Boundary conditions for column flotation - a study by transfer function representation of an axial diffusion model

Chiharu Tokoro, Y. Okano

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

Original languageEnglish
Pages (from-to)49-64
Number of pages16
JournalMinerals Engineering
Volume14
Issue number1
DOIs
Publication statusPublished - 2001 Jan
Externally publishedYes

Fingerprint

Flotation
transfer function
Pulp
Transfer functions
boundary condition
Boundary conditions
Tailings
tailings
flotation
pulp
bubble
Boundary layers
boundary layer
Mathematical models
particle

ASJC Scopus subject areas

  • Earth and Planetary Sciences(all)
  • Geochemistry and Petrology
  • Geotechnical Engineering and Engineering Geology

Cite this

Boundary conditions for column flotation - a study by transfer function representation of an axial diffusion model. / Tokoro, Chiharu; Okano, Y.

In: Minerals Engineering, Vol. 14, No. 1, 01.2001, p. 49-64.

Research output: Contribution to journalArticle

@article{b948e3ba403848e89c35951ea0da3f2f,
title = "Boundary conditions for column flotation - a study by transfer function representation of an axial diffusion model",
abstract = "The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.",
author = "Chiharu Tokoro and Y. Okano",
year = "2001",
month = "1",
doi = "10.1016/S0892-6875(00)00159-X",
language = "English",
volume = "14",
pages = "49--64",
journal = "Minerals Engineering",
issn = "0892-6875",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - Boundary conditions for column flotation - a study by transfer function representation of an axial diffusion model

AU - Tokoro, Chiharu

AU - Okano, Y.

PY - 2001/1

Y1 - 2001/1

N2 - The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

AB - The boundary conditions for an axial diffusion model were overviewed and then modified concerning the pulp layer boundaries in a flotation column. It has been confirmed through the transfer function representation that the four general boundary conditions for an axial diffusion model correspond to the particular cases of Wehner and Wilhelm's, which considers not only the reaction section itself but also those of its top and bottom sides. Various mathematical models have been proposed for the pulp layer in a flotation column and the most popular one may be an axial diffusion with first order reaction model of one stage. They are, however, unable to estimate the behaviors of free particles which have not attached to bubbles at the pulp-froth interface. In this study, therefore, the authors, represented the transportation of free particles in the pulp layer of a flotation column by the two-stage axial diffusion with first order reaction model. The Wehner and Wilhelm's, as well as Danckwerts' boundary conditions have been partly modified and then applied to the feed point, the pulp-froth interface and the tailing discharge point of the flotation column. The proposed models and their boundary conditions made it possible to estimate the behaviors of free particles at the pulp-froth interface.

UR - http://www.scopus.com/inward/record.url?scp=0035149482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035149482&partnerID=8YFLogxK

U2 - 10.1016/S0892-6875(00)00159-X

DO - 10.1016/S0892-6875(00)00159-X

M3 - Article

VL - 14

SP - 49

EP - 64

JO - Minerals Engineering

JF - Minerals Engineering

SN - 0892-6875

IS - 1

ER -