A theory of constant pressure filtration
TL;DR: In this article, two equivalent analyses that describe the one dimensional process of cake filtration are presented, which permit the prediction of density gradients in the solid material at any time, as it accumulates on the filter membrane.
About: This article is published in Chemical Engineering Science.The article was published on 1970-01-01. It has received 60 citations till now. The article focuses on the topics: Filtration & Porous medium.
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28 Oct 2002TL;DR: Porous Materials Water in Porous Materials Flow in porous materials Unsaturated Flows UnSaturated Flow in Building Physics Composite Materials Evaporation and Drying Topics in Water Transport Appendices Symbols Used Properties of Water Minerals, Salts and Solutions Other Liquids Other Data as mentioned in this paper
Abstract: Porous Materials Water in Porous Materials Flow in Porous Materials Unsaturated Flows Unsaturated Flow in Building Physics Composite Materials Evaporation and Drying Topics in Water Transport Appendices Symbols Used Properties of Water Minerals, Salts and Solutions Other Liquids Other Data
515 citations
TL;DR: In this article, a mini-review of the various theories in previous literature while considering the transport processes in filter cakes during filtration and consolidation is presented, along with the validity of some frequently adopted assumptions.
106 citations
TL;DR: In this paper, an assessment of the viability and utility of the conventional cake filtration theory was made by comparing the results based on the conventional theory with those obtained from more exact numerical analyses.
95 citations
TL;DR: In this article, the authors studied cake filterability and compressibility as a function of the particle shape and particle size distribution (PSD) and quantitatively assessed the impact of the PSD and the shape.
83 citations
Cites methods from "A theory of constant pressure filtr..."
...The first models for compressible cake (Smiles 1970) (Philip 1968) built during filtration were based on the differential equations of continuity and momentum, through a Lagrangian approach....
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TL;DR: In this article, a model of the polysaccharides prevalent in wastewaters which, on membrane filtration, may form a gel on the membrane surface which subsequently limits filtrate throughput is presented.
82 citations
References
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TL;DR: In this paper, the authors derived an equation governing the one-dimensional consolidation of a fully saturated clay layer on the basis of assumptions more general than those usually adopted, such as nonhomogeneity, time-effects intrinsic to the soil skeleton and compressibility of the pore fluid.
Abstract: Synopsis The equation governing the one-dimensional consolidation of a fully saturated clay layer are derived here on the basis of assumptions more general than those usually adopted. The limitation of small strains has not been imposed and the variation of soil compressibility and permeability during consolidation has been taken into account. Furthermore, although Darcy's law is assumed to be valid, it is recast in a form in which it is the relative velocity of the soil skeleton and the pore fluid that is related to the excess pore fluid pressure gradient. The consolidation of a thin clay layer, the self-weight stresses of which are negligible compared with those applied, is examined in detail. Non-homogeneity, time-effects intrinsic to the soil skeleton and compressibility of the pore fluid are incorporated in the theory, but a detailed consideration of their importance is deferred to later papers in which the case of the thick clay layer will also be presented. Les equation regissant la consolidation a...
688 citations
311 citations
TL;DR: In this paper, a theory is developed to describe the one-dimensional movement of electrolyte in clay-electrolyte systems that are free to swell in the direction of the electrolyte movement, based on the observation that Darcy's law describes flow of fluid relative to the comparatively immobile particles of clay.
Abstract: A theory is developed to describe the one-dimensional movement of electrolyte in clay-electrolyte systems that are free to swell in the direction of electrolyte movement. This theory develops from the observation that Darcy's law describes flow of fluid relative to the comparatively immobile particles of clay, and is based on a scale of length defined with reference to the distribution of mass of the clay rather than the more conventional fixed scale of length. It is shown, theoretically and experimentally, that in this scale of length the appropriate equation is the diffusion equation, for the use of which there exists a large body of information in soil physics and other literature.
132 citations
TL;DR: In this article, a correction factor modifying the specific filtration resistance previously defined by Ruth was developed, where the hydraulic pressure variation within a cake is known, and methods are presented for calculating the variation of flow rate with respect to distance and the change of fil-ration resistance in relation to slurry concentration.
Abstract: The definition of filtration resistance is re-examined in view of the new theory (12) of the variation of flow rate with respect to distance through a filter cake. In the new definition it is shown that the filtration resistance depends upon slurry concentration as well as applied pressure. A correction factor modifying the specific filtration resistance previously defined by Ruth (5, 6) is developed.
Where the hydraulic pressure variation within a cake is known, methods are presented for calculating the variation of flow rate with respect to distance and the change of filtration resistance in relation to slurry concentration.
122 citations
TL;DR: In this article, the internal flow mechanism in a filter cake is reexamined in view of the movement of solids during compression, and an improved definition of the average filtration resistance is developed on the basis of the new flow equation.
Abstract: The definition of filtration resistance is modified by considering relative solid-liquid velocity.
The internal flow mechanism in a filter cake is reexamined in view of the movement of solids during compression. Under conditions of short filtrations involving highly concentrated slurries, the velocity of solids is shown to be comparable to the velocity of the liquid. A differential equation is proposed for the flow through compressible cakes in which the pressure gradient is assumed proportional to the difference in average velocities of the liquid and solid rather than to the average velocity of the liquid alone.
An improved definition of the average filtration resistance is developed on the basis of the new flow equation.
101 citations