Application of the theory of kinematic waves to the centrifugation of suspensions

Anestis, G.; Schneider, Wilhelm

doi:10.1007/bf00533201

Cited by 46 publications

(98 citation statements)

References 3 publications

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“…Most notably, the vertical iso-concentration lines indicate that the concentration of the bulk suspension is a (decreasing) function of time, and the supernatesuspension interface has a curved trajectory. These properties have previously been found by Anestis and Schneider [1], who determined exact solutions to the centrifugation model under the assumption that a e = 0, i.e. A = 0, using the method of characteristics.…”

Section: Numerical Algorithmsupporting

confidence: 58%

“…where A e is defined in terms of a standard C°° mollifier oj e with suppu; e C {-£,£) via 1 , then it is sufficient to assume that TV( XuX2 )(u' 0 ) < oo. Moreover, the regularity assumption on f(u, •) used this paper can be weakened, see [14] for details.…”

Section: F(ux H ) -A(u{x H T)) Xmentioning

confidence: 99%

“…Consequently, (16) is indeed strongly degenerate. The special case a = 0 is included in our discussion and corresponds to the equation studied by Anestis and Schneider [1].…”

Section: Batch Centrifugation Of Flocculated Suspensionsmentioning

confidence: 99%

“…A = 0, using the method of characteristics. Of course, in the centrifugal case (in contrast to the gravitational) characteristics are not iso-concentration lines, see [1,3].…”

Section: Numerical Algorithmmentioning

confidence: 99%

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A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions

Bürger

Karlsen

2001

Hyperbolic Problems: Theory, Numerics, Applications

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Section: Numerical Algorithmsupporting

confidence: 58%

Section: F(ux H ) -A(u{x H T)) Xmentioning

confidence: 99%

“…Consequently, (16) is indeed strongly degenerate. The special case a = 0 is included in our discussion and corresponds to the equation studied by Anestis and Schneider [1].…”

Section: Batch Centrifugation Of Flocculated Suspensionsmentioning

confidence: 99%

“…A = 0, using the method of characteristics. Of course, in the centrifugal case (in contrast to the gravitational) characteristics are not iso-concentration lines, see [1,3].…”

Section: Numerical Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions

Bürger

Karlsen

2001

Hyperbolic Problems: Theory, Numerics, Applications

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“…Strictly speaking, that implies vessels of constant cross section, but gravity settling in vessels with varying cross sections has been analyzed in a one-dimensional approximation [6]. Retaining one spatial coordinate, it is also possible to describe particle separation due to centrifugal forces in cylindrical centrifuges [7][8][9][10]. Remarkably, the radial dependence of both the centrifugal force and the cross section can lead to kinematic shock waves with unusual properties [6][7][8]; cf.…”

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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Modeling of solid‐bowl batch centrifugation of flocculated suspensions

2005

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Solid‐bowl batch centrifuges are used to thicken particulate and flocculated suspensions in many varied applications. The volume fraction dependent material parameters of compressive yield stress and hindered settling function are used to describe the solid‐liquid separation of a two‐phase system caused by centrifugal acceleration. The solution of the transient conservation of momentum and mass equations in radial coordinates gives the volume fraction distribution as a function of time for the two cases of the initial suspension networked or un‐networked. Analytical solutions are given for the equilibrium distribution and the small‐scale time dependence. The governing equations for the transient behaviors are solved using a 4th‐5th order Runge‐Kutta adaptive step‐size numerical method. The results show three zones of behavior: a consolidating bed, a sedimentation zone, and a clear‐liquor zone. The volume fraction within the sedimentation zone is constant for the initially networked case, and constant with radius but diminishing with time for the initially un‐networked case. © 2005 American Institute of Chemical Engineers AIChE J, 2006

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Application of the theory of kinematic waves to the centrifugation of suspensions

Cited by 46 publications

References 3 publications

A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions

A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions

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

Modeling of solid‐bowl batch centrifugation of flocculated suspensions

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