Blocking filtration laws consist of four different filtration mechanisms: complete blocking, standard blocking, intermediate blocking, and cake filtration. Blocking filtration laws for describing both the pore blocking and cake formation have been extensively employed over the past several decades to evaluate the increase in filtration resistance with the progress of filtration in the field of classical particulate filtration. In recent years, blocking filtration laws become widely used also in membrane filtration such as microfiltration and ultrafiltration of colloids. This paper gives an overview of the developments of blocking filtration laws and equations under constant pressure and constant rate conditions reported for the filtrate flow of Newtonian and non-Newtonian fluids. The fouling index evaluating the degree of membrane fouling was examined on the basis of the blocking filtration equations. The blocking filtration laws were reexamined to extend the range of their application. Moreover, various combined models developed based on the blocking filtration laws were introduced for describing more rigorously the complicated filtration behaviors controlled by more than one mechanism which occurs successively or simultaneously.

Developments of Blocking Filtration Model in Membrane Filtration

Cake filtration analysis : the effect of the relationship between the pore liquid pressure and the cake compressive stress

Mechanism of cake formation in constant pressure filtrations

This work presents an overview of literature relative to the modelling of cake filtration and expression. Different approaches are compared to the so called conventional one in order to underline particular analogies and differences. In this way the derivation of fundamental equations (continuity equation and momentum balance) and the determination of the constitutive equations are discussed. Application of current models to complex materials such as sludge and pulp, and to simulation and design of industrial devices is also discussed.

Modelling of Cake Filtration: An Overview

To obtain a simple method for determining filtration characteristic values as functions of the applied pressure, filtration experiments are conducted by increasing the applied pressure with time stepwise. A procedure is presented for obtaining such average values as the void ratio eav and the specific filtration resistance αav on the basis of measurements of both the hydraulic pressure within the cake and the accumulated filtrate volume. In addition, an approximate method is developed in which the characteristic values of the local void ratio e and the local specific filtration resistance α are determined as functions of the local solid compressive pressure ps from calculations based upon the overall values of eav and αav of filter cakes. The relations obtained from step-up pressure filtration are fairly consistent with those from constant-pressure filtration and C-P (compression-permeability) cell data. The filtration behavior under constant-pressure and variable-pressure conditions is well evaluated by using these relations.

Determination of filtration characteristics based upon filtration tests under step-up pressure conditions.

To obtain accurate values of filtration characteristics as the ratio m of wet to dry cake mass and the average specific filtration resistance αav, constant-pressure filtration experiments were conducted using a filter having a hole at the top of the filter chamber. The relation between the cake thickness L and the filtrate volume v per unit medium area, which serves as a basis of the determination of m and αav, can be obtained on the basis of the principle of sudden reduction in the filtration area of the cake surface. The constant-pressure filtration characteristics obtained by this method were fairly consistent with the estimated values based on compression-permeability cell data. The values of m and αav are influenced by filtration pressure and by slurry concentration. However, these values remain constant during any one constant-pressure filtration experiment. On the basis of the constant-pressure filtration data obtained by this method under various pressure conditions, the local porosity e and the local specific filtration resistance α can be determined approximately.

Determination of filtration characteristics due to sudden reduction in filtration area of filter cake surface

Constant rate and variable pressure-variable rate filtration operations, which may be more frequently encountered in industrial filtrations involving centrifugal pumps, are investigated by using so-called power-law non-Newtonian fluids. Filtration pressure was manually controlled so that constant rate or variable pressure-variable rate filtration experiments were executed. Slurries of Hyflo Super-Cel in sodium polyacrylate-deionized water solutions were filtered, the slurry concentration s being 0.18. The flow behavior index N of the filtrate was about 0.3. Based upon the theories for constant pressure filtration of power-law non-Newtonian fluids presented in the previous paper, methods are presented for analyzing constant rate and variable pressure-variable rate filtration operations. The methods can be used for evaluating not only the overall filtration characteristics of the average specific resistance γav for filtration of power-law fluids and the ratio m of wetto-dry cake mass but also the detailed internal structures of the filter cake during filtration operations. It is also shown that good agreement exists between theories and experiments.

Constant rate and variable pressure-variable rate filtration of power-law non-newtonian fluids

La methode utilisee est basee sur la filtration a pression constante sur des surfaces cylindriques. Les caracteristiques de filtration et les structures internes du gâteau de filtration sont bien evaluees sur la base de mesure de compression-permeabilite de la cellule

Em Iritani

Papers

Determination of filtration characteristics due to sudden reduction in filtration area of filter cake surface

Constant rate and variable pressure-variable rate filtration of power-law non-newtonian fluids

Variable-pressure filtration of power-law non-newtonian fluids on cylindrical surfaces.