Macroscopic dynamics of flocculated colloidal suspensions

Lester, Daniel; Rudman, Murray; Scales, Peter J.

doi:10.1016/j.ces.2010.09.006

Cited by 21 publications

(11 citation statements)

References 68 publications

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“…This section covers the basic derivation of the 1-D Cartesian governing equation used in compressional rheology e readers are directed to several reviews (de Kretser et al, 2003;Landman and White, 1994;Stickland and Buscall, 2009) for more comprehensive details or for the derivation in radial coordinates, or to Lester et al (2010Lester et al ( , 2014 for examples of combining compression and shear. Balancing the hydrodynamic, hydrostatic, network pressure and acceleration forces acting in one-dimension z upon a volumetric element of the liquid and solid phases and eliminating the fluid pressure gradient gives:…”

Section: Theorymentioning

confidence: 99%

Compressional rheology: A tool for understanding compressibility effects in sludge dewatering

Stickland

2015

Water Research

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Section: Theorymentioning

confidence: 99%

Compressional rheology: A tool for understanding compressibility effects in sludge dewatering

Stickland

2015

Water Research

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“…, v f respectively are the solid and fluid phase velocities), the inter-phase force balance over the particulate network [23] simplifies to…”

Section: Governing Equationsmentioning

confidence: 99%

Correction of wall adhesion effects in batch settling of strong colloidal gels

Lester

Buscall

2015

Journal of Non-Newtonian Fluid Mechanics

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The batch settling test is widely used to estimate the compressive rheology of strongly flocculated colloidal suspensions, in particular the compressive yield strength and hydraulic permeability. Recently it has been discovered (D.R. Lester et al, J. Rheol., 58(5):12471276, 2014) that wall adhesion effects in these tests may be significantly greater than previously appreciated, which can introduce unbounded errors in the estimation of these rheological functions. Whilst a methodology to solve the underlying static problem and correct for wall adhesion effects has been developed, this method is quite complex and unwieldy, involving solution of a 2D hyper-elastic constitutive model for strong colloidal gels. In this paper we develop a highly simplified 1D visco-plastic approximation to the hyper-elastic model which admits analytic expressions for the equilibrium solids concentration profile and bed height. These expressions facilitate robust estimation of the compressive yield and wall adhesion strength via nonlinear regression of experimental data in the presence of small measurement errors.

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“…Similar problems might be found in several other application fields, and therefore this technique can be, and is currently being, extended to accommodate the study of related and more involved models. We mention that without much effort, a step forward could be made in including, for instance, more general rheological assumptions [40], and the sedimentation of polydisperse flocculated suspensions [9]. A further issue at the numerical level is the pointwise satisfaction of the divergence-free condition.…”

Section: Discussionmentioning

confidence: 99%

“…In that setting, only the equation for the concentration (1.1a) needs to be solved, while the mixture flow velocity is determined by boundary conditions. Only a limited number of papers, including [11,24,30,37,40,41,49], deal with the numerical study of sedimentation-consolidation models in two or three space dimensions.…”

Section: Related Workmentioning

confidence: 99%

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

Bürger¹,

Ruiz–Baier²,

Torres³

2012

SIAM J. Sci. Comput.

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Abstract.A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid describing the motion of the mixture. In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem reduces to two space dimensions. This poses the difficulty that the subspaces for the construction of a numerical scheme involve weighted Sobolev spaces. A novel finite volume element method is introduced for the spatial discretization, where the velocity field and the solids concentration are discretized on two different dual meshes. The method is based on a stabilized discontinuous Galerkin formulation for the concentration field, and a multiscale stabilized pair of P 1 -P 1 elements for velocity and pressure, respectively. Numerical experiments illustrate properties of the model and the satisfactory performance of the proposed method.

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Macroscopic dynamics of flocculated colloidal suspensions

Cited by 21 publications

References 68 publications

Compressional rheology: A tool for understanding compressibility effects in sludge dewatering

Compressional rheology: A tool for understanding compressibility effects in sludge dewatering

Correction of wall adhesion effects in batch settling of strong colloidal gels

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

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