Solid/liquid separation of flocculated suspensions
TL;DR: In this paper, a generalized approach to understand and prediction of solid-liquid separation methods based on the measurement of fundamental material properties is reviewed and applied to a variety of thickening and filtration processes.
About: This article is published in Advances in Colloid and Interface Science.The article was published on 1994-08-29. It has received 169 citations till now.
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TL;DR: In this article, a review of colloidal processing of ceramics is presented with an emphasis on interparticle forces, suspension rheology, consolidation techniques, and drying behavior.
Abstract: Colloidal processing of ceramics is reviewed with an emphasis on interparticle forces, suspension rheology, consolidation techniques, and drying behavior. Particular attention is given to the scientific concepts that underpin the fabrication of particulate-derived ceramic components. The complex interplay between suspension stability and its structural evolution during colloidal processing is highlighted.
1,211 citations
TL;DR: In this article, the effects of the surface charge and molecular weight of anionic and cationic polyacrylamide (PAM) on the surface chemistry, settling rates, floc sizes and sediment bed compactness of kaolinite suspensions has been investigated at pH 7.
275 citations
TL;DR: A new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments, of strongly degenerate parabolic-hyperbolic type for arbitrary N and particle size distributions is shown.
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 $N\times N$ coupled system of quasi-linear 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 convection-diffusion problems. The numerical scheme exploits...
163 citations
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...Our concept of effective solid stress has been adopted from soil consolidation theory [81, 92] but is consistent with and in some cases mathematically equivalent to the concepts of compressive yield stress [52, 67], effective pressure [40], or yield pressure [54] utilized by research workers with a focus on solid-liquid separation....
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TL;DR: The new approach is demonstrated to be robust relative to traditional methods such as specific resistance to filtration analysis and has an in-built integrity check and the data indicate that the volatile solids parameter is a strong indicator of the dewatering behaviour of sewage sludges.
124 citations
TL;DR: In this paper, the influence of aggregation phenomena on the compressive flow properties and drying behavior of nonaqueous and aqueous silica (SiO 2 ) suspensions of varying electrolyte (NH 4 Cl) concentrations were studied.
Abstract: The influence of aggregation phenomena on the compressive flow properties and drying behavior of nonaqueous and aqueous silica (SiO 2 ) suspensions of varying electrolyte (NH 4 Cl) concentrations were studied. Compressive rheology measurements, including sedimentation and centrifugal consolidation, were first conducted to investigate consolidation behavior in the absence of solvent evaporation. The volume-fraction-dependent osmotic pressure and compressive yield stress were determined for dispersed and flocculated SiO 2 suspensions, respectively. Consolidation behavior then was studied in situ by simultaneously measuring stress evolution and solvent loss as a function of drying time. The observed drying stress histories of the films were complex, consisting of several characteristic regions. First, there was an initial period of stress rise to a maximum drying stress. These measured stress values exhibited good agreement with the osmotic pressure and compressive yield stress at equivalent SiO 2 volume fractions for the dispersed and flocculated systems, respectively. Beyond the maximum drying stress there was a subsequent region of stress decay, which coincided with the draining of liquid-filled pores. No residual drying stress was detected for films prepared from salt-free SiO 2 suspensions, whereas salt-containing films exhibited residual drying stresses likely due to salt-bridging effects. Microstructural characterization of dried films prepared from aqueous SiO 2 suspensions revealed nonuniformities in the spatial distribution of colloidal particles and precipitated salt, with the highest concentrations located at the outer edges of the films. Such features result from capillary-induced transport of these species during drying, and they have important implications on colloidal processing of ceramic thick films and bulk forms.
119 citations
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TL;DR: In this article, the authors considered a large number of identical small rigid spheres with random positions which are falling through Newtonian fluid under gravity and determined the mean value of the velocity of a sphere (U).
Abstract: The dispersion considered consists of a large number of identical small rigid spheres with random positions which are falling through Newtonian fluid under gravity. The volume fraction of the spheres (c) is small compared with unity. The dispersion is statistically homogeneous, and the axes of reference are chosen so that the mean volume flux across any stationary surface is zero. The problem is to determine the mean value of the velocity of a sphere (U). In §3 there is described a systematic and rigorous procedure which overcomes the familiar difficulty presented by the occurrence of divergent integrals, essentially by the choice of a quantity V whose mean value can be found exactly and which has the same long-range dependence on the position of a second sphere as U so that the mean of U – V can be expressed in terms of an absolutely convergent integral. The result is that, correct to order c, the mean value of U is U0(1 – 6.55 c), where U0, is the velocity of a single sphere in unbounded fluid. The only assumption made in the calculation is that the centres of spheres in the dispersion take with equal probability all positions such that no two spheres overlap; arguments are given in support of this assumption, which is expected to be valid only when the spheres are identical. Calculations which assume a simple regular arrangement of the spheres or which adopt a cell model of the hydrodynamic interactions give the quite different result that the change in the mean speed of fall is proportional to , for reasons which are made clear.The general procedure described here is expected to be applicable to other problems concerned with the effect of particle interactions on the average properties of dispersions with small volume fraction of the particles.
1,158 citations
TL;DR: In this paper, the concentration or consolidation of suspensions of fine particles under the influence of a gravitational field has been analyzed and a constitutive equation is suggested for irreversibly flocculated suspensions undergoing consolidation which embodies the concept of a concentration-dependent yield stress Py(ϕ).
Abstract: The concentration or consolidation of suspensions of fine particles under the influence of a gravitational field has been analysed. The rate and extent of consolidation depends upon a balance of three forces, the gravitational driving force, the viscous drag force associated with flow of liquid in the sediment and a particle or network stress developed as a result of direct particle–particle interactions. In the case of colloidally stable suspensions, this particle stress is the osmotic pressure of the particles; in the case of flocculated or coagulated suspensions, it is the elastic stress developed in the network of particles. A constitutive equation is suggested for irreversibly flocculated suspensions undergoing consolidation which embodies the concept of a concentration-dependent yield stress Py(ϕ). This is then used to analyse the sedimentation behaviour of flocculated sediments and to derive expressions for the initial sedimentation rate. The initial rate of change of sediment height with time in a uniform gravitational or centrifugal field is given approximately by: [graphic ommitted] where B=Δρgϕ0H0/Py(ϕ0), u0 is the sedimentation rate of an isolated particle, ϕ0 is the initial (uniform) volume fraction of solids, r(ϕ0) is a dimensionless hydrodynamic interaction parameter, Δρ is the difference in density between solid and liquid, g is the gravitational or centrifugal acceleration and H0 is the initial sediment height. The theory accounts correctly for the equilibrium consolidation behaviour of strongly flocculated suspensions, and preliminary experimental data suggest that it is not inconsistent with their dynamic behaviour. The estimation of the yield stress Py(ϕ) from a batch centrifuge experiment is also described.
403 citations
TL;DR: In this paper, the authors investigated the rheology of strongly-flocculated dispersions of colloidal particles in a continuous network and showed that these networks possess a true yield stress in both shear and uniaxial compression (as realised in a centrifuge).
Abstract: The rheology of strongly-flocculated dispersions of colloidal particles has been investigated at particle concentrations where a continuous network is formed rather than a collection of discrete flocs. Such networks are shown to possess a true yield stress in both shear and in uniaxial compression (as realised in a centrifuge). Properties measured as a function of particle concentration and particle size include the yield stresses in shear (σ y ) and compression ( P y ); the limiting and strain-dependent, instantaneous shear moduli G O and G (γ); the elastic recovery at finite strains, and the rate of centrifugally-driven compaction. The yield stresses and moduli appear to show a power-law dependence on particle concentration with G O and P y , having the same power-law index and σ y a somewhat lower one. The data are in part consistent with predictions based on the idea that the networks have a heterogeneous structure comprising a collection of interconnected fractal aggregates. The behaviour as a function of particle size and concentration is however not completely scaleable as might be expected on this basis. Thus, whereas the shear yield stress could be scaled to remove its dependence on particle radius a and volume fraction φ (over the measured range 0.25 μm ⩽ a ⩽ 3.4 μm; 0.05 ⩽ φ ⩽ 0.25) as could the strain dependent modulus (0.25 ⩽ a ⩽ 1.3 μm; 0.08 ⩽ 0.25), the particle-size and concentration dependence of P y and G O could only be scaled for particles with radii between 0.16 and 0.5 μm, smaller and larger particles having different and much higher power-law index in respect of their concentration dependencies. In the case of the smaller particles the failure of the scaling is thought to be due to an anomaly since these particles distort significantly under the influence of the strong van der Waals forces and this causes the aggregates to be more compact then they otherwise would be. The reasons for the failure at larger sizes is not clear.
213 citations
TL;DR: In this article, a quantitative theory covering the full range of processes from transient settling of large, stable particles to the slow consolidation of flocculated suspensions of submicron particles is proposed.
Abstract: The consolidation or concentration of suspended particulate solids under the influence of gravitational forces is a problem of widespread practical and theoretical interest. The literature, which is scattered over several fields, contains most of the elements necessary for a complete understanding of gravity settling, but considerable controversy and confusion persists about their synthesis. Here we propose to construct a quantitative theory covering the full range of processes from transient settling of large, stable particles to the slow consolidation of flocculated suspensions of submicron particles. Conditions for the existence of shocks are identified and the basic equations describing the phenomena are solved numerically for several Peclet numbers.
169 citations
TL;DR: In this paper, the equations governing consolidation in a continuous-flow gravity thickener are developed based on the assumption that a flocculated suspension possesses a compressive yield stress Py(ϕ) that is a function of local volume fraction only.
Abstract: The equations governing consolidation in a continuous-flow gravity thickener are developed based on the assumption that a flocculated suspension possesses a compressive yield stress Py(ϕ) that is a function of local volume fraction only. These equations are used to model the steady state operation of a thickener. The bed height required to achieve a given underflow concentration is found to be a relatively sensitive function of the details of the Py(ϕ) function, particle flux through the thickener, and variations in the cross-sectional area of the thickener. The limiting values of the underflow concentration ϕu for a given flux or the limiting values of flux for a desired ϕu are studied and shown to exist only for cylindrical and converging thickeners.
115 citations