Sedimentation and Thickening

Bustos, María Cristina; Concha, F.; Bürger, Raimund; Tory, Elmer M.

doi:10.1007/978-94-015-9327-4

Cited by 106 publications

(52 citation statements)

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“…Under certain additional constitutive assumptions, the following set of equations can be derived from the solid and liquid component mass and linear momentum balances (see [4,13]):…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…In the context of batch sedimentation, the type-change interface, where φ = φ c is valid, separates the hindered settling zone from the compression zone. Its location is in general unknown a priori, which requires special treatments for the mathematical analysis and for the numerical solution, see the contribution by Bürger et al to this issue, [13] and chapter 9 of [18] for details. Eq.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…The field equation (Eq. (9)) together with these initial and boundary conditions was solved by the finite difference operator splitting method outlined in [18], see [13] …”

Section: The Mathematical Modelmentioning

confidence: 99%

“…The corresponding constitutive functions K(φ) and σ e (φ) had been determined in a similar way as by Tiller and Kwon [21] using ␥-ray absorption measurements. Using the approaches (13) and (14), Damasceno et al [35] this expression was cut at φ = φ max = 0.3. The particular mathematical model proposed in [8] does not include the hindered settling zone, nor is original experimental information available from which the initial settling rate could be inferred.…”

Section: Application To Continuous Sedimentationmentioning

confidence: 99%

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Applications of the phenomenological theory to several published experimental cases of sedimentation processes

Bürger

Concha

Tiller

2000

Chemical Engineering Journal

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In one space dimension, the phenomenological theory of sedimentation predicts the sedimentation-consolidation behavior of a flocculated suspension in dependence of two constitutive functions describing its material behavior, the solids flux density (or hindered settling function) and the solid effective stress. These functions are assumed to depend only on the local volumetric solids concentration. In this contribution, we review several experimental and theoretical studies of sedimentation in settling columns. We first resume the theories that have been employed to interpret the experimental measurements and then apply the phenomenological model to the available data. The two constitutive functions involved are determined from the published concentration, permeability and effective stress data. The mathematical model is then solved numerically using these functions, and the resulting predictions of settling behavior are compared with the respective authors' experimental findings and interpretations. In one case, the information obtained from a batch settling experiment is used to simulate continuous sedimentation.

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“…Under certain additional constitutive assumptions, the following set of equations can be derived from the solid and liquid component mass and linear momentum balances (see [4,13]):…”

Section: The Mathematical Modelmentioning

confidence: 99%

Section: The Mathematical Modelmentioning

confidence: 99%

“…The field equation (Eq. (9)) together with these initial and boundary conditions was solved by the finite difference operator splitting method outlined in [18], see [13] …”

Section: The Mathematical Modelmentioning

confidence: 99%

Section: Application To Continuous Sedimentationmentioning

confidence: 99%

See 2 more Smart Citations

Applications of the phenomenological theory to several published experimental cases of sedimentation processes

Bürger

Concha

Tiller

2000

Chemical Engineering Journal

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“…Many models have been developed for settling of flocculent particles in suspension. In a series of papers [4][5][6][7][8][9], presented a phenomenological theory of sedimentation of flocculated suspensions, which provides a valuable framework for the simulation of batch and continuous thickening of suspensions. Also, in a numerical method introduced by [10], a software was developed for the simulation of batch and continuous thickening of suspensions.…”

Section: Conditioner Dewaterability Sewage Sludgementioning

confidence: 99%

Effect of Conditioner on Dewaterability of Sewage Sludge

Obianyo¹,

Agunwamba²

2014

Nig. J. Tech.

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ABSTRACT ABSTRACTA model for dewaterability of conditioned sludge was derived A model for dewaterability of conditioned sludge was derived A model for dewaterability of conditioned sludge was derived A model for dewaterability of conditioned sludge was derived experiments experiments experiments experiments using six sand drying beds using six sand drying beds using six sand drying beds using six sand drying beds conditioner and served as control experiment. Ferric Chloride was added to the remaining five beds in the conditioner and served as control experiment. Ferric Chloride was added to the remaining five beds in the conditioner and served as control experiment. Ferric Chloride was added to the remaining five beds in the conditioner and served as control experiment. Ferric Chloride was added to the remaining five beds in the neighborhood of 1%, 2%, 3%, 4%, and 5% respectively, corresponding to 30g, 60g, 9 neighborhood of 1%, 2%, 3%, 4%, and 5% respectively, corresponding to 30g, 60g, 9 neighborhood of 1%, 2%, 3%, 4%, and 5% respectively, corresponding to 30g, 60g, 9 neighborhood of 1%, 2%, 3%, 4%, and 5% respectively, corresponding to 30g, 60g, 9 Seepage (sg) was derived as a linear function of time Seepage (sg) was derived as a linear function of time Seepage (sg) was derived as a linear function of time Seepage (sg) was derived as a linear function of time regression regression regression regression of seepage against time corresponding to 30g, 60g, 90g, 120g and 150g are 0. 860, 0.844, 0.781, 0.722 of seepage against time corresponding to 30g, 60g, 90g, 120g and 150g are 0.860, 0.844, 0.781, 0.722 of seepage against time corresponding to 30g, 60g, 90g, 120g and 150g are 0.860, 0.844, 0.781, 0.722 of seepage against time corresponding to 30g, 60g, 90g, 120g and 150g are 0.860, 0.844, 0.781, 0.722 and 0 and 0 and 0 and 0.535 .535 .535.535 respectively. respectively. respectively. respectively. Moisture content of sludge was 86.69% when no coagulant was added, it was 69.47%, Moisture content of sludge was 86.69% when no coagulant was added, it was 69.47%, Moisture content of sludge was 86.69% when no coagulant was added, it was 69.47%, Moisture content of sludge was 86.69% when no coagulant was added, it was 69.47%, 57.32%, 54.01%, 52.79% and 47.81% when 30g, 60g, 90g, 120g and 150g doses were used with a range of 38.88%. 57.32%, 54.01%, 52.79% and 47.81% when 30g, 60g, 90g, 120g and 150g doses were used with a range of 38.88%. 57.32%, 54.01%, 52.79% and 47.81% when 30g, 60g, 90g, 120g and 150g doses were used with a range of 38.88%. 57.32%, 54.01%, 52.79% and 47.81% when 30g, 60g, 90g, 120g and 150g doses were used with a range of 38.88%. Dewaterability enhancement ratio was 1:1 for co Dewaterability enhancement ratio was 1:1 for co Dewaterability enhancement ratio was 1:1 for co Dewaterability enhancement ratio was 1:1 for co for 30g, 60g, 90g, 120g, and 150g doses respectively for 30g, 60g, 90g, 120g, and 150g doses respectively for 30g, 60g, 90g, 120g, and 150g doses respectively for ...

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Model Equations and Instability Regions for the Sedimentation of Polydisperse Suspensions of Spheres

Bürger

Karlsen

Tory

et al. 2002

Z. angew. Math. Mech.

112

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The one‐dimensional kinematical sedimentation theory for suspensions of small spheres of equal size and density is generalized to polydisperse suspensions and several space dimensions. The resulting mathematical model, obtained by introducing constitutive assumptions and performing a dimensional analysis, is a system of first‐order conservation laws for the concentrations of the solids species coupled to a variant of the Stokes system for incompressible flow describing the mixture. Various flux density vectors for the first‐order system have been proposed in the literature. Some of them cause the first‐order system of conservation laws to be non‐hyperbolic, or to be of mixed hyperbolic‐elliptic type in the bidisperse case. The criterion for ellipticity is equivalent to a well‐known instability criterion predicting phenomena like blobs and viscous fingering in bidisperse sedimentation. We show that loss of hyperbolicity, that is the occurrence of complex eigenvalues of the Jacobian of the first‐order system, can be viewed as an instability criterion for arbitrary polydisperse suspensions, and that for tridisperse mixtures this criterion can be evaluated by a convenient calculation of a discriminant. We determine instability regions (or alternatively prove stability) for three different choices of the flux vector of the first‐order system of conservation laws. Consequently, mixed or non‐hyperbolic, rather than hyperbolic, systems of conservation laws are the appropriate general mathematical framework for polydisperse sedimentation. The stability analysis examines a first‐order system of conservation laws, but its predictions are applicable to the full multidimensional system of model equations. The findings are consistent with experimental evidence and are appropriately embedded into the current state of knowledge of non‐hyperbolic systems of conservation laws.

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Sedimentation and Thickening

Cited by 106 publications

References 0 publications

Applications of the phenomenological theory to several published experimental cases of sedimentation processes

Applications of the phenomenological theory to several published experimental cases of sedimentation processes

Effect of Conditioner on Dewaterability of Sewage Sludge

Model Equations and Instability Regions for the Sedimentation of Polydisperse Suspensions of Spheres

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