Chemisorption of estrone in nylon microfiltration membranes: Adsorption mechanism and potential use for estrone removal from water

Estrone is a representative steroid estrogen contaminant that has been detected in effluents from sewage treatment facilities, as well as in surface and ground waters. Our study shows that estrone can be readily removed from water via a unique chemisorption mechanism using nylon microfiltration membranes. Experiments on a laboratory in-line filtration system showed instant removal of estrone from 200 μg/l aqueous solutions by 0.45-μm nylon membranes (ca. 35 L per m² membrane). Comparisons with 0.45-μm PVDF, PTFE and glass microfiber membranes suggested that the significant estrone adsorption in nylon membrane should be predominately driven by a different mechanism rather than common physical adsorption. Fourier transform infrared spectroscopy study on nylon membranes and a model compound, N-methylacetamide, showed that the significant adsorption originated from the hydrogen bonding between terminal -OH groups on estrone molecules and nucleophile -CO groups in amide groups of nylon 6,6. The saturated nylon membrane showed very low leachability in ambient water, while it could be effectively regenerated in alkaline or ethanol solutions. Preliminary reusability study showed that the membrane maintained a consistent adsorption capacity for estrone during ten cycles of reuse. The chemisorption-based polymeric adsorption may provide a new alternative approach for removing estrone and potentially other trace organic contaminants from water.     

大型超滤水厂PVC和PVDF膜运行特性差异与优化

超滤技术已广泛应用于城镇给水处理厂,使得饮用水水质得到显著改善。不同材质超滤膜的运行周期、膜通量、跨膜压差(TMP)等的变化规律会有显著的差异,需要根据各自的特点对超滤系统进行运行参数调控与优化,以保证超滤系统的长期稳定运行。分析了山东某大型超滤水厂超滤系统长期运行的特点,对比了PVC膜和PVDF膜孔结构特征、膜通量、跨膜压差变化趋势及膜过滤阻力特性,调控和优化超滤系统运行参数,并进行了长时间的运行验证。结果表明,膜孔径和膜孔结构不同造成的膜污染是PVC膜与PVDF膜过滤特性差异的主要因素,恒定过滤周期运行模式下PVC膜通量加速衰减时段为82~220 min,造成PVC膜通量衰减了9. 14%,并形成了约5%的永久衰减膜通量,而PVDF膜的通量衰减并不明显,使得水厂超滤系统在恒定过滤周期(180min)运行模式下,出现了PVC膜的污染速率明显高于PVDF膜、系统的运行工况出现显著差异的现象。按照恒定过滤阻力模式运行时,PVC膜和PVDF膜的最佳过滤周期范围分别为82~108 min和96~155 min。水厂超滤系统在恒定过滤阻力运行模式下将PVC膜与PVDF膜在高温期和低温期的过滤周期分别调整为110、90 min和150、120 min,TMP的增长速率和化学维护清洗周期均基本一致,超滤系统实现了长期稳定运行。研究成果为我国超滤水厂中不同材质超滤膜的运行参数优化及协同稳定运行提供了参考。     

Alginate fibers as photocatalyst immobilizing agents applied in hybrid photocatalytic/ultrafiltration water treatment processes

Ca alginate polymer fibers were developed to effectively disperse and stabilize an efficient photocatalyst such as AEROXIDE^® TiO₂ P25 in their matrix. The biopolymer/TiO₂ fibers were prepared and tested either in the hydrogel non-porous form or in the highly porous aerogel form prepared by sc-CO₂ drying. Batch photocatalytic experiments showed that the porous, Ca alginate/TiO₂ fibers, exhibited high efficiency for the removal of methyl orange (MO) from polluted water. In addition, their high porosity and surface area led to high MO degradation rate which was faster than that observed not only for their non-porous analogs but also of the bulk P25 TiO₂ powder. Specifically, 90% removal for 20 μM MO was achieved within 220 min for the porous sc-CO₂ dried fibers while for their non-porous analogs at 325 min. The corresponding value (at 60 μM MO) for the porous sc-CO₂ dried fibers was 140 min over 240 min for the AEROXIDE^® TiO₂ P25 as documented in the literature. Furthermore the composite alginate/photocatalyst porous fibers were combined with TiO₂ membranes in a continuous flow, hybrid photocatalytic/ultrafiltration water treatment process that led to a three fold enhancement of the MO removal efficiency at 400 ml of 20 μM MO total treated volume and to dilution rather than condensation in the membrane retentate as commonly observed in filtration processes. Furthermore the permeability of the photocatalytic membrane was enhanced in the presence of the fibers by almost 20%. This performance is achieved with 26 cm² and 31 cm² of membrane and stabilized photocatalyst surfaces respectively and in this context there is plenty of room for the up-scaling of both membranes and fibers and the achievement of much higher water yields since the methods applied for the development of the involved materials (CVD and dry-wet phase inversion in a spinning set-up) are easily up-scalable and are not expected to add significant cost to the proposed water treatment process.     

Virus disinfection in water by biogenic silver immobilized in polyvinylidene fluoride membranes

The development of innovative water disinfection strategies is of utmost importance to prevent outbreaks of waterborne diseases related to poor treatment of (drinking) water. Recently, the association of silver nanoparticles with the bacterial cell surface of Lactobacillus fermentum (referred to as biogenic silver or bio-Ag⁰) has been reported to exhibit antiviral properties. The microscale bacterial carrier matrix serves as a scaffold for Ag⁰ particles, preventing aggregation during encapsulation. In this study, bio-Ag⁰ was immobilized in different microporous PVDF membranes using two different pre-treatments of bio-Ag⁰ and the immersion-precipitation method. Inactivation of UZ1 bacteriophages using these membranes was successfully demonstrated and was most probably related to the slow release of Ag⁺ from the membranes. At least a 3.4 log decrease of viruses was achieved by application of a membrane containing 2500 mg bio-Ag⁰_powder m⁻² in a submerged plate membrane reactor operated at a flux of 3.1 L m⁻² h⁻¹. Upon startup, the silver concentration in the effluent initially increased to 271 μg L⁻¹ but after filtration of 31 L m⁻², the concentration approached the drinking water limit ( = 100 μg L⁻¹). A virus decline of more than 3 log was achieved at a membrane flux of 75 L m⁻² h⁻¹, showing the potential of this membrane technology for water disinfection on small scale.     

Combination of one-dimensional TiO2 nanowire photocatalytic oxidation with microfiltration for water treatment

This paper proposed the fabrication of two different diameter one-dimensional TiO₂ nanowires, 10 nm TNW₁₀ and 20-100 nm TNW₂₀, via hydrothermal process using different alkaline sources. TNW₁₀ and TNW₂₀ were used as photocatalysts for the degradation of humic acid (HA), the major natural organic matters (NOMs) in surface and ground water, followed by microfiltration. The evaluation of photocatalytic activities of them showed that TNW₁₀ was superior to the commercial P25 TiO₂ while TNW₂₀ was as good as P25. The membrane filtration verified that the two types of nanowires could be completely reclaimed. The membrane fouling caused by TNW₁₀ and TNW₂₀ was much less than that of P25 due to more porous cake and less pore plugging. No apparent decrease on their photocatalytic activity was observed in repeated reuse experiments. These one-dimensional TiO₂ nanowires would provide a new route for the combination of photocatalytic oxidation and membrane filtration for water treatment.     

Novel, bio-based, photoactive arsenic sorbent: TiO2-impregnated chitosan bead

A novel sorbent for arsenic, TiO₂-impregnated chitosan bead (TICB), has been synthesized and successfully tested. Kinetic plots, pH dependence, isotherm data, and bead morphology are reported. Equilibrium is achieved after 185 h in batch experiments with exposure to UV light. The TICB system performs similarly to the mass equivalent of neat TiO₂ nanopowder. The point of zero charge (pzc) for TICB was determined to be 7.25, and as with other TiO₂-based arsenic removal technologies, the optimal pH range for sorption is below this pH_pzc. Without exposure to UV light, TICB removes 2198 μg As(III)/g TICB and 2050 μg As(V)/g TICB. With exposure to UV light, TICB achieves photo-oxidation of As(III) to As(V), the less toxic and more easily sequestered arsenic form. UV irradiation also results in enhanced arsenic removal, reaching sorption capacities of 6400 μg As/g TICB and 4925 μg As/g TICB, where arsenic is initially added as As(III) and As(V), respectively. Because the TICB system obviates filtration post-treatment, TICB is superior to TiO₂ nanopowder from the perspective of implementation for decentralized water treatment.     

Concurrent filtration and solar photocatalytic disinfection/degradation using high-performance Ag/TiO2 nanofiber membrane

A facile polyol synthesis was used for the deposition of Ag nanoparticles on electrospun TiO₂ nanofibers for the subsequent fabrication of Ag/TiO₂ nanofiber membrane. The permeate flux of the Ag/TiO₂ nanofiber membrane was remarkably high compared to commercial P25 deposited membrane. The Ag/TiO₂ nanofiber membrane achieved 99.9% bacteria inactivation and 80.0% dye degradation under solar irradiation within 30 min. The Ag/TiO₂ nanofiber membrane also showed excellent antibacterial capability without solar irradiation. Considering the excellent intrinsic antibacterial activity and high-performance photocatalytic disinfection/degradation under solar irradiation, this novel membrane proved to have promising applications in water purification industry.     

TiO2-WO3 nanocube-polyaniline hierarchical membrane for efficient removal of chromium in a photocatalytic membrane reactor

In this article, the rational design of a physically coated TiO₂-WO₃ nanocube-polyaniline photocatalytic membrane (hierarchical) reactor for the efficient reduction of chromium (VI) under visible light is discussed. The incorporation of TiO₂-WO₃ in the polyaniline (PANI) membrane provides excellent hydrophilicity and high photo-corrosion resistance and facilitates the rapid permeation of water with a flux rate of 12 L/m² h and higher Cr (VI) reduction. The exposure of bare PANI membranes in Cr (VI) solution leads to over-oxidation of PANI membrane and eventually leads to the destruction of the membrane. The hierarchical photocatalytic coating improves the lifetime of the membrane by blocking it from deprotonation. The photocatalytic membrane could offer 79.30% Cr (VI) reduction under visible light irradiation in a photocatalytic membrane reactor. After several reduction cycles, the membrane showed good self-cleaning ability. The present work suggests that TiO₂-WO₃ nanocube-coated PANI hierarchical membrane is a promising approach for the reduction and removal of Cr (VI) from wastewater.     

Comparison of fouling characteristics of two different poly-vinylidene fluoride microfiltration membranes in a pilot-scale drinking water treatment system using pre-coagulation/sedimentation, sand filtration, and chlorination

Two pilot-scale hybrid water treatment systems using two different poly-vinylidene fluoride (PVDF) microfiltration (MF) membranes (i.e. symmetric and composite) were operated at a constant permeate flux of 104.2l m(-2)h(-1) (=2.5 md(-1)) with a pre-coagulation/sedimentation, sand filtration (SF), and chlorination to produce potable water from surface water. Turbidity was removed completely. And humic substances, Al, and Fe were removed very well by the pilot-scale membrane system. To control microbial growth and mitigate membrane fouling, a NaOCl solution was injected into the effluent from SF before reaching the two membranes (pre-chlorination). However, it adversely affected membrane fouling due to the oxidization and adsorption of inorganic substances such as Al, Fe, and Mn. In the next run, the NaOCl was introduced during backwash (post-chlorination). As compared with the result of pre-chlorination, this change increased the operating period of the symmetric and the composite membranes from about 10 and 50 days to about 60 and 200 days, respectively.     

Transparent exopolymer particle removal in different drinking water production centers

Transparent exopolymer particles (TEP) have recently gained interest in relation to membrane fouling. These sticky, gel-like particles consist of acidic polysaccharides excreted by bacteria and algae. The concentrations, expressed as xanthan gum equivalents L⁻¹ (μg X_eq L⁻¹), usually reach hundred up to thousands μg X_eq L⁻¹ in natural waters. However, very few research was performed on the occurrence and fate of TEP in drinking water, this far. This study examined three different drinking water production centers, taking in effluent of a sewage treatment plant (STP), surface water and groundwater, respectively. Each treatment step was evaluated on TEP removal and on 13 other chemical and biological parameters. An assessment on TEP removal efficiency of a diverse range of water treatment methods and on correlations between TEP and other parameters was performed. Significant correlations between particulate TEP (>0.4 μm) and viable cell concentrations were found, as well as between colloidal TEP (0.05-0.4 μm) and total COD, TOC, total cell or viable cell concentrations. TEP concentrations were very dependent on the raw water source; no TEP was detected in groundwater but the STP effluent contained 1572 μg X_eq L⁻¹ and the surface water 699 μg X_eq L⁻¹. Over 94% of total TEP in both plants was colloidal TEP, a fraction neglected in nearly every other TEP study. The combination of coagulation and sand filtration was effective to decrease the TEP levels by 67%, while the combination of ultrafiltration and reverse osmosis provided a total TEP removal. Finally, in none of the installations TEP reached the final drinking water distribution system at significant concentrations. Overall, this study described the presence and removal of TEP in drinking water systems.     

The influence of capsular extracellular polymeric substances on the interaction between TiO₂ nanoparticles and planktonic bacteria

The role of capsular extracellular polymeric substances (EPS) at the surface of planktonic microorganisms was investigated for possible toxicity mitigation from titanium dioxide (TiO₂) nanoparticles, using variable EPS producing wild-type and isogenic mutant strains of Pseudomonas aeruginosa. Membrane integrity assays revealed that increased capsular EPS reduced cell membrane damage. Acting as a barrier to the cell membrane, capsular EPS permitted attachment of nanoparticles to the cell, while simultaneously delaying cellular damage caused by the production of reactive oxygen species (ROS). Modulations in ROS production were monitored in situ; while changes in the chemical composition of the microorganisms before and after exposure were examined with Fourier transform infrared spectroscopy (FTIR). The addition of methanol, a known radical scavenger, was shown to vastly reduce ROS production and membrane integrity losses, while not affecting physical interactions of nanoparticles with the microorganism. The results support that EPS provides an attachment site for nanoparticles, but more importantly act as a barrier to cell membrane oxidation from ROS. These observations provide better understanding of the overall importance of ROS in TiO₂ microbial toxicity.     

Protein fouling behavior of carbon nanotube/polyethersulfone composite membranes during water filtration

The protein fouling of membranes can be related to the hydrophobic and electrostatic interactions between proteins and the membrane material; i.e., protein fouling can be reduced by changing the membrane properties. In this study, multi-walled carbon nanotube/polyethersulfone (C/P) composite membranes were prepared via the phase inversion method in order to investigate protein fouling, with bovine serum albumin (BSA) and ovalbumin (OVA) used as the model protein for assessing the protein fouling behavior. The results show that the C/P composite membranes were fouled less compared to the bare polyethersulfone (PES) membrane at 4 h of static protein adsorption at neutral pH. Moreover, the irreversible fouling ratio of the C/P composite membranes was less than the bare PES membrane after 1 h of protein ultrafiltration, and the flux recovery ratio of the C/P composite membranes was higher than the bare PES membrane after 20 min of DI water filtration. Based on these results, C/P composite membranes were shown to have the potential to alleviate the effects of protein fouling, thereby enabling C/P composite membranes to be used for several runs of protein filtration after simple washing with water.     

Relation between EPS adherence, viscoelastic properties, and MBR operation: Biofouling study with QCM-D

Membrane fouling is one of the main constraints of the wide use of membrane bioreactor (MBR) technology. The biomass in MBR systems includes extracellular polymeric substances (EPS), metabolic products of active microbial secretion that adversely affect the membrane performance. Solids retention time (SRT) in the MBR is one of the most important parameters affecting membrane fouling in MBR systems, where fouling is minimized at optimal SRT. Among the operating parameters in MBR systems, SRT is known to strongly influence the ratio of proteins to polysaccharides in the EPS matrix. In this study, we have direct evidence for changes in EPS adherence and viscoelastic properties due to changes in the sludge removal rate that strongly correlate with the membrane fouling rate and EPS composition. EPS were extracted from a UF membrane in a hybrid growth MBR operated at sludge removal rates of 59, 35.4, 17.7, and 5.9 L day^-1 (corresponding SRT of 3, 5, 10, and 30 days, respectively). The EPS adherence and adsorption kinetics were carried out in a quartz crystal microbalance with dissipation monitoring (QCM-D) technology in several adsorption measurements to a gold sensor coated with Polyvinylidene Fluoride (PVDF). EPS adsorption to the sensor surface is characterized by a decrease of the oscillation frequency and an increase in the dissipation energy of the sensor during parallel flow of aqueous media, supplemented with EPS, above the sensor surface. The results from these experiments were further modeled using the Voigt based model, in which the thickness, shear modulus, and shear viscosity values of the adsorbed EPS layers on the PVDF crystal were calculated. The observations in the QCM-D suggested that the elevated fouling of the UF membrane is due to higher adherence of the EPS as well as reduction in viscosity and elasticity of the EPS adsorbed layer and elevation of the EPS fluidity. These results corroborate with confocal laser scanning microscopy (CLSM) image analysis showing thicker EPS in close proximity to the membrane surface operated at reactor conditions which induced more fouling at elevated sludge removal rates.     

Modification of poly(vinylidene fluoride) ultrafiltration membranes with poly(vinyl alcohol) for fouling control in drinking water treatment

A commercial poly(vinylidene fluoride) flat sheet membrane was modified by surface coating with a dilute poly(vinyl alcohol) (PVA) aqueous solution followed by solid-vapor interfacial crosslinking. The resulting PVA layer increased membrane smoothness and hydrophilicity and resulted in comparable pure water permeation between the modified and unmodified membranes. Fouling tests using a 5 mg/L protein solution showed that a short period of coating and crosslinking improved the anti-fouling performance. After 18 h ultrafiltration of a surface water with a TOC of approximately 7 mg C/L, the flux of the modified membrane was twice as high as that of the unmodified membrane. The improved fouling resistance of the modified membrane was related to the membrane physiochemical properties, which were confirmed by pure water permeation, X-ray photoelectron spectroscopy, and contact angle, zeta potential and roughness measurements.     

Water Management In Textile Industry: Technical And Economic Aspects

Textile industry is an intensive water use sector. Consequently, enormous quantities of wastewater are generated from different manufacturing processes. Numerous opportunities for water reuse could be exploited by rational management of water use and reuse via segregation and upgrading of specific effluents using membrane filtration systems comprising ultrafiltration (UF) and reverse osmosis (RO). This paper is an endeavor to develop technoeconomic indicators for extended water reuse applications in textile industry using UF and RO. Extensive data gathered from a typical Egyptian dye house have been utilized to rationalize water use and reuse management based on different levels of pollutants in waste streams. A developed rationale enabled the identification of four applicable intervention scenarios comprising three reuse scenarios ranging from limited reuse (about 25%) to maximum reuse (about 87%) and a total end of the pipe treatment scenario. The financial assessment for a typical wastewater load (about 3500 r m/day) reveals that the maximum reuse scenario comprising UF, two stage RO in addition to direct use and low press RO is the most preferred one. Further, sensitivity analysis indicates that the annual cost of the total end of pipe treatment scenario will equal the annual cost of the maximum reuse scenario when the unit cost are US$ 0.5, 0.43 and 0.3 per cubic meter for wastewater treatment, RO and UF respectively.     

Comparison of the removal of hydrophobic trace organic contaminants by forward osmosis and reverse osmosis

We compared the rejection behaviours of three hydrophobic trace organic contaminants, bisphenol A, triclosan and diclofenac, in forward osmosis (FO) and reverse osmosis (RO). Using erythritol, xylose and glucose as inert reference organic solutes and the membrane pore transport model, the mean effective pore size of a commercial cellulose-based FO membrane was estimated to be 0.74 nm. When NaCl was used as the draw solute, at the same water permeate flux of 5.4 L/m² h (or 1.5 μm/s), the adsorption of all three compounds to the membrane in the FO mode was consistently lower than that in the RO mode. Rejection of bisphenol A and diclofenac were higher in the FO mode compared to that in the RO mode. Because the molecular width of triclosan was larger than the estimated mean effective membrane pore size, triclosan was completely rejected by the membrane and negligent difference between the FO and RO modes could be observed. The difference in the separation behaviour of these hydrophobic trace organics in the FO (using NaCl the draw solute) and RO modes could be explained by the phenomenon of retarded forward diffusion of solutes. The reverse salt flux of NaCl hinders the pore diffusion and subsequent adsorption of the trace organic compounds within the membrane. The retarded forward diffusion effect was not observed when MgSO₄ and glucose were used as the draw solutes. The reverse flux of both MgSO₄ and glucose was negligible and thus both adsorption and rejection of BPA in the FO mode were identical to those in the RO mode.     

Membrane vis-LED photoreactor for simultaneous penicillin G degradation and TiO2 separation

The hybrid membrane photoreactor (MPR) combining a photoreactor irradiated with visible-light-emitting diode (vis-LED) and a cross-flow microfiltration (MF) membrane module was investigated in both closed-loop and continuous flow-through modes for the simultaneous degradation of penicillin G (PG) and separation of visible-light responsive TiO₂ particles, namely C-sensitized-N-doped TiO₂ (T300) and C-N-S tridoped TiO₂ (T0.05-450). The turbidity of permeate water was <0.2 NTU for both T300 and T0.05-450 suspensions in the MPR system operated at different transmembrane pressures (TMPs) and cross-flow velocities (CFVs), indicating effective separation of TiO₂ particles by the MF membrane. The operations at a higher TMP or lower CFV were more prone to induce TiO₂ deposition on the membrane surface without backwashing, which resulted in the membrane fouling, the loss of TiO₂ from the photoreactor and the decrease of PG photocatalytic degradation efficiency. 75% and 84% of PG were degraded in the closed-loop MPR without backwashing operated at 10 kPa and 0.15 m s⁻¹ after 4 h of vis-LED irradiation using 1.0 g L⁻¹ of T300 and T0.05-450, respectively. With backwashing of the membrane, the PG photocatalytic degradation efficiencies in the closed-loop MPR could be significantly enhanced to achieve 93% and 95% using 1.0 g L⁻¹ of T300 and T0.05-450, respectively, which were almost comparable to those achieved in the batch photoreactor. Due to its shorter hydraulic residence time in the photoreactor, the PG degradation efficiency in the continuous flow-through MPR with backwashing was lower than that achieved in the closed-loop MPR.     

Preparation of free‐standing chitosan membranes for Chlorella vulgaris harvest and examination on suppression of algae‐fouling properties

Free‐standing chitosan membranes were prepared using genipin as crosslinker, using several molecular weights of polyethylene glycol (PEG) as a void‐forming agent. The membrane surface formation and chitosan polymer chain crosslinking were confirmed through SEM and FTIR, respectively. The water flux was remarkably increased with increasing molecular weight of PEG employed in preparation of composite chitosan membrane (J∝[PEG(MW)]0.85), it appeared over 6000 Da of PEG. During Chlorella vulgaris harvest using chitosan membranes, focus was made on algae‐fouling caused by the deposition of cells and extracellular organic matter, and it was found that membranes employing lower molecular weight of PEG (under 10000 Da) had been maintaining the high flux recovery after alternating filtration cycles, in addition to PEG20000 containing membrane. The chitosan membrane prepared with lower molecular weight of PEG exhibited better suppression of algae‐fouling properties. The Chlorella vulgaris harvesting results indicated that cell rejection rate reached above 98%.     

纳米TiO_2改性膜生物反应器处理污水的研究

采用啧涂纳米TiO2的方法对聚偏氟乙烯（PVDF）微滤膜进行改性,用改性膜生物反应器（MBR）和非改性MBR处理污水,对比了两者的出水水质、膜通量和膜过滤阻力。结果表明,两套MBR的出水水质均可达到《生活杂用水水质标准》（CJ25．1—89）的要求;纳米TiO2改善了膜表面的亲水性和粗糙度,从而使改性MBR的清水膜过滤阻力和不同抽吸压力下的膜过滤阻力均低于非改性MBR的,而其在不同抽吸压力下的稳定膜通量则高于非改性MBR的。     

Colloid straining within saturated heterogeneous porous media

The transport of 0.46 μm, 2.94 μm, 5.1 μm and 6.06 μm latex particles in heterogeneous porous media prepared from the mixing of 0.78 mm, 0.46 mm and 0.23 mm quartz sands was investigated through column transport experiments. It was observed that the 0.46 μm particles traveled conservatively within the heterogeneous porous media, suggesting that under the experimental conditions employed in this research the strong repulsive interactions between the negatively charged latex particles and the clean quartz sands led to minimal colloid immobilization due to physicochemical filtration. The immobilization of the 2.94 μm, 5.1 μm and 6.06 μm latex particles was thus attributed to colloid straining. Experimental results showed that the straining of colloidal particles within heterogeneous sand mixtures increased when the fraction of finer sands increased. The mathematical model that was developed and tested based on results obtained using uniform sands (Xu et al., 2006) was found to be able to describe colloid straining within heterogeneous porous media. Examination of the relationship between the best-fit values of the clean-bed straining rate coefficients (k₀) and the ratio of colloid diameter (d_p) and sand grain size (d_g) indicated that when number-average sizes were used to represent the size of the heterogeneous porous media, there existed a consistent relationship for both uniform sands and heterogeneous sand mixtures. Similarly, the use of the number-averaged sizes for the heterogeneous porous media produced a uniform relationship between the colloid straining capacity term (λ) and the ratio of d_p/d_g for all the sand treatments.