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

Bürger, Raimund; Concha, F.; Tiller, Frank M.

doi:10.1016/s1383-5866(00)00090-3

Cited by 65 publications

(31 citation statements)

References 35 publications

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“…This paper is co-ordinated with the author's contributions with Evje et al [11] and with Concha and Tiller [12] to this issue. In [11], attention is focused on the computational treatment of the field equation of the phenomenological model, which exhibits some unusual features making the application of simplistic standard schemes impossible.…”

Section: Latin Symbols A(φ)mentioning

confidence: 99%

Phenomenological foundation and mathematical theory of sedimentation–consolidation processes

Bürger

2000

Chemical Engineering Journal

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The phenomenological theory of sedimentation describes a flocculated suspension as a mixture of the solid and the fluid as two superimposed continuous media. Starting from the mass and linear momentum balances for each component, this theory yields, through constitutive assumptions and an order-of-magnitude analysis, three coupled partial differential equations describing the sedimentation-consolidation behaviour of the suspension in several space dimensions. The study and numerical solution of this system of equations has started only recently, but results are available for the one-dimensional case, in which these modelling equations reduce to a scalar hyperbolic-parabolic strongly degenerate partial differential equation with appropriate initial and boundary conditions. In this contribution, the research work performed by several groups of mathematicians on the formulation, analysis and numerical solution of mathematical sedimentation models is reviewed, with an emphasis on theoretical and numerical results for the simulation of the behaviour of compressible slurries.

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Section: Latin Symbols A(φ)mentioning

confidence: 99%

Phenomenological foundation and mathematical theory of sedimentation–consolidation processes

Bürger

2000

Chemical Engineering Journal

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“…The present constitutive modeling practices (e.g. Tiller and Khatib, 1984;Bürger et al, 2000) can approximate the behavior of a microventing system in an average sense, but do not account for the mechanics of the process. More work needs to be done in this area.…”

Section: Resultsmentioning

confidence: 99%

The Channeling (Microventing) Phenomenon in Young Marine Sediments

Papanicolaou¹

2003

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LONG-TERM GOALSTo understand, evaluate, and quantify physical processes involved in the erosion, deposition, and transport of sediments. This involves short-term and long-term effects, and characterization of those effects based on sediment source and fluid mechanics. The outcome of this work will be a deeper understanding of the processes involved, and further development of predictive capabilities. OBJECTIVESThe objective of the present research is to explore the causes of microventing, a phenomenon generally occurring in cohesive sediments during their deposition and consolidation. Microvents are characterized by volcano-like formations, remnants of the expulsion of fluid and sediment along a vertical channel through the sediment layer. The size of these vent formations ranges from the order of millimeters to several centimeters, hence the term "microvent." Several causes proposed for microvents may be generally grouped as biological processes and mechanical processes. An example of a biological process is the production of subsurface gas due to organic decomposition; rising bubbles can produce microvents. The present study is concerned only with mechanical processes, which are hypothesized to be: A) Pressure fluctuations in pore fluid; B) Solids concentration perturbations near sediment-suspension interface; C) Gas expulsion by sediment compression. The overall scope of this investigation is to describe the microventing process in pure clay sediments and in young marine sediment deposits. Specific tasks of this project are: I) Identify whether microventing occurs in consolidation of kaolinite from a low initial concentration II) Identify the control parameter for microventing through different methods of detection III) Perform controlled tests to determine threshold of fluidization Incorporate this knowledge into a numerical code This information will ultimately be used in a quantitative model that predicts the rate of deposition and consolidation of sediment, but does not presently account for microvents (Papanicolaou and Diplas, 1999). Knowledge of microvent formation is also important in defining the erosional stability of young sediments, and such information will be useful to scientists and engineers in several disciplines, including those focusing on the prediction of fate and transport of contaminated sediments and those focusing on the refinement of existing remediation techniques in riverine and estuarine systems .

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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: 91%

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

Cited by 65 publications

References 35 publications

Phenomenological foundation and mathematical theory of sedimentation–consolidation processes

Phenomenological foundation and mathematical theory of sedimentation–consolidation processes

The Channeling (Microventing) Phenomenon in Young Marine Sediments

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

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