A theoretical and experimental study on cake filtration with sedimentation

Sedimentation occurs in almost all cake filtration. To study the role of sedimentation during filtration, filtration-permeations were carried out for suspensions of various concentrations. The average specific cake resistances calculated by the traditional method using the filtration data and initial concentration of suspension give different values according to the suspension concentrations. But the average specific cake resistances from the permeation period show almost the same values in spite of the various suspension concentrations. To exclude the influence of sedimentation, a complete sedimentation was performed before beginning filtration and then filtration-permeation of the sediment was performed. The average specific cake resistance from the filtration period calculated with the mass fraction of sediment and that from the permeation period coincide very well. These values also coincide well with the former average specific resistances during permeation within the experimental error limits. It can be concluded that the average specific cake resistances by permeation operation give almost the same values for various concentrations of suspension. A new definition of a cake and a new concept of the filter medium Rm are proposed based on the analysis of experimental results.     

Cake formation and growth in cake filtration

In this study we develop an experimental method to help understand the formation and growth of dust cakes. An on-line pressure-displacement measurement system is developed to measure the thickness of the dust cakes. A higher filtration superficial velocity resulted in a higher degree of compaction in the dust cakes and thus a higher specific cake resistance, hence a better collection efficiency could be achieved. The empirical equations for cake solidosity and specific cake resistance as a function of the filtration superficial velocity are derived. We find that the cake filter is influenced by the cake thickness and the filtration superficial velocity. The results of this study can be applied to granular bed filters for the removal of dust particulates in advanced coal-fired power systems.     

Porosity distribution in highly compressible cake: Experimental and theoretical verification of the dense skin

The rate of filtration and the water content of cake are influenced by the existence of a dense skin in a highly compressible cake. The phenomenon of the dense skin has been rarely studied, and its existence has not been verified experimentally. In this study, the porosity variation in a very compressible cake is measured by using a new experimental apparatus, and with this the existence of dense skin has been established experimentally. ‘Unified theory on solid-liquid separation’, a recently developed theory, is utilized for calculating the porosity variation in a very compressible cake.     

The preparation and filtration characteristics of Dextran-MnO2 gel particles

Different kinds of Dextran-MnO₂ gel particles are prepared in different conditions, depending on variables such as the molecular weight of dextran and formation temperature. Some physical properties and filtration characteristics of these gel particles are measured and discussed. Although the mean sizes of these gel particles are very close to each other, their filtration characteristics are far different due to their mechanical strength and compressibility. A typical filtration curve of gel particles can be divided into three regions, and a retardation cake compression during the filtration can be observed from the curve. The particle formation temperature has a trivial effect on their mechanical strength. An increase in formation temperature leads to only a slight decrease in particle size. On the other hand, gel particles are formed by using dextrans with three different molecular weights - 70,000 (sample A), 500,000 (sample B) and 2,000,000 Da (sample C) - and are used in filtration experiments. The results show that the molecular weight of dextran plays a major role in determining particle mechanical strength; the sequence of particle hardness is sample B > sample A > sample C. The dynamic analysis method proposed by Hwang and Hseuh [K.J. Hwang, C.L. Hseuh, J. Membr. Sci. 214 (2003) 259] is employed to estimate the local cake properties in a filter cake, e.g., solid compressive pressure, porosity and specific filtration resistance. Because sample C has the highest compressibility, it constructs a cake with the lowest porosity and the highest specific filtration resistance; and consequently, the lowest filtration rate. Although the mechanical strength of sample B is higher than that of sample A, its wider particle size distribution results in lower cake porosity and higher filtration resistance, as well as a lower filtration rate. It could be said that the filtration rate decreases with an increase in the molecular weight of dextran.     

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.     

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.     

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.     

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.     

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.     

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.     

Approach from physicochemical aspects in membrane filtration

In membrane filtration, solution environment factors such as pH and solvent density are important in controlling the filtration rate and the rejection of the particles and/or the macromolecules. The filtration rate and the rejection in membrane filtration have been investigated from physicochemical aspects. It was shown that the properties of the filter cake formed on the membrane surface play a vital role in determining the filtration rate in mem-brane filtration. It was clearly demonstrated that such filtration behaviors as the filtration rate and the rejection are highly dependent on the electrical nature of the particles and/or the macromolecules. Furthermore, it was shown that the solvent density ρ has a large effect on the steady filtration rate in upward ultrafiltration.     

Static filtration of purified sodium bentonite clay suspensions. Effect of clay content

The effect of clay content on the static filtration properties of purified Na-montmorillonite suspensions was studied at two different pressures. The results of filtering parameters are as expected. When the clay percentage increases, the thickness (e) of the obtained cake increases, leading to the decrease of water loss (WL), and consequently, to the decrease of permeability (k). These decreases of WL and k are more important for the low applied pressure than for the high one.The differences between values of the different experimental parameters (WL and e) obtained at applied pressures of 5.7×10⁵ and 1.5×10⁵ Pa, as a function of clay content in the initial samples, show some singular points. At the clay content corresponding to the sol–gel transition (SGT), already determined by rheological measurements, ΔWL presents a change in concavity and Δe shows a maximum. Localisation of this maximum seems to be a simple way to detect the SGT by performing static filtration experiments of two series' of clay suspensions at two different pressures.According to the water contents obtained at the two pressures, all the cakes were localised in region (2), defined by Norrish (1954) as the “macroscopic” swelling paste of Na-montmorillonite. At low applied pressure, the texture of the cakes is identified by transmission electron microscopy (TEM). Generally, at low magnification, all samples are globally homogeneous. However, they present some regions more dense than others. At high magnification, the number of layers per particle seems to depend on SGT. Indeed, in the cake corresponding to 1% w/w of clay in the initial suspension, isolated layers are most frequent and particles with two to four layers per particle are scarce. In the cake obtained from the gel (3% w/w of clay) the most frequent stacking is about three layers per particle, and isolated layers almost disappear. In the cake obtained from gel, at the SGT (5.5% w/w of clay) which is the less oriented sample, the most frequent stacking is statistically also around three layers per particle but with a greater number of particles, some isolated layers appear again. After the sol–gel transition, in the cake obtained from the 7% sample (which is the most oriented sample), the number of particles increases but the number of layers in each particle decreases (two layers per particle most frequently occurs), and the number of isolated layers again rises. The frequent distances between the aggregates and particles were estimated on the TEM images of the cakes obtained at 1.5×10⁵ Pa. The distances between the particles of the cakes obtained under 5.7×10⁵ Pa was identified by X-ray diffraction (XRD). All these distances measured by the two techniques are compared with a linear extrapolation of Norrish's (1954) experimental data. At SGT, the cakes obtained at the two pressures correspond to aggregates connected with several distance configurations. However, the cakes obtained from the 3% initial clay content always show two distances (19 and 39 Å) at high pressure. At low pressure, one distance is about 300 Å, and the other is about 65 Å. This last distance disappears in the cake obtained from the more diluted suspension (1%) and only the higher distance persists. The 3% initial clay suspension seems to correspond to a “local osmotic transition”, which occurs between aggregated particles (or small aggregates) in the semi-diluted suspensions and isolated particles and/or layers in the more diluted suspensions.     

A rigorous cake filtration theory

The currently accepted concepts of the parabolic filtration correlation stipulate that the filtration rate decreases inversely as the flow resistance which is proportional to the extent of the filter cake; that non-parabolic behavior is characteristic of only compressible cakes which exhibit an average resistance which is not constant but depends on slurry concentration, filtrate rate and applied pressure; that the septum resistance is separate from, but additive to, the cake resistance and is obtained from the intercept of the V_F^? vs V_F line; that the average porosity of compressible cakes decreases during a filtration which causes the exit flow rate to exceed the entrance flow rate; that internal variations can only be obtained via compression-permeability simulations; and that the local resistance decreases monotonically from the septum to the cake surface.A filtration theory based on the rigorous, multiphase equations of change finds, contrary to the concepts listed above, that the least permeable part of the cake at the cake-septum interface (K₀) controls the filtrate rate and a decreasing pressure gradient across this minimum K₀ causes the filtrate rate to decrease; that deviations from parabolic behavior are independent of cake compressibility (incompressible cakes are rare, if they exist at all) but can be expected when ?_α*, s, -ΔP_c, K₀ and (dP*/dξ)|_ξ=0 are not constant; that the septum resistance is intrinsically included in K₀ which appears in the slope and not the intercept of V_F^?1 vs V_F; that the average porosity is constant and the exit flow rate exceeds the entrance flow rate due to a difference between the surface porosity and the average porosity; that internal variations can be obtained directly from filtration data alone and do not require a compression-permeability simulation; and that the local filtration resistance can exhibit a minimum as a result of using a non-linear transformation from cake length to cake mass.     

Effect of Cake Compression on the Performance of Centrifugal Dewatering

The effect of cake compression on the centrifugal dewatering is investigated under various rotating speeds and different kinds of cakes. A numerical method is proposed to estimate the capillary pressure and cake permeability under various cake saturations. The most dewatering in this study are operated at the funicular state of cake. The cake permeability decreases, while the capillary pressure increases rapidly, with the decrease of cake saturation during a centrifugal dewatering. The cake saturation can also be simulated once the relations among capillary pressure, cake permeability, and cake saturation are known. The deviations between simulated saturations and experimental data for compressible talc cakes are less than 2%. The centrifugal dewatering of compressible cake includes two mechanisms, the water squeeze due to cake compression and the centrifugal drainage due to pressure difference. The role of cake compression is dominant at the initial 500 s of the dewatering period, and these two factors are almost equal in magnitude as well as in importance when the cake approaches its equilibrium saturation. The porosity and compressibility of cake play the major roles in determining the equilibrium cake saturation. The equilibrium saturation of the compressible talc cake with a lower porosity is much higher than that of incompressible Al₂O₃ cake under a fixed rotating speed. An increase in rotating speed (centrifugal effect) results in a lower equilibrium cake saturation for either compressible or incompressible cakes; however, the increase in rotating speed is more efficient for an incompressible cake in the centrifugal dewatering.     

Effect of Cake Compression on the Performance of Centrifugal Dewatering

The effect of cake compression on the centrifugal dewatering is investigated under various rotating speeds and different kinds of cakes. A numerical method is proposed to estimate the capillary pressure and cake permeability under various cake saturations. The most dewatering in this study are operated at the funicular state of cake. The cake permeability decreases, while the capillary pressure increases rapidly, with the decrease of cake saturation during a centrifugal dewatering. The cake saturation can also be simulated once the relations among capillary pressure, cake permeability, and cake saturation are known. The deviations between simulated saturations and experimental data for compressible talc cakes are less than 2%. The centrifugal dewatering of compressible cake includes two mechanisms, the water squeeze due to cake compression and the centrifugal drainage due to pressure difference. The role of cake compression is dominant at the initial 500 s of the dewatering period, and these two factors are almost equal in magnitude as well as in importance when the cake approaches its equilibrium saturation. The porosity and compressibility of cake play the major roles in determining the equilibrium cake saturation. The equilibrium saturation of the compressible talc cake with a lower porosity is much higher than that of incompressible Al₂O₃ cake under a fixed rotating speed. An increase in rotating speed (centrifugal effect) results in a lower equilibrium cake saturation for either compressible or incompressible cakes; however, the increase in rotating speed is more efficient for an incompressible cake in the centrifugal dewatering.     

Study of the separation of yeast by microsieves: In situ 3D characterization of the cake using confocal laser scanning microscopy

In situ 3D characterization of Aquamarijn microsieves fouling was achieved using Confocal Laser Scanning Microscopy (CLSM). A filtration chamber allowing direct microscopic observation of microbial cell deposition and cake characterization, specially designed for in situ observations, was used. Fluorescent dyed Saccharomyces cerevisiae yeast suspensions were filtered through 0.8 μm and 2 μm pore diameters silicon nitride microsieves under constant flow rate. The on-line yeasts deposition was recorded and the cake construction was followed layer by layer. Based on the 3D image processing, cake properties (particle arrangement, homogeneity, thickness and porosity). The compressibility of the yeast cake was analyzed. Finally, cake removal efficiency was also studied during microsieve cleaning operation.     

Filtration properties of two Tunisian clays suspensions: effect of the nature of clay

The knowledge of the filtration properties are very important and can ascertain if a clay is suitable or not for use as a lining material for waste disposal. The general objective of our work is to determine a relation between structure and microtexture of two Tunisian clays (C1 and C2) and macroscopic properties of cakes formed by filtration. The result of permeability by water and waste solution (pH = 3) shows that the clay C2 is more impermeable than C1. In addition, the cake obtained after filtration test by filter-press for both clays present many interesting observations. However, for a ratio of (40%) of clay–water, the thickness of cake (e) in the case of C2 is more important (e = 10mm) than for C1 (e = 7mm). Similarly, the water retention (WR) is of order 34% for C2 and 26% for C1. This is due to the mineralogical composition of sample C2 which is essentially the smectite (swelling clay). Although, (WR) and (e) are slightly changed using the waste solution, it exist a lowering of plasticity of clay filter cake. This is illustrated by the SEM images that showed an interconnected micro-crack for the cake of sample C2, due to the degradation by acidic attack.     

Regeneration of oils used for deep frying: A comparison of active filter aids

A number of products are promoted for the purpose of regenerating used frying oils. These materials are referred to as “active” filter aids. They are purported to adsorb polar compounds, which are the products of oil degradation, and to retain them for removal by filtration. To evaluate some of these materials, portions of a used oil were treated with each of several “active” filter aids and filtered in a commercial-type recirculating oil filter. The triglycerides and any adsorbed compounds were extracted from the filter cake with a series of increasingly polar organic solvents. The composition of each of the filter cakes was quantitatively determined. The materials tested in this study were diatomaceous earth, acid-activated bleaching earth, activated aluminas, silica, carbon and synthetic magnesium silicate. Significant differences in the adsorbent characteristics of the materials were found. Adsorption of polar oil degradation compounds ranged from 2 mg of polar compounds per gram of diatomaceous earth to about 200 mg/g magnesium silicate.     

A WASHING THEORY FOR UNSATURATED FILTER CAKES USING THE CAPILLARY MODEL

A rigorous washing theory is developed using the area averaging technique for unsaturated filter cakes. Limiting cases of the resulting equations are investigated. The assumptions used in the modelling are verified.

The mass transfer parameters, which are evaluated by the application of the moment analysis, are shown to be directly proportional with the volumetric flow rate of the wash liquor. Experimental results also indicate that, for a given wash liquor volumetric flow rate, the increase in the cake thickness causes an increase in the mass transfer parameters.

It should be noted that the proposed model is applicable for large particle sizes. As particle size becomes finer and the size distribution becomes wider, the model should be modified by including dead void spaces containing pockets of the mother liquor in the filter cake     

Cake filter scale-up, simulation and data acquisition—A new approach

This paper details a unique, automated filtration apparatus and the newly developed Filter Design Software (FDS) which facilitates equipment selection, scale-up and simulation through an integrated experimental and theoretical approach.By way of example, experimental data were obtained with the apparatus over constant, variable and stepped pressure regimes. Inherent suspension properties were maintained throughout by utilising a computer-controlled pressure regulator and cake formation was monitored by micro-pressure transducers capable of providing up to seven independent measures of liquid pressure within 3.3 mm of the filter medium surface. For constant pressure and moderately compressible talc cakes the liquid pressure increased with cake height in a non-linear manner and generally exhibited a concave profile. When a pressure step was applied following a period of constant pressure filtration, the cake structure typically required up to 30 s to reach a new pseudo-equilibrium state. During this time the reciprocal filtrate flow rate vs. filtrate volume plot was non-linear and the liquid pressures in the cake increased rapidly before remaining nearly constant. When the cake was thicker or the pressure step larger, the liquid pressure measured closer to the filter medium remained either constant following the increase in pressure or increased slowly over the 360 s duration of the pressure step which indicates potential difficulties with the stepped pressure test.The filtration data were analysed using FDS to obtain scale-up coefficients and the impact of using incorrect scale-up coefficients on likely filter performance at the process scale is shown. The simulation capabilities of FDS are also highlighted through a case study in which, by way of example, the influence of crystal formation and other operating parameters on the filter cycle for a pharmaceutical product are shown. Simulations quantify how crystal form can detrimentally influence all phases of a cycle and lead to, for instance, slower filtration and wetter filter cakes.