Applications of polydisperse sedimentation models

Berres, Stefan; Bürger, Raimund; Tory, Elmer M.

doi:10.1016/j.cej.2005.02.006

Cited by 29 publications

(19 citation statements)

References 76 publications

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“…It is basically this global stability property for which the MLB model (or equivalent models that are possibly termed differently) has become the model of choice in applications of polydisperse sedimentation [24,33,62,71,99,100]. This model gives rise to system of firstorder conservation laws.…”

Section: Discussionmentioning

confidence: 98%

“…On the other hand, in [10] it is explicitly proved that for N ¼ 2, the model based on (1.12) is hyperbolic; it is, however, unclear whether such a result holds for general N. An extensive discussion of hindered-settling functions for monodisperse and bidisperse suspensions and a verification by means of direct numerical simulation of polydisperse systems, including the formulas by Batchelor (1.10) and Davis and Gecol (1.11), is given by Cunha et al [66]. Batchelor's approach (1.10) is also discussed in [71]; as is argued in that paper, any extension of Batchelor's work to higher concentrations is strictly empirical. Moreover, since these models do not permit to obtain a hyperbolicity result that is general with respect to N and the particle sizes involved, they will not be selected for study herein.…”

Section: Limitations and Alternate Treatmentsmentioning

confidence: 96%

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On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Basson¹,

Berres

Bürger

2009

Applied Mathematical Modelling

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a b s t r a c tPolydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah-Lockett-Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson-Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.

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Section: Discussionmentioning

confidence: 98%

Section: Limitations and Alternate Treatmentsmentioning

confidence: 96%

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Basson¹,

Berres

Bürger

2009

Applied Mathematical Modelling

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“…Also, the coagulation due to differential settling can be ignored due to the relatively low settling velocities resulting by the low densities of the flocs. The settling velocity hindering is insignificant for these levels of solids volume fraction as it can be shown by employing the corresponding theories [17]. Moreover, Lyn et al [13], based on model observations, concluded that for conditions of relatively small particles concentrations in sedimentation tanks, the flocs coalescence do not affect the flow field and the effects on the concentration field and the removal efficiency may be of secondary importance.…”

Section: Flow Solvermentioning

confidence: 94%

A CFD methodology for the design of sedimentation tanks in potable water treatment

Goula

Kostoglou

Karapantsios

et al. 2008

Chemical Engineering Journal

124

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“…To be mentioned are, among others, sedimentation of particles with two or more different sizes [22][23][24][25][26][27][28][29] and the associated experiments [24,30,31]; sedimentation and centrifugation of flocculated suspensions [32][33][34][35]; accounting for consolidation processes [36,37] with associated experiments [38,39]; and accounting for the flow of suspension into the vessel and out from it (e.g., thickeners under start-up conditions) [40]. With regard to the aim of the present analysis, as described below, it may be of interest to note that wall effects, like the Boycott effect as well as deposition of particles at the sidewalls or gliding of particles along the sidewalls, are not taken into account in the one-dimensional, unified analysis of batch and continuous thickening in vessels with varying cross section given in [34].…”

Section: Introductionmentioning

confidence: 99%

On basic equations and kinematic-wave theory of separation processes in suspensions with gravity, centrifugal and Coriolis forces

Schneider

2017

Acta Mech

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Neglecting inertial and viscosity effects in the bulk flow is a common assumption in the analysis of separation processes in suspensions under the action of gravity or centrifugal and Coriolis forces. While there is a number of examples of particular solutions, the general form of the basic equations for three space dimensions, together with the appropriate boundary and initial conditions, is still uncertain and, with regard to certain aspects, even controversial. An essential point is a proper choice of the variables. Here it is proposed to introduce the mass density of the mixture, the mean mass velocity of the mixture and the total volume flux as a set of dependent variables. After some manipulations, a complete set of basic equations is obtained. It consists of two continuity equations, a generalized drift-flux relation, and two linearly independent components of a vector equation describing the total body force as irrotational. Then, by eliminating the mean mass velocity of the mixture from the set of unknowns, a generalized kinematic-wave equation is derived. It describes kinematic waves that are embedded in a bulk flow that may be one-, two-or three-dimensional. Concerning boundary conditions at solid walls, one has to ascertain whether the total body force at the wall points into the suspension or out of it. In the former case, a thin boundary layer of clear liquid is formed at the wall, whereas in the latter case a thin sediment layer may either stick at the wall or slide along it. Each of those three possibilities leads to a particular boundary condition for the bulk flow in terms of the dependent variables. In addition, initial conditions and kinematic shock relations are briefly discussed. Finally, the application of the kinematic-wave theory to the settling process in rotating tubes is outlined.

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Applications of polydisperse sedimentation models

Cited by 29 publications

References 76 publications

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

A CFD methodology for the design of sedimentation tanks in potable water treatment

On basic equations and kinematic-wave theory of separation processes in suspensions with gravity, centrifugal and Coriolis forces

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