions Echrom(R) and Ediv(R) damp the image wave, whereas the effect of the wave aberration X(R) is to disorder amplitude and phase according to real and imaginary part of exp(iX(R)) , as is schematically sketched in fig. 1.Since in ordinary electron microscopy only the amplitude of the image wave can be recorded by the intensity of the image, the wave aberration has to be chosen such that the object component of interest (phase or amplitude) is directed into the image amplitude. Using an aberration free objective lens, for X=0 one sees the object amplitude, for X= π/2 (“Zernike phase contrast”) the object phase. For a real objective lens, however, the wave aberration is given by X(R) = 2π (.25 Csλ3R4 + 0.5ΔzλR2), Cs meaning the coefficient of spherical aberration and Δz defocusing. Consequently, the transfer functions sin X(R) and cos(X(R)) strongly depend on R such that amplitude and phase of the image wave represent only fragments of the object which, fortunately, supplement each other. However, recording only the amplitude gives rise to the fundamental problems, restricting resolution and interpretability of ordinary electron images:

The Effect of Nonlinear Amplitude Growth on the Speech Perception Benefits Provided by a Single-Sided Vocoder

2019 ◽  
Vol 62 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Jessica M. Wess ◽  
Joshua G. W. Bernstein
Keyword(s):  
Transfer Functions ◽  
Spatial Configuration ◽  
Free Field ◽  
Spatial Separation ◽  
Compression And Expansion ◽  
Interaural Difference ◽  
Interaural Differences ◽  
Single Sided Deafness ◽  
Perceptual Separation ◽  
Loudness Growth

PurposeFor listeners with single-sided deafness, a cochlear implant (CI) can improve speech understanding by giving the listener access to the ear with the better target-to-masker ratio (TMR; head shadow) or by providing interaural difference cues to facilitate the perceptual separation of concurrent talkers (squelch). CI simulations presented to listeners with normal hearing examined how these benefits could be affected by interaural differences in loudness growth in a speech-on-speech masking task.MethodExperiment 1 examined a target–masker spatial configuration where the vocoded ear had a poorer TMR than the nonvocoded ear. Experiment 2 examined the reverse configuration. Generic head-related transfer functions simulated free-field listening. Compression or expansion was applied independently to each vocoder channel (power-law exponents: 0.25, 0.5, 1, 1.5, or 2).ResultsCompression reduced the benefit provided by the vocoder ear in both experiments. There was some evidence that expansion increased squelch in Experiment 1 but reduced the benefit in Experiment 2 where the vocoder ear provided a combination of head-shadow and squelch benefits.ConclusionsThe effects of compression and expansion are interpreted in terms of envelope distortion and changes in the vocoded-ear TMR (for head shadow) or changes in perceived target–masker spatial separation (for squelch). The compression parameter is a candidate for clinical optimization to improve single-sided deafness CI outcomes.

NETWORK TRANSFER FUNCTIONS. AN APPLICATION TO EXTENDED SURFACES

Equipment ◽  
2006 ◽  
Author(s):  
M. Alarcon ◽  
F. Alhama ◽  
C. F. Gonzalez-Fernandez
Keyword(s):  
Transfer Functions ◽  
Extended Surfaces
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