The filtering of a suspension of solid particles

Kapranov, Yu. I.

doi:10.1016/s0021-8928(99)00074-x

Cited by 6 publications

(4 citation statements)

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“…Although it may be enhanced by attraction forces between the particles and the solid surfaces, clogging also occurs for noncolloidal particles with a diameter smaller than the pore size, which means that it is essentially a collective effect. Despite its practical importance, only a few studies have focused on the foundations of this phenomenon in specific conditions [5,6], while most other previous approaches were phenomenological [3,4,7]. Here from simple experiments with suspensions of noncolloidal particles in different fluids flowing under gravity through a sieve, we show that clogging is basically a matter of probability; i.e., a sufficient number of particles must be present at the same time at the right place.…”

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confidence: 79%

General Probabilistic Approach to the Filtration Process

Roussel¹,

Nguyen²,

Coussot

2007

Phys. Rev. Lett.

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We show experimentally that clogging is basically a matter of the probability of the presence of particles. We describe this process as a function of the main variables of the process, namely, the ratio of particle to mesh hole size, the solid fraction, and the number of grains arriving at each mesh hole during one test, with the help of a simple model, the predictions of which are in very good agreement with our experimental data.

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confidence: 79%

General Probabilistic Approach to the Filtration Process

Roussel¹,

Nguyen²,

Coussot

2007

Phys. Rev. Lett.

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“…He used approximate equations and assumed that the rate of entrainment of particles of the flow in the medium was proportional to the deviation of the concentration from a certain equilibrium value. At the same time, a comparison with the experiments of [4,5] shows that, in many cases, the kinetics of sedimentation is strongly affected by tile velocity of filtration. Schematization of a pore space used in [6,7] introduces new additional empirical constants, and the system of balance equations obtained for averaged quantities is approximate [5].…”

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confidence: 80%

“…At the same time, a comparison with the experiments of [4,5] shows that, in many cases, the kinetics of sedimentation is strongly affected by tile velocity of filtration. Schematization of a pore space used in [6,7] introduces new additional empirical constants, and the system of balance equations obtained for averaged quantities is approximate [5]. A correct form of this system (without a continuity equation for liquid phase) is given in [8].…”

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Changes of a porous structure in flow of a monodisperse medium

Kapranov¹

2000

J Appl Mech Tech Phys

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The motion of fluids with suspended particles in porous media is considered. A mathematical model for the interaction of a monodisperse suspension with a porous structure is proposed. Changes in the parameters of the medium and the flow are studied for equilibrium regimes.The need to study the motion of fluids containing dispersed phases in porous media arises in many practical problems. Among these problems are purification of fluids by filtration, reduction in the conductivity of the neax-weU zone of a bed due to penetration of a flushing fluid filtrate into it, evaluation of the effects of reinforcing of the emulsified phase by mechanical impurities in working wells, etc. [1][2][3].Semiempirical models are widely used for analysis of these phenomena. The filtration of lowconcentration suspensions was considered by Shekhtman [2]. He used approximate equations and assumed that the rate of entrainment of particles of the flow in the medium was proportional to the deviation of the concentration from a certain equilibrium value. At the same time, a comparison with the experiments of [4,5] shows that, in many cases, the kinetics of sedimentation is strongly affected by tile velocity of filtration. Schematization of a pore space used in [6,7] introduces new additional empirical constants, and the system of balance equations obtained for averaged quantities is approximate [5]. A correct form of this system (without a continuity equation for liquid phase) is given in [8].In the method of network modeling [1], a porous medium is replaced by a fixed set of points (pores) connected by channels with randomly distributed radii. Here the fundamental difficulties are related to the significant limitation of ttm network size, considerable number of additional parameters, and application of a number of percolation hypothesis that are substantially quasistationaxy in character.The present paper extends the approach proposed in [9] to the motion of a monodisperse suspension (the corresponding approximate model is given in [10]). This makes it possible not only to formulate an exact system of equations for integral characteristics in a comparatively simple way but also to describe changes in the structural parameters of the medium in the sedimentation process. The class of equilibrium regimes obtained in this case serves as a basis for construction of fundamental relations for integral models.1. Formulation of the Model. We consider the motion of a fluid carrying suspended particles of the same radius t~ through a porous medium. The flow is one-dimensional and is along the x axis. Let t be time, v(x, t) be the velocity of filtration, re(x, t) be the porosity, and N(x, t) and c(x, t) be the number and volume concentrations of particles in the flow. The solid and liquid phases in the suspension, and the matrix of the porous medium are considered incomPressible.A volume element of a porous medium at an arbitrary point x is assumed to consist of sieve-like layers that axe adjacent to each other and perpendicular to the flow and whose ...

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A one-velocity model of suspension flow through a high-porous medium

Leontiev

2019

J. Phys.: Conf. Ser.

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A one-velocity model for slow flows of a suspension through a high-porous medium is proposed. The model involves the momentum equation (Brinkman equation) and two continuity equations for the suspension and suspended particles. The particle migration due to spatially varying frequency of particle-matrix collisions is heuristically accounted for. As other known diffusion models, the proposed one is not universal and is valid only for simple flow patterns (e.g., shear flows). A generalization of the proposed model for deep bed filtration is also given.

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The filtering of a suspension of solid particles

Cited by 6 publications

References 4 publications

General Probabilistic Approach to the Filtration Process

General Probabilistic Approach to the Filtration Process

Changes of a porous structure in flow of a monodisperse medium

A one-velocity model of suspension flow through a high-porous medium

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