Phenomenological model of filtration processes: 1. Cake formation and expression

Bürger, Raimund; Concha, F.; Karlsen, Kenneth H.

doi:10.1016/s0009-2509(01)00115-4

Cited by 80 publications

(52 citation statements)

References 41 publications

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“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php lution and is conserved when we vary the model functions V (φ) and σ e (φ) to reduce sediment diffusivity. In the monodisperse case, it turned out that using the expression V (φ) = (1 − φ) n−2 for all ranges of concentration values (as, for simplicity, done here) leads to an overestimation of particle diffusivity in the sediment, and better agreement was obtained by using piecewise definition of V (φ) or of the resulting flux density function f M (φ); see [15,16]. The emphasis here is on a gradual variation of the parameters, which leaves the nature of the model unaltered.…”

Section: Sediment Diffusivitymentioning

confidence: 87%

“…The model outlined herein should thus be useful for simulations in any of the industrial applications cited in section 1. In particular, the model can also be applied to centrifugal configurations and pressure filtration (see [15,21] for the monodisperse cases) and thereby be employed to simulate the manufacturing and final composition of ceramic materials with functionally graded material properties (see [9,10,11]). Comparing our Figures 2 and 3 illustrates that the effective stress is a decisive factor when the variation of sediment composition should be continuous.…”

Section: Sediment Diffusivitymentioning

confidence: 99%

See 1 more Smart Citation

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

Tory¹,

Karlsen²,

Bürger³

et al. 2003

SIAM J. Appl. Math.

140

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Abstract. We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments ("sedimentation with compression" or "sedimentation-consolidation process"). For N solid particle species, this theory reduces in one space dimension to an N × N coupled system of quasilinear degenerate convection-diffusion equations. Analyses of the characteristic polynomials of the Jacobian of the convective flux vector and of the diffusion matrix show that this system is of strongly degenerate parabolic-hyperbolic type for arbitrary N and particle size distributions. Bounds for the eigenvalues of both matrices are derived. The mathematical model for N = 3 is illustrated by a numerical simulation obtained by the Kurganov-Tadmor central difference scheme for convectiondiffusion problems. The numerical scheme exploits the derived bounds on the eigenvalues to keep the numerical diffusion to a minimum.Key words. polydisperse suspensions, sedimentation, systems of conservation laws, strongly degenerate parabolic-hyperbolic systems, central difference approximation AMS subject classifications. 35K65, 35L40, 35L65, 65M06, 76T05 DOI. 10.1137/S00361399024081631. Introduction. Mathematical models for the (controlled) sedimentation of polydisperse suspensions of small particles, which belong to a finite number of species differing in size or density and are suspended in a viscous fluid, are important to many applications such as the chemical engineering, ceramic, pulp and paper, and food industries, mineral processing, wastewater treatment, and medicine [3,50,88,89,101,122]. The characteristic behavior of such mixtures is differential sedimentation, which leads to areas of different composition if an initially homogeneous suspension is allowed to settle. In this paper, we consider the additional property that the solid particles possibly form a compressible sediment layer. A mathematical model for polydisperse suspensions forming compressible sediments is developed, analyzed, and simulated, focusing on three different aspects.First, we show how two existing sedimentation models-one for monodisperse flocculated suspensions, which are described by scalar strongly degenerate parabolichyperbolic equations, and one for polydisperse suspensions of rigid spheres differing

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Section: Sediment Diffusivitymentioning

confidence: 87%

Section: Sediment Diffusivitymentioning

confidence: 99%

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

Tory¹,

Karlsen²,

Bürger³

et al. 2003

SIAM J. Appl. Math.

140

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“…Filtration as a mechanical method which is commonly applied for solid-liquid separation [2] while improving sludge cake filterability is one of several ways to enhance biosludge dewaterability [3]. The standard CST test was first developed by [4].…”

Section: Introductionmentioning

confidence: 99%

Modelling the Relationship between Sludge Filtration Resistance and Capillary Suction Time

Arimieari¹,

Ademiluyi²

2018

JEP

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This study modeled the relationship between Sludge Filtration Resistance (SFR) and Capillary Suction Time (CST) using the data generated from different concentrations of CaCl 2 for SFR and CST empirically using the Equation proposed by Christensen et al. (1993). The main purpose of conducting CST and SRF tests at wastewater treatment plants is to save operating costs by evaluating the optimal dose of the sludge conditioner, known as the dose of coagulant that yields the minimal capillary suction time or resistance to filtration. In order to establish a relationship between the SFR with CST, there is a relatively good correlation between CST and SFR. The results showed that the values of CST decreased with increasing CaCl 2 concentration, and a good dewaterability could be obtained at the CaCl 2 dosage of 18 g with the corresponding CST of 5.52 s for 20 mm internal cylinder and 30.84 s for 14.5 mm internal cylinder. The results of SFR tests shown decreased with an increase in CaCl 2 dosage. The optimal CaCl 2 dosage was 18 g and the corresponding SFR was 2.65 × 10 8 N•s/m 5. The results of this study for CST recommend larger diameter cylinder to be used to test heavy sludge because the larger cylinder significantly reduces the variability and the time taken to conduct the CST tests.

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“…The description of dynamic filtration and consolidation processes used for this work is based on an approach and a numerical algorithm developed by Bürger et al [1,2]. In this model the material properties are characterized by two material functions: the permeability as a function of the solids volume fraction, k(f), on the one hand, and the compressive yield stress as a function of the solids volume fraction, p s (f), on the other hand 1) .…”

Section: Introductionmentioning

confidence: 99%

“…In this model the material properties are characterized by two material functions: the permeability as a function of the solids volume fraction, k(f), on the one hand, and the compressive yield stress as a function of the solids volume fraction, p s (f), on the other hand 1) . The permeability k determines the hydrodynamic interaction between the solid and the liquid phase and, thus, the kinetics of the fluid transport within the filter cake.…”

Section: Introductionmentioning

confidence: 99%

Filtration of Colloidal Suspensions – MRI Investigation and Numerical Simulation

et al. 2006

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The principle mechanisms of solid-liquid separation processes are sedimentation and filtration, both including the formation and compression of a liquid-saturated bulk. The compressive properties of the bulk determine the operating parameters of solid-liquid separation devices and the achievable separation results. Information about the solids volume fraction of the bulk is essential for a better understanding of the physical mechanisms and precise modeling. A numerical model for the calculation of the local solids volume fraction during formation and compression of filter cakes and sediments was developed. The calculated results are compared with experimental NMR data.

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Phenomenological model of filtration processes: 1. Cake formation and expression

Cited by 80 publications

References 41 publications

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

Modelling the Relationship between Sludge Filtration Resistance and Capillary Suction Time

Filtration of Colloidal Suspensions – MRI Investigation and Numerical Simulation

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