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In this study, we designed three turbulence promoters using three-dimensional (3D) printing technology for cross-flow microfiltration. Designing turbulence promoters with optimal geometry for microfiltration systems remains a key challenge. The effects of the operating conditions, such as cross-flow velocity, transmembrane pressure and geometry of the turbulence promoter on the filtration flux and cake properties were investigated. The distribution of the fluid velocity was examined using computational fluid dynamics (CFD). For normal microfiltration tests without promoters, the filtration flux merely increased by 10% when the cross-flow velocity increased from 0.1 to 0.5 m/s under a transmembrane pressure of 20 kPa. Therefore, the turbulence promoters were individually added into the channel of the microfiltration device to induce vortices in the flow stream and increase cross-flow velocity. Three turbulence promoters with different configurations (circular, diamond and elliptic) were made with a 3D printer. The elliptic type of promoter with a hydraulic angle of 90° displays the flux enhancement by approximately 30–64% under a transmembrane pressure of 20 kPa compared to the normal type of microfiltration, whereas the diamond type of promoter with a hydraulic angle of 60° shows a lower flux enhancement by approximately 7–16% under the same transmembrane pressure. Overall, adding the turbulence promoter to the microfiltration module shows a great potential to significantly mitigate membrane fouling and enhance filtration flux in cross-flow microfiltration.

For increasing the shear stress on a membrane surface to reduce the fouling caused by solid deposition to improve the membrane filtration operation, various hollow fiber arrangements in a filter channel were investigated using computational fluid dynamics. In the simulation process, the velocity and pressure distributions and the effect of shear stress distributions on the membrane surface were analyzed under various hollow fiber arrangements and operating parameters, including fiber diameter (D), transverse pitch (S T ), and longitudinal pitch (S L ). These parameters lead to a dimensionless Reynolds number Re and the related friction coefficient C fD , which can be used to identify the relationship between different operating conditions. The study results indicated that C fD of the staggered arrangement was approximately 1.5 times greater than that of the aligned arrangement under the same operating conditions. The fouling tendency in the staggered arrangement was less and more favorable than that in the aligned arrangement, and with a higher S L /D ratio and lower S T /D ratio. With the results from this study, a design direction for optimal geometry to prevent membrane fouling and reduce power consumption was proposed, and can be used as the basis for hollow fiber membrane module design in the future.

A dynamic membrane was formed by introducing powder-activated carbon (PAC) prior to the cross-flow microfiltration of seawater. The microbes and organic matter in the seawater were removed efficiently through the interception, adsorption, and biodegradation of the PAC dynamic membrane. The properties of PAC dynamic membranes formed under various operating conditions were analyzed. The relationship between the specific filtration resistance of a dynamic membrane and transmembrane pressure was regressed as a power-type empirical equation for a given cross-flow velocity. An increase in cross-flow velocity led to higher specific filtration resistance because of the smaller particle size distribution. The thickness of a dynamic membrane increased with the transmembrane pressure but decreased with the cross-flow velocity. The thickness was correlated with the ratio of tangential to normal drag forces exerted on the PAC particles on the membrane surface. The filtrate quality for PAC dynamic membrane filtration was analyzed. Humic acid (HA) and turbidity were not detected. The chemical oxygen demand (COD) and dissolved organic carbon (DOC) had maximum removals of approximately 80% and 92%, respectively. The behavior by which HA was adsorbed on a PAC conformed to the Freundlich isotherm, and the modified Wheeler equation produced appropriate estimates of the breakthrough time. The breakthrough time increased with the thickness of the dynamic membrane. This study presents a method by which the filtration performance, such as filtration flux, thickness, and breakthrough time of the dynamic membrane, can be predicted directly from operating conditions.

In this study, we investigated the performance of powdered activated carbon dynamic membranes (PAC DMs) in fouling mitigation strategies during cross-flow microfiltration for high-efficiency seawater pretreatment. By altering the fouling mechanism and water molecule pathway, PAC DMs successfully enhanced the pseudo-steady-state filtration flux and rejection of cross-flow microfiltration by 53% and 29%, respectively, compared to filtration without a PAC DM. Moreover, Fenton oxidation processes (FOPs) application in the DMs’ cross-flow cleaning was studied and showed promising results, recovering up to 28% of the initial filtration flux when used alone and 52% when combined with alkaline cleaning. This study provides insight into the utilization FOPs cleaning technology for PAC DMs cross-flow cleaning, allowing the automation and optimization of DMs operation.

The efficient deliquoring process has been developed for achieving high-rate and high-degree deliquoring of municipal excess activated sludge, which exhibits relatively low dewaterability. In the method developed, low-pressure filtration combined with flocculation led to high-rate deliquoring of sludge due to the formation of large flocs. Subsequently, ultrahigh-pressure expression combined with water permeation through the filter cake which promoted the re-dispersion of flocs in the cake resulted in high-degree deliquoring of the cake. It should be noted that the moisture content in the compressed cake was finally reduced to 31 wt% by expression operation under action of an ultrahigh pressure of 15 MPa. This extremely low value of the cake moisture content implies that the liquid contained within the microorganism cells was partially removed by the mechanical pressure when the ultrahigh pressure is applied to the cake in the course of expression. The relation between the equilibrium porosity in the compressed cake and solid compressive pressure was empirically represented by a power function. The kinetics of ultrahigh-pressure expression such as the time variation of the moisture content in the compressed cake was accurately described by combining the multi-stage creep model with the modified Terzaghi model describing the primary consolidation.

Microalgae are promising feedstock for biodiesel production due to their lipid content. Rotating-disk dynamic microfiltration was used for microalgae concentration in this study. The effects of operating conditions, namely disk rotation speed, suspension feed rate, and transmembrane pressure (TMP), on the filtration flux and cake properties are discussed. Because all microalgae cells were rejected by the filter membrane, the main cause of filtration resistance was highly compressible cake that exhibited a compressibility factor of 0.66. An increase in the disk rotation speed led to 40–300% increase in pseudosteady filtration flux. Applying a high TMP yielded high filtration flux at a low disk rotation speed. However, the opposite result was obtained at a high rotation speed. Nearly the same filtration fluxes were produced at a disk rotation speed of 300 rpm even when the TMPs were different. The flow fields in the rotating-disk dynamic microfilter were simulated using software of computational fluid dynamics, Fluent. The shear stress at the membrane surface is a major factor affecting cake formation. A two order-of-magnitude increase in the shear stress by increasing the disk rotation speed will decrease the cake mass by 80% and enhance the filtration flux to about 10 times in the conditions of this study. A linear relationship between mean cake mass and the ratio of filtration flux to mean shear stress derived from the force balance model was verified using experimental data measured in various operating conditions. The methods proposed by this study provide a way to estimate the cake mass and filtration flux directly from operating conditions.

Glucose and enzyme in a high concentration enzymatic hydrolysis suspension were separated using hollow fiber cross-flow diafiltration. The operating condition effects on the filtration performance are discussed. Over 86% of the enzymes were retained using a 10 kDa polysulfone membrane. Most glucose molecules penetrated through the membrane into the filtrate. The major filtration resistances are due to the cake formation on the membrane surface and enzyme blocking in the membrane pores in addition to the appreciable virgin membrane resistance. The cake mass is correlated with the drag force ratio tangential to the filtration directions and the average specific cake filtration resistance is expressed as a power-function of the transmembrane pressure with a cake compressibility of 0.3. The empirical equation related the resistances due to internal membrane fouling to the operating conditions established by conducting experimental data regression. The filtration flux can be estimated accurately by substituting the results calculated using the empirical equations into the basic filtration equation. An increase in cross-flow velocity or transmembrane pressure leads to higher filtration flux. The filtration flux increases ca 2-fold as the cross-flow velocity increases from 0.3 to 1.5 m/s under a transmembrane pressure of 60 kPa. The filtration flux increases over 3-fold as the transmembrane pressure increases from 20 to 100 kPa. Two kinds of modified operating methods are used to improve the filtration flux. A pulse feeding method may increase the filtration flux by 25%, while the step-increase pressure method improves the filtration flux by over 34%. Forming a thin cake under low pressure in the early filtration period has great potential to significantly mitigate membrane pore blocking and enhance filtration flux.

Several novel hydrocyclones are designed to improve fine particle separation using computational fluid dynamics. The effects of inlet size, number of inlets and top-plate types on the particle separation efficiency and cut-size sharpness are discussed based on the same feed flow rates. The fluid and particle flows are simulated using a segregated, steady-state, 3-dimensional implicit numerical solver supplied by FLUENT software. The governing equations are coupled using the SIMPLE algorithm, while the Reynolds stress model is employed for the hydrocyclone turbulent model due to its' anisotropic nature. Particle trajectories are simulated based on a Lagrangian frame considering the continuous phase interactions. The simulated particle separation efficiencies approximately agree with the available experimental data. The results show that increasing the inlet number and narrowing the inlet width are effective ways to improve the particle separation efficiency due to the increase in fluid velocity in the cylindrical parts of hydrocyclone. A cone-shaped top-plate reduces the fine particle circulation area near the outer surface of overflow conduit, significantly improving the separation efficiency of fine particles. However, increasing the cone angle has a contrary effect because of the decrease in particle residence time. Although installing an extra guide-channel from the inlet may also improve the fine particle separation efficiency, it is not effective for particle classification because of reduced particle cut-size sharpness.

Online monitoring techniques can play a major role in understanding and controlling the mechanisms involved in the fouling of membrane filtration systems. The present study describes the application of an in situ optical method to monitor the growth of a fouling layer using a photointerrupt sensor array. To verify the validity of this method, the effects of the voltage applied, slurry concentration and membrane materials on the signal from the sensor array were examined. In addition, the application of this method in monitoring the growth of the fouling-layer thickness during the filtration of a high-turbidity influent stream under constant flux was studied. The results from three-dimensional (3D) fouling contour studies showed that the average fouling-layer thickness increased proportionally with time during the initial period in response to the rapid deposition of particles on the membrane surface, after which the growth rate of the fouling layer decreased. The 3D fouling contour analyses suggest that this online monitoring technique provides an effective in situ measurement of fouling-layer thickness and distribution. The photo-sensor array proved to be a promising online monitoring technique for scanning membrane surfaces on demand and can be applied to a pilot-scale water treatment unit for use in the real-time profiling of changes in fouling-layer thickness.

The sugars produced by enzymatic hydrolysis of rice straw are separated using cross-flow diafiltration in this study. The effects of membrane type, membrane pore size, cross-flow velocity and transmembrane pressure on the filtration flux, sugar rejection, and sugar mass flux transported to the filtrate are discussed. The filtration flux increases with increasing cross-flow velocity or transmembrane pressure. When the membrane made of mixed cellulose ester (MCE) is used, over 70% filtration resistances are caused by the membrane fouling; while the resistance due to virgin membrane is dominant when regenerated cellulose (RC) membranes are used. A force balance model is applied to relate the filtration flux and filtration resistance to operating conditions. The calculated data of filtration flux based on this model agree fairly well with experimental data. In addition, a theoretical model is used to explain the sugar transmission through the cake and membrane pores. The sugar rejection coefficient decreases ...

The membrane pore size and operating condition effects on the filtration flux, membrane fouling and solute rejections in cross-flow microfiltration of BSA/dextran binary suspension are studied. Two flat sheet microfiltration membranes with mean pore sizes of 0.1 and 0.025 μm are used as filter media in these experiments. The filtration flux increases with increasing cross-flow velocity and filtration pressure because of less membrane fouling or higher filtration driving force. The filtration resistance caused by membrane fouling is much higher than that caused by concentration polarization or virgin membrane. This impact is more significant under higher transmembrane pressures. The membrane fouling extent due to dextran adsorption is expressed as pore size reduction and fouled layer depth, which can be estimated theoretically based on hydrodynamic models. The dextran rejection decreases with increasing Reynolds number in the membrane pores and approaches constant when the Reynolds number exceeds a critical value. This is attributed to the increase in wall shear stress and molecular deformation in the membrane pores. A higher cross-flow velocity results in higher dextran rejection because of the sweeping effect occurring on the membrane surface. The BSA rejection under various operating conditions can be reasonably explained by the membrane sieving effect. The BSA rejection decreases linearly with increasing pore size in the fouled membrane with no obvious cross-flow velocity effect on BSA rejection found. The effects of the dextran concentration and Reynolds number in the membrane pores on the dextran adsorption layer thickness are also discussed.

Membrane fouling in BSA/dextran binary suspension cross-flow microfiltration under various operating conditions is studied. The mechanisms for membrane fouling based on the SEM and CSLM observations under various suspension concentrations are proposed. BSA aggregates deposit onto the membrane surface while dextran molecules adsorb into the membrane pores, resulting in filtration resistances. The BSA deposition is mainly determined by the drag forces exerted on BSA aggregates on the membrane surface. Dextran adsorption is affected by the dextran concentration and applied pressure. The concentration effects on the filtration flux and filtration resistance are also discussed. The filtration fluxes for BSA/dextran mixtures are located between those for two pure substances and decrease with the increase in either the BSA or dextran concentration. However, the dextran concentration impact is more significant because the filtration resistance caused by membrane blocking is much higher than that caused by cake formation in most conditions. The filtration resistances due to concentration polarization, cake formation and membrane internal fouling can be estimated directly from the operating conditions using the semi-theoretical methods proposed in this study.

The gel particle softness effect on cross-flow microfiltration performance is studied. Three kinds of soft gel particles with a similar size distribution but different softness and compression behaviors were prepared and used in these experiments. The particle softness is the most important factor affecting the pseudo-steady filtration flux compared to the other operating variables in the conditions of this study. A filter cake formed by softer particles is compressed into a more compact structure, consequently, resulting in higher filtration resistance and lower filtration flux. The particle deposition probability is analyzed using a force balance model. An increase in particle softness leads to lower particle deposition probability as well as lighter cake mass due to the drastic flux decay. The cake compression during filtration is described using the Voigt in series model. The cake porosity suddenly decreases and the specific cake filtration resistance drastically increases in the early filtration period. The skin cake layer formation in that period plays the most important role in determining the cross-flow microfiltration performance. The cake mass and average specific filtration resistance calculation results using the proposed methods agree fairly with the available experimental data.

In this study, bovine serum albumin (BSA) molecules are separated from suspended particles using submerged membrane filtration. Several methods, including constant-pressure filtration with backwash, air bubble sparging and a stepwise increase in pressure, are used to reduce filtration resistance and to enhance filtration flux. The effects of filtration pressure, backwash flow rate, backwash duration, air flow rate and stepwise pressure increase on filtration flux, filtration resistances, BSA rejection and BSA production are discussed. The results show that internal fouling of the filter membrane is the most important contributor to the overall filtration resistance, while cake formation is the main determinant of BSA rejection. An increase in filtration pressure leads to lower filtration flux and lower BSA rejection due to more severe internal fouling of the membrane. Although additional periodic backwash or air bubble sparging increases the filtration flux relative to solely constant-pressure filtration, the filtration flux and BSA production when using a stepwise pressure increase is much higher than with the other operations, especially when the latter is combined with a periodic backwash. Moreover, the calculated filtration flux and BSA rejection results for constant-pressure filtration under various filtration pressures agree fairly well with experimental data.

The selective deposition of fine particles in a constant-flux submerged microfiltration system is studied. The effects of operating conditions, such as filtration flux, injected air flow rate and air bubble size, on the particle deposition probability, cake mass and average specific cake filtration resistance are discussed. Smaller particles have more opportunity to deposit onto the membrane surface. The particle size distribution in the filter cake increases with increasing the filtration flux or bubble size, but with decreasing the injected air flow rate. The external forces exerted on the depositing particles are analyzed based on hydrodynamics and DLVO theory. The drag forces due to suspension flow, permeate flow, and bubble flow play the major role in determining the particle stability on the membrane surface. Interparticle forces are dominant for submicron particles, while gravitational force increases its weight as particle size exceeds 5 μm. A force balance model is used for estimating the particle deposition probability. An increase in filtration flux or a decrease in air flow rate leads to higher particle deposition probability, heavier cake, or lower average specific cake filtration resistance. The deposition probability is higher by injecting bigger bubbles under a specified air flow rate due to the lower bubble generation frequency. Consequently, a decrease in bubble size causes to lighter cake but higher average specific filtration resistance. The validities of the model predictions for particle deposition probability, cake mass and average specific filtration resistance are demonstrated by experimental data.

Filtration characteristics and membrane fouling in BSA/dextran binary suspension cross-flow microfiltration is studied. An increase in cross-flow velocity or transmembrane pressure leads to higher pseudo-steady filtration flux due to less membrane fouling or higher driving force. The fouled membrane pore size and fouled layer thickness under various conditions are estimated using a theoretical model based on the Hagen–Poiseuille law. The fouled membrane pore size decreases with increasing transmembrane pressure due to ever increasing fouling. The fouled layer thickness becomes thicker and invariant with operating conditions under a lower pressure drop through the fouled membrane. Molecular adsorption occurs on the pore walls until a specific wall shear stress is reached in the membrane pores. However, the fouled layer becomes thinner when the pressure drop exceeds a critical value. An increase in cross-flow velocity results in a larger fouled membrane pore size and a thicker fouled layer in such condition. The dextran molecular deformation under higher transmembrane pressure causes a thinner fouled layer and an ultimate equilibrium adsorption in the membrane pores. Furthermore, an increase in cross-flow velocity leads to higher BSA and dextran rejection due to the sweeping effect on the membrane surface. The BSA rejection increases with transmembrane pressure due to the reduction in membrane pore size, while the decrease in dextran rejection under higher transmembrane pressure is attributed to the molecular deformation. The “coil-stretched” deformation of dextran molecules can be indicated using the Deborah number. The fouled membrane pore size and dextran rejection decrease with increasing Deborah number and remain constant as the Deborah number exceeds a critical value. Taking the filtration flux and solute rejection into consideration, operating a cross-flow microfiltration system under lower cross-flow velocity and higher transmembrane pressure is more efficient from the selectivity and mean dextran mass flux view points.

A fast and simple fabrication process, viz. a wet-chemical reduction process, was utilized for preparation of a cobalt-based catalyst to be used for hydrogen generation from alkaline NaBH4 solution. Characteristics of this cobalt-based catalyst were carried out by using various instruments, such as SEM/EDS, XPS, ICP, VSM, BET and TGA. The surface chemistry of the obtained catalyst is mainly cobalt oxides, not cobalt borides. Ferromagnetic property of the cobalt-based catalyst makes it convenient for being recycled from spent NaBH4 solution. The rate of hydrogen generation from catalyzed hydrolysis of alkaline NaBH4 solution was determined as a function of temperature, NaBH4 concentration, and NaOH concentration in the presence of prepared catalysts. In general, stable generation rate of highly pure hydrogen near 200 mL min−1 g−1 was achieved in 100 mL of 5 wt% NaBH4 solution containing 5 wt% NaOH solution and 200 mg of Co/IR-120 catalyst, in which no temperature runoff was observed during the course of hydrogen production. The activation energy of NaBH4 hydrolysis reaction was found at 66.67 kJ mol−1, which was comparable with others reported in the open literatures.

Three kinds of porous gel particles with different compression properties were prepared and used in “dead-end” filtration experiments. Incorporating the conventional cake compressibility index, two additional parameters for particle compression, retardation time and softness index, are introduced to discuss the porous gel particle viscoelastic compression behaviors and filtration characteristics, including the variations of filtration flux, cake mass, cake porosity, water inside the particles and specific cake filtration resistance during filtration. A cake compression mechanism including four stages is proposed to explain the filtration curve trend for d t / d v vs. v for different gel particles. The concave trend in the compression stage is more obvious for gel particles that exhibit longer retardation time or a smaller particle softness index, or under lower filtration pressure. The variation in cake porosity during compression can be described using a Voigt in series model. Cake mass (including dry solid and the internal water) decreases quickly in the early filtration stage because of the rapid percolation of particle internal water, and then increases gradually after the cake compression retardation time due to the formation of new cake layers. A power relationship between the average specific cake filtration resistance and filtration pressure can be regressed. However, the specific cake filtration resistance value varies with time due to both cake and particle compression. A long compression retardation time or a high particle softness index implies that the particles possess high elastic and deformable natures. Consequently, the particles will form an extremely compact and high resistance cake. These effects become trivial when the compression parameters exceed the critical values. In conclusion, the compression behaviors of cakes formed by soft particles can be well interpreted using the relationships between cake compressibility and particle compression properties, such as the retardation time and softness index.

Effect of gas–liquid flow pattern on the performance of air-sparged cross-flow microfiltration of yeast suspension is studied. The pseudo-steady filtration flux and the cake properties under various operating conditions are measured and discussed. The shear stress acting on the membrane surface and the critical condition for particle deposition are analyzed theoretically based on hydrodynamic models. The cake mass is markedly reduced by increasing the wall shear stress. However, the average specific cake filtration resistance increases with increasing the wall shear stress due to more compact cake structure. The increase in the average specific filtration resistance of cake due to air-sparging is more significant in bubbly flows. Consequently, the filtration flux will be increased by air-sparging due to the cake reduction in slug flow microfiltration. However, a contrary result is obtained for bubbly flows due to the drastic increase in the average specific filtration resistance of cake. Therefore, a microfiltration operating under slug flow is more effective to enhance the filtration flux by air-sparging. In addition, the proposed model provides a method to quantitatively relate the filtration flux to operating parameters. The relationships are also strongly dependent on the gas–liquid flow pattern.

Particles with a mean diameter of 5 μm were filtered by a ceramic tubular membrane to study the effects of backwash on the performance of submerged membrane filtration. A periodic backwash can completely remove the formed cake, diminishing a part of membrane internal fouling, and, therefore, recover the filtration flux. In a membrane-blocking/cake formation comparable filtration system, the filtration resistance due to membrane-internal fouling is over twice as high as that due to cake formation. The irreversible filtration resistance increases progressively during operation, and it can be regressed to a power-type empirical relationship. Filtration period data were analyzed using blocking models. Membrane blocking occurs in the early filtration periods and is followed by cake filtration. The filtration flux can be simulated by employing blocking models and empirical equations for filtration resistance. The backwash effectiveness was examined by comparing filtrate productivity and washing efficiency. The calculated results of productivity under various backwash durations agree well with experimental data. An increase in backwash flux or duration leads to higher productivity, when the duration is shorter than 2 min; however, the productivity may be decreased with an increase of backwash duration due to the back pumping of more filtrate. A longer filtration time in each cycle results in higher backwash efficiency since a formed cake may efficiently prevent further membrane pore clogging and is more easily removed by a backwash. The optimal backwash conditions can be determined appropriately by the proposed method, with respect to both backwash efficiency and filtrate productivity.

The mechanism of centrifugal filtration of microbe/protein bio-suspension is studied. The bio-suspension is prepared by adding baker yeast and albumin bovine serum (BSA) into a buffer solution at pH 7.0; and the BSA molecules are purified from the mixture in a swing-arm centrifuge under rotational speeds ranging from 500 to 4000 rpm. A numerical program is established for estimating the concentration profiles of yeast cells in the filter chamber, the cake growth rate, the cake properties and filtration rate. The variations of the average specific filtration resistance and average porosity of cake are estimated based on a Voigt-in-series compression model. The simulated results of cake properties and filtrate rate agree fairly well with the available experimental data. In addition, the separation efficiency of BSA can be predicted accurately under various conditions once the BSA permeation through the cake and the filter septum is analyzed. To compare the separation efficiency of BSA in the centrifugal and cross-flow microfiltration systems, use of centrifugal filtration with a centrifugal effect just over the critical value is an optimum on the viewpoint of operating time, separation efficiency, and energy-saving.

The flux enhancement in cross-flow microfiltration of submicron particles by sparged air-bubble is studied. The effects of operating conditions, such as air-bubble velocity, suspension velocity and filtration pressure, on the cake properties and filtration flux are discussed thoroughly. The results show that the pseudo-steady filtration flux increases as the air-bubble velocity and filtration pressure increase. The sparged air-bubble can significantly improve filtration flux, but the flux enhancement is more remarkable in the lower air-bubble velocity region. A gas–liquid two-phase flow model is adopted for estimating the shear stress acting on the membrane surface under various operating conditions. The cake mass can be significantly reduced by increasing the shear stress acting on the membrane surface. However, the SEM analysis illustrates that the particle packing structure becomes more compact as the air-bubble velocity increases. This results in a slightly higher average specific cake filtration resistance under higher air-bubble velocity. Consequently, a minimum flux occurs at the critical shear stress, e.g., τ w = 1.1 N/m 2 in this study, when these effects are both taken into consideration. As the shear stress increases by increasing the suspension or gas-bubble velocity, the filtration flux decreases in the low shear stress region but, on the contrary, quickly increases in the high shear stress region. Furthermore, a force balance model is derived for understanding the particle deposition on the membrane surface. The relationship among filtration flux, shear stress and overall filtration resistance is obtained and verified by experimental data.

Particle fouling mechanisms in “dead-end” microfiltration is analyzed using blocking models. The blocking index and resistance coefficient of the models during microfiltration are calculated under various conditions. The major factors affecting these model parameters, such as the filtration rate, the amount of particles simultaneously arriving at the membrane surface and particle accumulation, are discussed thoroughly. Instead of the four different blocking models previously proposed, a membrane blocking chart is established for relating the blocking index, filtration rate, and particle accumulation. Blocking index variation during microfiltration can be interpreted using this chart. Membrane blocking occurs during the initial filtration periods until the condition reaches a critical value; then, the blocking index suddenly drops to zero by following up the cake filtration model. Once the normalized resistance coefficient is regressed to an exponential function of the blocking index under a wide range of conditions, the blocking models can be used to quantitatively explain filtration flux attenuation by solving a unitary mathematical equation. Comparing the experimental filtration rates obtained under different conditions with the simulated results reveals a good agreement between them and demonstrates the reliability of this analysis method.

The effects of operating conditions, such as cross-flow velocity, filtration pressure and the pH of suspension, on the filtration rate, the cake properties and the protein rejection in a cross-flow microfiltration of fine particle/protein binary suspensions are studied. Experiments are carried out using the binary suspensions prepared by polymethyl methacrylate (PMMA) submicron particles and bovine serum albumin (BSA) proteins. The mass, thickness, porosity and specific filtration resistance of the filter cakes under various operating conditions are measured and well discussed. The results show that the cake properties are important factors in determining filtration rate and BSA rejection. The filtration rate increases with increasing cross-flow velocity and filtration pressure, while the highest filtration rate occurs at pH 6.7. A hydrodynamic model is derived to estimate the cake properties and filtration rates under various conditions. The calculated results are in good agreement with the experimental data. In addition, the BSA rejection increases with increasing cross-flow velocity; but a trivial variation with filtration pressure is found. For a given filtration pressure and cross-flow velocity, the BSA rejection at pH 6.7 is higher than those at the other pH values. The standard capture equation is used to relate the BSA rejection and the cake thickness. The obtained screen parameter remains constant under a given cross-flow velocity.

The properties of cakes formed using soft colloids in “dead-end” microfiltration were studied. The empirical power functions were used to relate the local cake properties. However, the cake compressibility factors are functions of time due to the retardation effect of cake compression. A dynamic analysis method is proposed to estimate the cake properties during soft colloid microfiltration. The results show that the entire filtration course can be divided into three stages. At the beginning of filtration, the deposition and rearrangement of the colloidal particles on the membrane surface cause the overall filtration resistance to increase. The average porosity and average specific filtration resistance of the cake vary slightly during this period of filtration. In the second stage, a rapid increase in filtration resistance and a decrease in cake porosity due to cake compression and colloid deformation can be found. A compact skin layer begins to be formed next to the filter membrane in this stage. The skin thickness is about 10–20% of the entire cake but this layer exhibits about 90% of the overall filtration resistance. The average cake porosity increases gradually in the third stage due to the loose packing in the newly formed cake. This trend can be reflected in the d t /d v versus v filtration curves and is demonstrated by the experimental data. The structure of the cake formed in each stage was observed using scanning electronic microscopy (SEM).

The charge effects on the particle aggregation and the performance of cross-flow microfiltration of submicron particles are studied. A cell model is proposed to model the packing of aggregates in a filter cake. The effective densities of aggregates are estimated by an empirical equation, and the porosity and the specific filtration resistance of the filter cake under various electrolyte concentrations are calculated based on a force analysis. The packing structure in a filter cake can be divided into two modes. The region near the filter membrane has a compact structure and a high filtration resistance, while the portion of cake near the cake surface has a high porosity and a low filtration resistance due to the separation of particles or aggregates. For acid suspension with low electrolyte concentrations ( I I >0.01 M), the compression of electric double layer and the decrease of zeta potential result in a high cake porosity and low specific filtration resistance of cake due to the aggregation of particles. The pseudo-steady filtration rate therefore increases with increasing the electrolyte concentration due to the increase of aggregate sizes. The calculated results of average cake properties, such as the porosity and the specific filtration resistance of cake, under various operating conditions agree fairly well with the experimental data.

Effects of membrane morphology and operating conditions on the performance of cross-flow microfiltration are studied. Three kinds of membranes with the same mean pore size of 0.1 μm are selected for filtration experiments. They are MF-Millipore, Durapore and Isopore membrane. The variations of cake and membrane resistance during filtration using these membranes are measured and used for blocking analysis. Although complete pore blocking occurs, Isopore membrane results in the highest filtration rate due to less cake formation. The filtration rate of Durapore membrane is lower than that of Isopore membrane. It is because, more particles deposit on the surface of Durapore membrane to form filter cake. MF-Millipore membrane results in the lowest filtration rate due to the most cake formation and a serious pore blocking. The pore structures of each membrane are modeled in order to understand the mechanisms of pore blocking. At the initial stage of filtration, a standard blocking occurs in MF-Millipore membrane, an intermediate blocking in Durapore membrane, and a complete blocking in Isopore membrane. These blocking models are transferred to cake filtration after 10 min for all kinds of membranes. The pore blocking in each membrane is also observed and demonstrated by scanning electronic microscopy. Furthermore, filtration rate increases with either increasing cross-flow velocity or increasing filtration pressure.

Crossflow microfiltration of mono-dispersed deformable particles of Saccharomyces cerevisiae and Ca-alginate, and rigid PMMA particles was conducted to compare the structure of the flux-limiting layer. The effects of particle deformation due to the frictional drag and mass of the cake, and the area contact among particles on the reduction of porosity were examined to determine how these variations lead to an increase in filtration resistance. The dynamic analysis proposed by Lu and Hwang (AIChE J. 41 (1995) 1443–1455) was modified to examine cake formation during crossflow filtration of deformable particles by taking the transient effect of cake compression and the effect of the area contact between particles into consideration. In situ measurement of filter cake thickness using the infrared reflection method was applied to verify the theoretical results. Both experimental and simulated results showed that the cake formed by deformable particles exhibits a rapid increase in flow resistance or a decrease in local porosity and a high resistant limiting layer is formed next to the filter medium during filtration due to the deformation of particles.

The mechanism of cross-flow microfiltration of submicron microbes is studied. Experiments are carried out using pseudomonas suspensions. The effects of operating conditions on the filtration performance are discussed. The results show that the filtration rates increase with increasing the cross-flow velocity, while decrease with increasing the filtration pressure. The Brownian dynamic simulation method is adopted for simulating the trajectories of microbes in cross-flow microfiltration. The deposition flux of microbes on the membrane surface can then be estimated from the simulated trajectories. Based on the continuity equation of cake compression and Kozeny equation, a dynamic analysis method is developed for simulating the distributions of local cake properties, such as porosity and specific filtration resistance in the filter cake. The deformation of microbes, the area contact between microbes and the creeping effect of cake compression are taken into consideration. The simulated values of average cake properties agree with the experimental data. It can be found that a skin layer controlled the filtration rate will form next to the membrane surface. Although the thickness of the skin layer is only about 10% of the whole cake, it plays the major role on the filtration resistance. Increasing the filtration pressure results in more compact skin layer; therefore, a lower filtration rate is obtained. Moreover, a higher cross-flow velocity will results in a thinner but more compact cake, a higher filtration rate can be given.

The effect of particle size distribution on the performance of batchwise centrifugal filtration is studied. By analyzing the velocity of particles in a filter, a numerical program is designed for simulating the migration and deposition of particles. The particle size distributions and the average specific filtration resistances of cake are then estimated under various rotating speeds of the centrifuge. A large deviation of particle concentration profiles in the filter chamber will occur if the particle size distribution is not taken into consideration. A more heterogeneous cake will form under a lower rotating speed due to the sedimentation effect of particles. The predicted results of particle size distribution and average specific filtration resistance of cake agree well with the available experimental data.

The local properties of filter cakes, such as porosity and specific filtration resistance, in cross-flow microfiltration of submicron particles are studied based on an analysis of force. The packing of particles in a filter cake can be divided into two modes. When the solid compressive pressure is smaller than the critical value, there exists an equilibrium distance between neighbouring particles due to the electrostatic repulsive force, and the local cake porosity can be estimated by using the cell model proposed in this study. When the solid compressive pressure is greater than the critical value, the compressive force can overcome the repulsive barrier, the particles then come into contact with neighbours, and the power-type empirical relationship between cake porosity and solid compressive pressure can be employed to estimate the local cake porosity. It can be found that the half of the cake near the filter membrane has a compact structure, and a high filtration resistance within the operating conditions of this study. On the other hand, the portion of cake near the cake surface has a high porosity due to the separation of particles. By using this model, the effect of electrolyte concentration on cake properties can be analyzed, and the estimated values of average porosity and average specific filtration resistance under various electrolyte concentrations, cross-flow velocities, and filtration pressures agree fairly well with the experimental data.

Three-dimensional particles deposition on four basic woven structures was studied numerically by analyzing forces acting on the depositing particles and was applied to estimate the change of clarity of filtrate at the initial stage of filtration. The effects of woven structures, feed concentration and particle/pore size ratio on the transient behavior of cake filtration and the variation of medium resistances at the beginning stage of cake filtration were analyzed quantitatively. The simulated results show that the filtration period at the initial stage can be divided into the three modes of standard pore blocking, intermediate blocking and cake formation in accordance with the law of blocking for all types of pores. Furthermore, the critical concentration proposed by previous investigators is also confirmed quantitatively in this study.

The mechanism of cross-flow filtration of power law slurry is studied through a hydrodynamic approach. The trajectories of particles in the filtration are analyzed in order to estimate the mass flux of particle deposition on the filter septum. An agreed tendency is found between the calculated results of particle flux and the experimental data. A dynamic simulation method based upon the continuity equation of cake compression and the differential-form filtration equation of power law slurry is proposed. By substituting a set of experimental data of filtration rate vs. time into the iteration procedures, the local cake properties and their variations during a course of cross-flow filtration can be simulated. The calculated results of average cake porosity and average specific filtration resistance agree very well with the experimental data.

The mechanism of cake formation in constant pressure filtration of power law slurry is studied. By analyzing the forces exerted on the depositing particles, the critical friction angles, θ c , are estimated under various conditions. The lowest value of θ c is found when the frictional drag and the interparticle force are of the same order of magnitude. The packing structure of particles on the cake surface has been simulated, and the results indicate that a more compact cake will be obtained if a power law slurry with smaller n (flow behavior index) is filtered. A numerical program besed upon the continuity equation and the Rabinowitsch-Mooney equation is also designed to estimate the variations of local cake properties during a course of constant pressure filtration. The calculated results of cake porosity and specific filtration resistance agree very well with the experimental data.

A hydrodynamic mechanism of slurry particles depositing onto a filter septum in a turbulent cross-flow filtration is proposed. The distribution of fluid velocity and the particle concentration within the cross-flow filtration system are numerically analyzed to study the rate of particle deposition, the growth of the cake, and the attenuation of filtration rate during operation. The effects of the operating parameters on the characteristics of the cross-flow filtration are discussed.