An experimental and theoretical study on the initial period of cake filtration

Experimental measurements were made of the average specific cake resistance during the initial period of cake filtration, and the theoretical calculations about the period were also performed. The “filtration-permeation method” in the filtration cell of small area was used to measure the flow rate during the initial period of filtration, which is essentially characterized by the large flux due to fast flow rate and the rapid change of flow rate within a relatively short time interval. The measured average specific cake resistances of thin cakes which represent the cakes of initial period had very large values compared to the overall average specific cake resistance. This experimental result was contrary to the conventional theory about the initial period. Applying the “unified theory on solid-liquid separation” to the initial period, the average specific cake resistances at the initial period can have the large values--more than two times greater than that of the overall value.     

Effects of pore size, suspension concentration, and pre-sedimentation on the measurement of filter medium resistance in cake filtration

Theoretical and experimental study was conducted on the factors influencing the measurement of filter medium resistance by Ruth’s equation. It was determined that a filter medium having small pore size does not always give high filter medium resistance. The appropriate pore size of filter medium for filtration was analysed. The resistances of filter media measured with thick suspensions by Ruth’s equation have negative values. This phenomenon can be analyzed as the effect of sedimentation during the long filtration time due to thick suspension. When sedimentation occurs before the start of filtration, the filter medium resistance measured by Ruth’s equation gives a large value. It was determined that the result of the filtration of sediment was included in the filter medium resistance. A new method for measuring filter medium resistance by the filtration of the sediment is proposed. This method excludes the effects of suspension concentration and pre-sedimentation.     

The role of P<Subscript>i</Subscript>, P<Subscript>o</Subscript>, and P<Subscript>f</Subscript> in constitutive equations and new boundary conditions in cake filtration

The constitutive equations proposed by Tiller and Shirato were analyzed and a new constitutive equation originating from the sediment thickness was proposed. A new boundary condition of the filter cake based on the solid compressive pressure of the first solid layer,p _f , was also proposed. Accurate average specific cake resistances at various pressures and the thickness of cake were calculated with the new constitutive equation and boundary conditions. The influence ofp _f on the cake thickness and average porosity was studied theoretically. Using three constitutive equations, it was proved that the compressibility n obtained from filtration results instead of CPC (compression-permeability cell) of very compressible cake could not have an exact value.     

Numerical modelling of filtration with and without sedimentation runs

From experimental batch runs of filtration with sedimentation above the cake formed, a procedure is proposed and applied to experimental data for obtaining the relationships between the settling solids velocity in the hindered settling zone, the local specific resistance and the effective pressure and the solids concentration. Considering the material and momentum balances in the hindered settling zone above the cake, in the cake and in the filter membrane, a simulation program was obtained that satisfactorily reproduces the experimental runs of filtration with sedimentation runs. This simulation work confirms the hypothesis considered in the theory of filtration with sedimentation runs, e.g. the fact that the characteristic lines arise tangently from the cake surface. In addition, the method developed for obtaining the different relationships considered has been demonstrated as correct. The simulation of filtration without sedimentation runs (stirring the suspension above the cake) has also been studied.     

Local solidosity of microcrystalline cellulose during dead-end filtration and sedimentation

Solid–liquid separation by filtration and sedimentation are important operations used in a wide range of industries. One important characteristic of both the filtration and sedimentation processes is the solidosity of the filter cake/sediment that is formed, affecting the efficiency and design of the separation. In this study local solidosity was investigated using a γ-attenuation method during both filtration and sedimentation experiments for microcrystalline cellulose, a highly crystalline cellulose with particles of about 2–80 μm in diameter. Constitutive relationships for the solidosity were investigated using both filtration (i.e. cake build-up and expression) and sedimentation data for experiments at different pH and suspension concentrations. The sedimentation behaviour under these different conditions was also investigated. It was found that a three parameter empirical model could be used to describe the constitutive relationship between local solidosity and local solid compressible pressure for the sediment formed and the filter cake after both cake build-up and expression. This correlation worked well for the material investigated even at low solid compressible pressures.     

Rheology,Sedimentation, and Filtration of TiO2 Suspensions

It is shown that with aqueous suspensions of colloidal oxide and hydroxide particles simple rheometric and sedimentation experiments allow the determination of the optimum pH for filtration and washing. This approach is more practical than zeta potential measurements, as explained by a theoretical review and illustrated by experiments with industrial TiO₂ white pigments of varying surface chemistry. Besides, the solids content of the filter cake and its dependence on pH is correctly predicted from the rheology of the suspension, thus giving an idea of the mechanism of filter cake formation. This follows from a comparison to the results of filtration experiments. There, the influences of filter vacuum as well as of pH and solids content of the pigment feed suspension on filtration capacity and washing efficiency have been studied. The experiments also illustrate an inexpensive method of how to find the optimum set of parameters for an economical drum filter operation in the plant.     

A unified theory on solid-liquid separation: Filtration, expression, sedimentation, filtration by centrifugal force, and cross flow filtration

Based upon a new conception that the solid compressive pressure on a cake surface is not null, almost of all solid-liquid separation operations have been re-examined. For cake filtration, the phenomenon caused by the solid compressive pressure on a cake surface is discussed for thin cake. New expression and hindered sed-imentation theories are developed by above new conception using Darcy’s equation. Application of the new conception to centrifugal filtration and tangential filtration is also discussed. Above results lead to the conclusion that cake filtration, expression, hindered sedimentation, centrifugal filtration and tangential filtration can be described with a unified theory, and the main difference between the operations is only the boundary condition of cake.     

The Effect of Particle Sedimentation on Gravity Filtration

ABSTRACT

Simulation of cake formation of mono-sized and dual-sized particles under gravitational sedimentation and filtration is presented. The dynamic analysis proposed by Lu and Hwang in 1993 is applied to examine the local cake properties formed under a falling head by considering the hindered settling effect of particles in the slurry and the variation of the pressure drop across the filter septum. Results of this study show that, at a given position in a cake, the solid compressive pressure reaches a maximum value and then decreases for a gravity filtration due to the decrease in the driving head. A cake constructed with dual-sized particles has a more compact structure than does one with mono-sized particles, and larger particles will form looser packing than will smaller ones for mono-sized particles. A dual-dispersed suspension with a lower fraction of large particles will result in the lowest cake porosity and the highest specific filtration resistance of cake. Comparison of the porosity distribution in filter cake formed by means of gravity filtration and constant head filtration shows that the porosity near the filter septum of gravity filtration has a convex behavior while that of constant head filtration has a tendency toward concavity. This discrepancy is mainly due to the change in the driving head during the filtration process. Both theoretical and experimental results show that the uniformity of particle size distributions in the filter cake will be much better when the relative settling velocity between large and fine particles is reduced.     

ON THE SPECIFIC RESISTANCE OF CAKES OF MICROORGANISMS

The mean specific resistance of the cakes of various microorganisms was evaluated by measurement of either a change in the amount of permeate with time or of steady-state flux under constant pressure. The mean specific resistance was different with different shapes and sizes of microorganisms. The large differences arose from different packing structures of the cake. The effect of a filter aid on the filtration rate and cake structure was studied experimentally and theoretically. The effects of a filter aid were best explained by a series model, in which a cake layer composed of microbial cells and a layer of randomly distributed microbial cells and filter aid are packed on the membrane surface in series with respect to the directions of permeation.     

Experiment and calculation of filtration processes in an external-loop airlift ceramic membrane bioreactor

Air sparging is recognized as an effective way to increase permeate flux in membrane filtration processes. The application of air sparging with an external-loop airlift ceramic membrane bioreactor was studied at different gas flow rates, biomass concentrations and suction pressures. A 180% increase in permeate flux was obtained while filtering a 2 g/L activated sludge wastewater suspension with the airlift cross-flow operation for U_g=0.21 m/s. The mechanism of flux enhancement in the case of slug flow in tubular membrane was discussed. The region near the gas slug was divided into three different zones: falling film zone, wake zone and remaining liquid slug zone. Air sparging significantly lowered cake thickness and consequently cake resistances for the wake region and the falling film region. A novel model combining hydrodynamic of gas-liquid two-phase flow and cake resistance was developed to simulate the process. The model was validated with experimental data with an error of 8.3%.     

Cross‐Flow Microfiltration of Fine Particles Suspended in Polymeric Aqueous Solution

Abstract

The filtration characteristics of cross‐flow microfiltration of fine particles suspended in polymeric aqueous solution are studied. Polymethylmethacrylate (PMMA) submicron particles are suspended in polyacrylamide (PAA) aqueous solution to prepare the suspensions used in experiments. Effects of operating conditions, such as cross‐flow velocity, filtration pressure, and PAA concentration, on the filtration flux and the cake properties are discussed. The results show that an increase in cross‐flow velocity or filtration pressure causes the filtration flux to be higher, but the filtration flux decreases with an increase in PAA concentration. Since the flow behavior indices of three prepared suspensions are almost the same, the average specific filtration resistance of cakes under various cross‐flow velocities and PAA concentrations remain almost constant; and then the cake mass plays a major role in determining the filtration resistance and the filtration flux. A force balance model is derived for particle deposition on the membrane surface. Once the empirical coefficients are obtained from experimental data, the filtration flux at pseudo‐steady state can be predicted accurately.     

Particulate clusters and permeability in porous media

The permeability of particulate colloidal titanium dioxide, P25, was investigated during sedimentation, permeation and filtration when suspended in water at a consistent ionic strength similar to tap water. Happel's cell model of permeability was used to determine the apparent particle size during these processes, and compared with the size of particle clusters measured using laser diffraction under identical ionic conditions and varying degree of shear. The primary particle size of the P25 was determined to be 28 nm, from consideration of the surface area and density of the particles, and the cluster size during permeation and filtration was close to 100 nm. During sedimentation the cluster size was determined to be close to 10 μm, which is the same size obtained by laser diffraction when measuring under conditions of low shear. Using the above two sizes (28 nm and 10 μm) as limits in Happel's permeability model it was possible to determine an ‘operating envelope’ of permeability that matched the experimentally measured values for the sedimentation, permeation and filtration processes.     

Filtration characteristics of activated sludge in hybrid membrane bioreactor with porous suspended carriers (HMBR)

The suspended carriers were efficient in controlling membrane fouling in hybrid membrane bioreactor with porous suspended carriers (HMBR). The purpose of this study consisted in investigating the effect of suspended carriers on the sludge suspension, especially the filterability of sludge suspension. The filterability of sludge suspension in HMBR and general membrane bioreactor (MBR) were investigated and compared in parallel conditions by dead-end filtration for better evaluating the influence of suspended carriers on the sludge suspension. Several aspects of sludge suspension such as filtration resistance, specific cake resistance and particle size were discussed. During long-term operation the filtration resistances rose gradually in the early stage (about 100 days) and then increased rapidly, but there was a slight difference between MBR and HMBR with the prolongation of operation time. The granulometric analysis revealed that the mean particle size of sludge suspension of HMBR decreased more sharply than that of MBR, because the fluidized carriers in HMBR would impose shear stresses on sludge flocs and induce the destruction of the network of sludge zoogloea. Dead-end filtration experiments indicated that the resistance-increasing rates of three portions of sludge suspension were in the order of supernatant > dissolved organics > microbial flocs. In order to further understand the filterability of sludge suspension, the specific cake resistance (α or α.C) of sludge suspension and supernatant in HMBR and MBR were determined. During long-term operation the α and α.C increased with operation time. These results revealed that the suspended carriers in HMBR had appreciably negative effect on the biological characteristics and filterability of the sludge suspension, but they were efficient in controlling membrane fouling during continuous operation of HMBR.     

EXPERIMENTAL DETERMINATION OF THE PERMEABILITY AND RELATIVE VISCOSITY FOR FINE LATEXES AND YEAST SUSPENSIONS

The specific cake resistances of thin layers of fine latexes and of yeast cells have been determined from flux data for pressure drops of up to 100 kPa in a static filtration device. A single correlation has been developed that relates the cake resistance to particle diameter for monodisperse rigid latex spheres with diameters between 1.0 and 6.7 μm. The specific resistance of the yeast cell layers was found to be almost 50 times larger than that of the rigid latex spheres of the same median diameter

The relative viscosities of a 7.3 μm latex and yeast cell suspensions have been measured in a cone-and-plate viscometer. Empirical correlations relating the relative viscosity to the solids volume fraction were developed from linear regression of the data for each suspension. A correlation was also developed that relates the relative viscosity of the yeast cell suspension to the cell count. The effective shear-viscosities were not observed to exhibit a significant shear-rate dependence. However, an apparent viscosity increase with time was observed. This is attributed to radial migration of the particles as a result of interactions with the surface of the cone.     

The origin of high hydraulic resistance for filter cakes of deformable particles: cell-bed deformation or surface-layer effect?

This study reports a numerical approach for modeling the hydraulic resistance of a filter cake of deformable cells. First, a mechanical and osmotic model that describes the volume fraction of solids in a bed of yeast cells as a function of the compressive pressure it experiences is presented. The effects of pressure on the compressibility of yeast cells beds were further investigated both by filtration experiments and by centrifugal experiments based on the multiple speed equilibrium sediment height technique. When comparing the latter measurements with compression model calculations, we observed that the method based on centrifugal experiments suffers from rapid relaxation of the compressed bed. Concerning the filtration experiments, specific resistance of well-defined bed of cells were calculated by a combination of the compression model with a formulation for hydraulic resistivity developed using the Lattice Boltzmann method. We further explain the experimental values observed for the hydraulic resistance of cell beds, assuming that the first layer of cells in contact with the membrane partially blocks the membrane area open to flow. In such a case, the blocked area seems to be a constant fraction of the normal cell-cell contact area.     

Cake properties of nanocolloid evaluated by variable pressure filtration associated with reduction in cake surface area

A potential method has been developed for evaluating simultaneously both the average specific resistance and average porosity of the filter cake formed in unstirred dead‐end ultrafiltration of nanocolloids such as bovine serum albumin solution and silica sol. The method consists of variable pressure filtration followed by constant pressure filtration. The relation between the average specific cake resistance and the pressure drop across the cake was determined from the evolution of the filtration rate with time in the course of the variable pressure filtration period, based on the compressible cake filtration model. The average porosity was evaluated from the significant flux decline caused by a sudden reduction in the cake surface area in the middle of the constant pressure filtration period. The pressure dependences of both the average specific cake resistance and average cake porosity were obtained from only two runs which differed from each other in the pressure profiles. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3869–3877, 2014     

Measurements of Growth Rate of Filter Cake in Vertical Single-Pass Ultrafiltration Using Hollow Fiber Membrane Module

Vertical ultrafiltration experiments of silica colloid and bovine serum albumin solution were conducted in the single-pass mode by using a hollow fiber membrane module and beneficial in measuring the time evolution of the growth rate of the filter cake during filtration. The extremely small mass flux of the concentrate enabled us to highly concentrate the feed solution on the principle of vertical ultrafiltration in which the filter cake formed on the membrane surface is exfoliated continuously. Both growth and re-entrainment rates of the filter cake formed in vertical ultrafiltration were evaluated from the experimental data of the filtration rate and the mass fraction ratio of the concentrate on the basis of the mass balance within the hollow fiber membrane module. As a consequence, it was found that the re-entrainment rate of the filter cake increased almost linearly with the filtration time in the initial period of filtration and then tended to rapidly approach a constant value. The filter cake stopped growing under this dynamically balanced condition. The variations of the average specific resistance of the filter cake with time were also determined from the time evolutions of both the filtration rate and the growth rate of the filter cake.     

Modeling of Particle Fouling and Membrane Blocking in Submerged Membrane Filtration

Abstract

The models of particle fouling and membrane blocking in a submerged membrane filtration are developed in this study. The effects of operating conditions, such as aeration intensity (air flow rate) and filtration pressure, on the filtration flux, membrane blocking, and cake formation are discussed thoroughly. The experimental results show that the filtration resistances due to cake formation and membrane blocking play significant roles in determining the overall filtration resistance, but the latter one is more dominant. An increase in aeration intensity leads the filtration flux to increase due to the reduction of cake formation on the membrane surface. However, a higher filtration pressure causes more severe membrane internal blocking and then to lower filtration flux. The cake properties and the filtration resistance due to membrane blocking are analyzed and can be regressed to empirical functions of filtration pressure. A force balance model for particle deposition on the membrane surface is also derived. In order to estimate the shear stress acting on the membrane surface, the diameter, shape, and rising velocity of air bubbles are analyzed based on hydrodynamics. Once the model coefficients are obtained, the pseudo‐steady filtration flux under various conditions can be estimated by the proposed model and the basic filtration equation. The calculated results agree fairly well with the available experimental data.     

Magnetic field enhanced press-filtration

The proposed hybrid process represents a new application of a magnetic field which directly influences a classical press filtration. The new technology offers high potential in the field of magnetic pigment production and iron oxide processing as well as bio-separation with functionalized magnetic particles. Especially in the field of fine-scale particulate product systems high specific cake resistances result in slow cake building and dewatering kinetics, which leads to economic inefficiency.Experimental and theoretical investigations show that the magnetic field has strong influence on cake building. Two major effects were observed: (I) In inhomogeneous magnetic fields magnetic particles experience a magnetic force counter directed to the pressure force, that results in slow down of cake formation; (II) Interparticle magnetic forces lead to structured cake formation.This gives on one hand the possibility to uncouple fluid and magnetic particle motion to force a cake built-up in designated location of the filter chamber. The result is a big increase of the overall filtrate mass flow and therefore an improvement of filtration kinetics. On the other hand due to the particle's magnetization including the formation of an attracting north and south-pole chainlike agglomerates can be observed. This leads to a “structured” cake building and therefore higher permeability.This work will show the effect of a superposed magnetic field on press filtration of ferromagnetic iron oxide particles (Fe₃O₄) in a lab-scale filter press.     

Effect of cake layer structure on colloidal fouling in reverse osmosis membranes

A series of reverse osmosis (RO) membrane filtration experiments was performed systematically in order to investigate the effects of various hydrodynamic and physicochemical operational parameters on a cake layer formation in colloidal and particulate suspensions. Bench-scale fouling experiments with a thin-film composite RO membrane were performed at various combinations of trans-membrane pressure (TMP), cross-flow velocity (CFV), particle size, pH, and ionic strength. In this study, silica particles with two different mean diameters of 0.1 and 3.0 μm were used as model colloids. Membrane filtration experiments with colloidal suspensions under various hydrodynamic operating conditions resulted that more significant permeate flux decline was observed as TMP increased and CFV decreased, which was attributed to the higher accumulative mass of particles on the membrane surface. Results of fouling experiments under various physicochemical operating conditions demonstrated that the rate of flux decline decreased significantly with an increase of the ionic strength as well as particle size, while the flux decline rate did not vary when solution pH changed. The experimentally measured cake layer thickness increased with a decrease in particle size and solution ionic strength. Furthermore, the model estimation of cake layer thickness by using a cake filtration theory based on the hydraulic resistance of membrane and cake layer was performed under various ionic strength conditions. The primary model parameters including accumulated mass and specific cake resistance were calculated from the cake layer resistance. This result indicated that the formation of cake layer could be closely related with solution water chemistry. The model estimated cake layer thickness values were in good agreement with the experimentally measured values.