Sedimentation and Thickening

by Bustos, Maria Cristina; Concha, Fernando; Burger, Raimund; Tory, E. M.

ISBN13: 9780792359609

ISBN10: 0792359607

Format: Hardcover

Pub. Date: 1999-11-01

Publisher(s): Kluwer Academic Pub

Other versions by this Author

eCampus.com Device Compatibility Matrix

Click the device icon to install or view instructions

Apple iOS | iPad, iPhone, iPod

Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire

Windows 10 / 8 / 7 / Vista / XP

Mac OS X | **iMac / Macbook

Enjoy offline reading with these devices

iPad, iPhone, iPod

Android 2.2 +

Kindle Fire

Windows
10 / 8 / 7 / Vista / XP

Mac

List Price: ~~$129.64~~

Rent Textbook

Select for Price

Add to Cart

There was a problem. Please try again later.

Rent Digital

Online:30 Days access
Downloadable:30 Days

$19.80

Online:60 Days access
Downloadable:60 Days

$26.40

Online:90 Days access
Downloadable:90 Days

$33.00

Online:120 Days access
Downloadable:120 Days

$39.60

Online:180 Days access
Downloadable:180 Days

$42.90

Online:1825 Days access
Downloadable:Lifetime Access

$65.99

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$42.90*

Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $33.00

Summary

This book presents a rigorous phenomenological theory of sedimentation processes as encountered in Solid-liquid separation vessels, known as thickeners, in the mineral industries. This theory leads to mathematical simulation models for batch and continuous sedimentation processes, which can be stated as initial-boundary value problems of hyperbolic conservation laws and so-called degenerate parabolic equations. Existence and uniqueness theories for these equations are presented, including very recent results, and the most important problems are solved exactly, where possible, or numerical examples are given. A study of thickener design procedures based on these simulation models is presented. The book closes with a review of alternative treatments of thickening, which may not fall within the scope of the mathematical model developed.Audience: This book is intended for students and researchers in applied mathematics and in engineering sciences (metallurgical, chemical, mechanical and civil engineering) and provides self-contained chapters directed to each audience.

Contents

vii

Preface

Introduction

(1)

Sedimentation processes in history

(3)

Modern thickening reasearch

(3)

Theory of mixtures

(20)

Introduction

(1)

Theory of mixtures

(20)

Kinematics

(9)

Mass balance

(5)

Linear momentum balance

(5)

Sedimentation of ideal suspensions

(8)

Introduction

(1)

Kinematical sedimentation process

(8)

Kynch theory of batch sedimentation

(2)

Kynch theory of continuous sedimentation

(4)

Sedimentation with compression

(17)

Introduction

(3)

Macroscopic balance

(1)

Local balances

(1)

Constitutive assumptions

(4)

Kinematical constraints

(1)

Dynamical constraints

(1)

Constitutive equations

(1)

Dimensional analysis

(2)

Dynamical variables

(4)

Solid effective stress and pore pressure

(2)

Interaction force at equilibrium

(1)

Excess pore pressure

(1)

Solid flux density function

(1)

Dynamical sedimentation processes

(1)

Extension to several space dimensions

(2)

The initial value problem for a scalar conservation law

(20)

Weak solutions for a scalar conservation law

(1)

Method of characteristics

(1)

Uniqueness of the solution

(9)

Oleinik's condition E (Oleinik 1957)

(2)

Lax's shock admissibility criterion (Lax 1957, 1971, 1973)

(1)

Entropy admissibility criterion (Lax 1971, 1973)

(1)

Viscosity admissibility criterion (Hopf 1969, Lax 1971)

(1)

Kruzkov's formulation (Kruzkov 1970)

(1)

Uniqueness of the solution

(2)

Existence of the global weak solution

(9)

Properties of the Lax-Friedrichs scheme

(6)

Convergence of the Lax-Friedrichs scheme

(3)

The Riemann problem for a scalar conservation law

(23)

Introduction

(1)

The Riemann problem for a convex flux density function

(3)

Flux density function with one inflection point

(7)

Properties of the flux density function

(3)

Construction of the global weak solution

(4)

Flux density function with two inflection points

(12)

Geometrical properties of the flux density function

(4)

Construction of the global weak solution

(8)

The initial-boundary value problem for a scalar conservation law

(16)

Formulation of the problem

(1)

Characterization of the entropy solution

(4)

Entropy conditions

100

(5)

Existence of the entropy solution

105

(2)

Uniqueness and admissible states

107

(4)

Admissible states at the boundaries

108

(1)

Geometrical interpretation of the sets of admissible states

109

(2)

Batch sedimentation of ideal suspensions

111

(38)

Initial value problem

111

(1)

Modes of sedimentation

112

(1)

Construction of the solution

113

(20)

Flux density function with one inflection point

113

(6)

Flux density function with two inflection points

119

(14)

Non-homogeneous initial concentration

133

(4)

Numerical computation of curved trajectories

137

(2)

Dafermos' polygonal approximation method

139

(10)

Polygonal flux-density function

139

(3)

Continuous flux-density function

142

(1)

Application to batch sedimentation

143

(6)

Continuous sedimentation of ideal suspensions

149

(35)

Mathematical model for continuous sedimentation

149

(1)

Modes of continuous sedimentation

150

(1)

Flux density function with one inflection point

151

(11)

Case I: Both f'(a) and f'(ϕ∞) are positive

151

(5)

Case II: f'(a) is positive and f'(ϕ∞) is negative

156

(3)

Case III: Both f'(a) and f'(ϕ∞) are negative

159

(3)

Flux density function with two inflection points

162

(14)

Case I: f'(a), f'(b) and f'(ϕ∞) are positive

163

(5)

Case II: f'(a) f'(a) is positive and f'(b) and f'(ϕ∞) are negative

168

(4)

Case III: f'(a), f'(b) and f'(ϕ∞) are negative

172

(4)

Control of continuous sedimentation

176

(8)

Model of the control problem

177

(1)

Construction of the entropy solution

178

(6)

Mathematical theory for sedimentation with compression

184

(16)

The initial-boundary value problem

184

(2)

Initial and boundary conditions

184

(1)

Type degeneracy and smoothness assumptions

185

(1)

Definition of generalized solutions

186

(2)

The space BV(QT)

186

(1)

Definition of generalized solutions

187

(1)

Jump condition

188

(3)

Entropy boundary condition

191

(1)

Existence, uniqueness and stability

191

(3)

The regularized problem

191

(2)

Existence of the solution of the regularized problem

193

(1)

Existence of a generalized solution

193

(1)

Stability and uniqueness of generalized solutions

194

(1)

Properties of generalized solutions

194

(4)

Range of generalized solutions

194

(1)

Construction of the boundary value at z = L

195

(1)

Entropy boundary condition at z = L

195

(2)

Boundary condition at z = 0

197

(1)

Monotonicity of concentration profiles

197

(1)

Discontinuous solid effective stress function

198

(2)

Numerical simulation of sedimentation with compression

200

(15)

Numerical algorithm

201

(3)

Parameters

204

(1)

Batch sedimentation

205

(3)

Batch settling of a uniform suspension

205

(1)

Repeated batch sedimentation

205

(1)

A membrane problem

206

(1)

Expansion of overcompressed sediment

207

(1)

Simultaneous expansion and batch sedimentation

207

(1)

Continuous thickening

208

(7)

Filling and emptying of a thickener

208

(1)

Transition between three steady states

209

(6)

Thickener design

215

(21)

Inroduction: definition, equipment and operation

215

(1)

Classcial methods

216

(3)

Mishler's equation

216

(1)

Coe and Clevenger's method

217

(2)

Kinematical design methods

219

(10)

Analysis of the batch sedimentation curve

220

(1)

Design methods based on a batch sedimentation process

221

(4)

Thickener design methods based on a continuous Kynch sedimentation process

225

(4)

Design method based on a dynamical sedimentation process

229

(7)

Sedimentation of a compressible suspension at steady state

229

(1)

Capacity of an ICT treating a flocculated suspension

230

(4)

Adorjan's method of thickener design

234

(2)

Alternate treatments and open problems

236

(17)

Introduction

236

(1)

Inertial and end effects

237

(1)

Heterogeneity problems

238

(4)

Spatial heterogeneity of homogeneous components

238

(2)

Heterogeneity of solid particles

240

(2)

Constitutive equations

242

(7)

Channeling and collapse

249

(2)

Roberts' equation

251

(2)

Bibliography

253

(12)

Notation Guide

265

(10)

Subject Index

275

(8)

Author Index

283

Sedimentation and Thickening

Rent Textbook

Rent Digital

New Textbook

Used Textbook

How Marketplace Works:

Summary

Table of Contents

Digital License