External Mass Transfer Coefficient Research Articles

Ultrasound-enhanced adsorption of amino acids from aqueous solution onto macroporous resins for green separation: Mass transfer mechanism and acoustic cavitation properties

The utilization of green technology for the recovery of renewable components has garnered significant attention. In this study, efficient and rapid separation of amino acids from aqueous solutions was achieved through ultrasound-assisted macroporous resin adsorption. The numerical simulation revealed the underlying mechanism of mass transfer during ultrasound-assisted adsorption and clarified the impact of acoustic properties on the adsorption process. Low-frequency (LFUS, 20 kHz) caused the damage of resin structure and the increase of adsorption capacity whereas these were less influenced by high-frequency ultrasound (HFUS, 1056 kHz). The external mass transfer coefficient was increased by 161% and 45% during LFUS- and HFUS-assisted adsorption than agitation-assisted adsorption. In addition, both US modes contributed to an enhancement of surface diffusion coefficient by over 100%. The predominant factor governing the intraparticle diffusion for amino acid adsorption was found to be pore volume diffusion, accounting for more than 70% of the overall process. Both LFUS and HFUS were observed to augment the influence of surface diffusion within the overarching diffusion phenomenon, aligning with the concurrent elevation of the surface diffusion coefficient. Furthermore, the mechanism of ultrasound-assisted adsorption was illustrated from the aspect of physical and sonochemical effects generated by the acoustic cavitation. The accumulated acoustic pressure of LFUS exceeded that of HFUS by a factor of 105, reflecting its strong physical effects. The connection between the mass transfer behaviour and acoustic bubble properties during ultrasound-assisted adsorption can provide guidance for the industry to apply ultrasound as a green technology to separate and recover renewable biomaterials from wastewater.

Feasibility of nitrate adsorption from aqueous solution by nitrogen and oxygen-modified pine bark biochar: experimental and computational approach

Efficient and economical wastewater treatment has presented itself as a global challenge. In this context, adsorption is one of the most effective methods to remove contaminants from wastewater. The present study evaluated the feasibility of chemically modified pine bark biochar’s nitrate adsorption ability. Pine bark biochar was modified with urea and sulfuric acid to remove nitrate from an aqueous solution. The physicochemical properties of the biochar samples, such as pH, pH at point of zero charges, surface atomic composition, surface morphology, and surface area, were evaluated. The equilibrium adsorption data were fitted to the Langmuir and Freundlich isotherm models. The kinetic data were fitted to different kinetic models (pseudo-first order, pseudo-second order, intraparticle diffusion, and Elovich). The adsorption data fitted well with the Langmuir and pseudo-first order models. The maximum nitrate adsorption capacity was found to be 1.548 mg g−1. Mass transfer studies were conducted to identify the rate-limiting step, values of the external mass transfer coefficient, and diffusion coefficient in the nitrate adsorption process by the modified biochar. The external mass transfer coefficients were in the range of 2.2 × 10–11–2.86 × 10–10 m s−1. The intraparticle diffusion coefficient ranged from 6.53 × 10–10 to 1.78 × 10–9 m2 s−1. The Biot number value less than 100 indicated that the adsorption was controlled by film diffusion. Interaction energies between nitrate ions and model biochar structures were calculated DFT-based quantum chemical software (Gaussian). The positive interaction energy values (2.3485–2.485 eV) suggested nitrate adsorption on model biochar structures was thermodynamically not feasible.Graphical

Adsorption kinetics and equilibrium performance of Di-n-butyl phosphate on XAD-4 and XAD-7 from alkaline medium

ABSTRACT The present study investigates the feasibility of adsorption method for the removal of Di-n-butyl phosphate from sodium carbonate solution on adsorbents such as XAD-4 and XAD-7. The fundamental aspects of equilibrium and kinetics of adsorption have been studied. The experimental equilibrium data were fitted well with Sips isotherm, and maximum solid uptake capacity for monolayer coverage (qm) was found to be 0.363 × 10−3 mol/g and 0.385 × 10−3 mol/g for XAD-4 and XAD-7, respectively. The adsorption kinetics was well described by the pseudo-first-order model, and estimated first-order rate constant values were found to be 0.041 min−1 for XAD-4 and 0.027 min−1 for XAD-7. The transport mechanism of solute from the bulk solution to adsorbent was described in detail with suitable mathematical model, and experimental kinetic data were superimposed on numerically solved concentration profiles to calculate external mass transfer coefficient (kf) and effective diffusivity (De). The values of kf and De were estimated as 4.632 × 10−7 m/s and 8.849 × 10−13 m2/s, respectively, for XAD-4, whereas for XAD-7, the values were found to be 2.132 × 10−6 m/s and 1.389 × 10−12 m2/s. XAD-7 is found to have slightly better adsorption capacity and transport characteristics than XAD-4.

An engineered biochar for treatment of selenite contaminated water: Mass transfer characteristics in fixed bed adsorption

Biochar composites have been gaining attention in recent years as a promising and cost-effective material for wastewater treatment. In the present study, a novel procedure was developed to create a biochar (BC) composite impregnated with binary zinc (Zn) and iron (Fe) oxides (denoted as ZnFeBC). The procedure was optimized to enhance selenite, Se(IV), adsorption performance of the ZnFeBC composite. The modified biochar composite had excellent pore characteristics with a specific surface area of 854 m2/g. The maximum Se(IV) adsorption capacity of an unary Zn-loaded biochar composite was 520 µg/g, which significantly increased to 4,100 µg/g after the iron oxide impregnation. Isotherm experiments suggested that the adsorption process was likely through homogeneous monolayer adsorption. The ZnFeBC composite exhibited excellent performance over a broad range of pH values, with the highest Se(IV) adsorption capacities observed at lower pH values (maximums at pH 3). X-ray absorption near edge structure spectroscopy (XANES) indicated that the redox reaction of Se oxyanions did not occur during the adsorption process. ZnFeBC was successfully used to remove Se(IV) from a mining lake water matrix in a fixed-bed adsorption system. Additionally, a mass transfer model optimizing effective diffusion and external mass transfer coefficients was developed to comprehensively assess the adsorption system. Overall, ZnFeBC exhibited great potential as an adsorbent for treating Se(IV) contaminated waters and the developed mass transfer model is useful for scaling up fixed-bed adsorption systems.

Mechanism modeling and application of Salvia miltiorrhiza percolation process

Percolation is a common extraction method of food processing industry. In this work, taking the percolation extraction of salvianolic acid B from Salvia miltiorrhiza (Salviae Miltiorrhizae Radix et Rhizoma) as an example, the percolation mechanism model was derived. The volume partition coefficient was calculated according to the impregnation. experiment. The bed layer voidage was measured by single-factor percolation experiment and the internal mass transfer coefficient was calculated by the parameters obtained by fitting the impregnation kinetic model. After screening, the Wilson and Geankoplis, and Koch and Brady formulas were used to calculate the external mass transfer coefficient and the axial diffusion coefficient, respectively. After substituting each parameter into the model, the process of percolation of Salvia miltiorrhiza was predicted, and the coefficient of determination R2 was all greater than 0.94. Sensitivity analysis was used to show that all the parameters studied had a significant impact on the prediction effect. Based on the model, the design space including the range of raw material properties and process parameters was established and successfully verified. At the same time, the model was applied to the quantitative extraction and endpoint prediction of the percolation process.

Adsorption mechanism and mass transfer modeling of cesium and europium ions adsorption onto hematite-loaded polyacrylamide-gel composite: Pore Volume and Surface Diffusion Model Approach

The overall adsorption rate of cesium (Cs+) and europium (Eu3+) ions onto hematite-loaded polyacrylamide-gel composite (HPAC) in single and binary pollutant systems was explained with diffusional model that takes into consideration both external mass transfer and intra-particle diffusion. The influence of changing system temperature on the overall adsorption rate of Cs+ and Eu3+ onto HPAC was studied. The fitting process of the experimental data with the three studied isotherm models (Langmuir, Freundlich and Prausnitz–Radke (P-R)) showed that Prausnitz–Radke model has the highest correlation coefficients with the smallest average relative error percentage. The maximum P-R adsorption capacity of HPAC decreased from 2.06 and 3.35 L/g in single pollutant solution to 1.02 and 1.51 L/g in binary pollutant solution at 298 K for Cs+ and Eu3+,respectively. The values of surface diffusion coefficient (DS) ranged within 10−8 for Cs+ and 10−8-10−9 cm2/s for Eu3+ in both studied single and binary pollutant systems. The external mass transfer coefficient (KF) was in the range of 10−4 for Cs+ and 10−3 cm/s for Eu3+ in both studied systems. Lastly, the Biot number (Bi) exposed that the diffusion inside the particle controlled the studied cations's adsorption onto HPAC material.

Interplay between membrane imperfections and external concentration polarization

Reverse osmosis membranes provide a highly effective and efficient barrier against various kinds of pollutants. Their reliability depends on the integrity of the active layer: in case the active layer is damaged and contains imperfections, unfiltered feed solution can contaminate the permeate. Various types of integrity monitoring techniques have been developed to verify membrane performance, of which the rejection of fluorescent dyes is a well-established technique. Fluorescent dyes are however relatively small solutes for which the membranes can display non-zero diffusive permeability, such that not all dye passage can be attributed to membrane imperfections. Additionally, fluorescent dyes are subject to external concentration polarization (ECP) during filtration, causing a flux-dependent enrichment at the membrane surface, further complicating the analysis of dye rejection data. This study presents a model to discern between membrane permeability, enrichment by ECP and passage through imperfections. The consequences of imperfections on solute passage are explored, showing that imperfections only contribute significantly to the passage of solutes with a low membrane permeability. This leads to underestimates of the external mass transfer coefficient, with the error being increasingly large with decreasing membrane permeability coefficient, relative to the case of an imperfection-free membrane. This error is then related to the proportionality of the Sherwood number, used to calculate external mass transfer coefficients, with solute diffusivity, allowing the quantification of the contribution of imperfections to water flux. The model was experimentally verified using Pyranine rejection in two membrane types, both operated in a lab-scale flat sheet crossflow test system, finding proof of imperfections in one membrane type.

Phosphate removal by Ca(OH)2-treated natural minerals: Experimental and modeling studies

Adsorption of phosphate phosphorus (PO4-P) from wastewater onto eco-friendly geosorbents has gained great attention aiming at recovering an essential nutrient for crop production. Notably, the literature on PO4-P aqueous-phase adsorption kinetics is limited to the application of either empirical reaction-based models lacking a physical significance or over-simplified diffusion-based models frequently used outside their applicability area. In this study, equilibrium and kinetic experiments are presented under a wide range of phosphate concentrations (50–500 mg P/L) using sustainable and low-cost modified adsorbents. The kinetics of PO4-P adsorption from aqueous solutions onto Ca(OH)2-treated zeolite (CaT-Z) and bentonite (CaT-B) was analyzed by a dimensionless two-phase homogeneous surface diffusion model (TP-HSDM) assuming constant diffusivity coupled with the double selectivity isotherm equation (DSM). The TP-HSDM fit to the data at four initial P concentrations (50, 100, 200 and 300 mg/L) resulted in an average relative error of 14.6% and 17.4% from the experimental data for CaT-Z and CaT-B, respectively. The average surface diffusion coefficient (Ds) ranged from 2.5 × 10-10 to 8.7 × 10-10 cm2/s for CaT-Z and from 1.6 × 10-10 to 4.78 × 10-9 cm2/s for CaT-B. The external mass transfer coefficient (kf) ranged from 2.72 × 10-4 to 8.38 × 10-4 cm/s for CaT-Z and from 5.63 × 10-4 to 2.24 × 10-3 cm/s for CaT-B. The dimensionless Biot (Bi) number exhibited values in the order of magnitude of 105 indicating that the intraparticle diffusion is the controlling mass transfer mechanism for both materials.

Mathematical Modelling of the Removal of Basic Blue Dye from Effluent by a Mineral Membrane

Water contamination is a major challenge due to the discharging of wastes into the natural resources. In this study, a novel branched pore adsorption model was developed by utilizing external mass transfer coefficients, Kf , effective diffusivity, and lumped microspore diffusion rate parameters. This describes sorption kinetics from long-term adsorption that occurs between an adsorbent and an adsorbate. An investigation of the effects of dye concentration on Basic Blue 9 removal was conducted. Then by considering of initial and boundary conditions the government equations were solved. Using this model, the Basic Blue 9 (or methylene blue is an industrial inhibitor) was removed from a bentonite sample polluted by Basic Blue 9. The maximum adsorption capacity was achieved by using of Freundlich analysis. Based on the experimental data, theoretical concentration - time adjusted models were developed using a FORTRAN computer program to fit the experimental data more precisely and confirm the precision and accuracy of this research.

Pore volume and surface diffusion model to characterize batch adsorption of Cu(II) over chemically modified Cucurbita moschata biosorbent: simulation using gPROMS

Abstract This work describes the successful application of the pore volume and surface diffusion (PVSD) model characterizing the batch adsorption of Cu(II) on a chemically modified Cucurbita moschata biosorbent. The PVSD model captures the convective transport of Cu(II) from the bulk solution to the biosorbent surface, followed by its surface and pore diffusion inside the biosorbent. The adsorption of Cu(II) is mimicked using the Langmuir isotherm. The algebraic, ordinary, and partial differential equations, involved in the PVSD model, are solved using the general process modeling system (gPROMS). The model simulation results, depicted by the Cu(II) concentration decay curve, show an excellent match with experimental data. The external mass transfer coefficient (≈10−3 m/s) indicated no restriction on approaching Cu(II) toward the biosorbent surface. Within the biosorbent, surface diffusion was dominant over pore volume diffusion. The statistical analysis of the PVSD model results has been done by calculating R2, Chi-square value, normalized standard deviation, p-value, and root-mean-square error. The PVSD model approach presented in this work could be beneficial to other heavy metal–biosorbent systems.

Intensification of autocatalytic methyl oleate synthesis in continuous flow rotating recycle reactor under hybrid radiation: Process optimization and Scale-up

Intensification of the autocatalytic esterification of methanol with oleic acid for producing methyl oleate (biodiesel) was accomplished using a continuous flow rotating reactor under recycle mode. To exaggerate the biodiesel yield, highly efficient hybrid electromagnetic radiation (near-infrared and microwave irradiation) was used as an energy source. Spherical-shaped nano-zinc-titanate photocatalyst (low band-gap energy: 2.01 eV and low recombination rate) was prepared and utilized in the aforementioned novel reactor. Box-Behnken statistical optimization technique was applied to attain the optimum condition (catalyst concentration 30 wt%, reaction temperature 333 K, methanol: oleic acid mole ratio 11:1, LHSV: 0.20 min−1) resulting in maximum biodiesel yield. Moreover, at optimum rotating speed (∼235 rpm), high external and internal mass transfer coefficients were achieved which rendered a remarkably augmented reaction rate under ideal reactor behavior (Dispersion number: 6.42 × 10−7). A geometric-based COMSOL model was simulated which confirmed uniformity of hybrid irradiation and temperature distribution within the rotating catalytic packed bed; which was applied for the development of a parallel-autocatalytic reaction kinetic model. Langmuir Hinshelwood kinetics of the parallel autocatalytic esterification is well represented in the experimental data (RSSQ=1.52×10-7). Without recycle stream, the reaction exhibited a non-autocatalytic reaction with a lower yield of 79.04 % biodiesel within 0.20 min−1 LHSV, whereas, under recycle mode, the biodiesel yield was increased up to 93.55 % even at a higher LHSV of 0.25 min−1. For larger-scale production of the methyl oleate, the ASPEN PLUS simulator has been deployed for a throughput scale-up factor of 1000 (geometric similarity), which corroborates well with lab-scale yield/reactor performance.

Modeling of Batch Organic Dye Adsorption Using Modified Metal‐Organic Framework‐5

AbstractModeling and simulation of batch adsorption of the organic dye methylene blue (MB) by modified metal‐organic framework‐5 (MOF‐5) were investigated. The reported data on the adsorption of MB dye onto Wells‐Dawson acids (H6P2W18O62)‐immobilized MOF‐5 were employed. The film‐pore diffusion model was developed based on external mass transfer coefficient and pore diffusion coefficient that govern the mass transfer process in batch organic dye adsorption. Applying the estimated parameters, the MB adsorption by using modified MOF‐5 was examined to evaluate the effects of MOF‐5 modification, initial dye concentration, temperature, and the dosage of adsorbent. The adsorption capacity of modified MOF‐5 (H6P2W18O62/MOF‐5) was higher than pure MOF‐5. Besides, a lower initial MB dye concentration, higher temperature, and lower adsorbent dosage resulted in higher MB dye adsorption capacity.

Enfoques analítico e híbrido neuro-diferencial para la descripción de la remoción de contaminantes de sistemas acuosos

In this study, both analytical and hybrid-neuro-differential formulations were developed for describing the contaminant removal from wastewater by adsorption. The sorption isotherm, expressed as a straight-line equation (single segment or piecewise function) or artificial neural network (ANN), was coupled to the balance equations describing the pollutant transfer in adsorbent and wastewater phases, and their contact interface. The resulting wastewater adsorption remediation model (WARM) is valid for both batch and continuous operations, does not consider a dominant internal or external resistance to mass transfer or instantaneously equilibrated adsorbent, and has an analytical solution when a straight-line isotherm is used. The applicability of current model was tested in the analysis of two experimental datasets from literature describing the removal of the anionic dye direct red 23 (DR23) by graphene oxide (GO) and 4-nitrophenol (4NP) on calcium alginate-multiwall carbon nanotube beads (CAMCNB), where internal and external mass transfer coefficients and sorption isotherm parameters were simultaneously estimated by nonlinear regression. The analytical and hybrid-neuro-differential formulations were further compared with a numerical one where the WARM was coupled to Langmuir isotherm. Besides, the model was also used to explore different scenarios for continuous operation with all tested isotherms. It was demonstrated that the proposed formulations based on straight-line and ANN isotherms achieved a good reproduction of both dynamic and equilibrium experimental data, with similar fitness indices to that obtained with other non-linear equilibrium models.

Removal of indoor air ozone using carbon-based filters: Systematic development and validation of a predictive model

Exposure to ozone can cause several adverse health effects on human beings. Carbon-based filters are usually used for the removal of ozone from indoor air. The main problem with Carbon-based filters technology is the exhaustion of carbon because of irreversible reactions with ozone. Therefore, the knowledge of the service life of filters is crucial for building engineers and designers. Since testing at low indoor concentrations is time-consuming and expensive, the existing standards suggest experimenting with high concentrations. Thus, predictive models need to be developed to estimate the service life of filters. This work provides a model to estimate the breakthrough curves of three different combined (multi-layer) filters. The model augmented mass transfer equations with a reaction rate model and divided them into interpellet mass transfer and kinetic models. First, the reaction rate parameters were measured by fitting the model onto experimental data of all filters challenged with 9 ppm or 90 ppm of ozone. This was followed by validating the model for lower concentrations. In addition, to show the model validity for real-life application, its prediction was compared with the experimental data collected using the full-scale experimental setup and higher velocity. There was excellent agreement between the model prediction and the experimental results for all filters. Furthermore, an inter-model comparison was performed to determine the importance of different mass transfer steps. The results showed internal diffusion and axial dispersion as rate-limiting steps along with reaction. Finally, a sensitivity analysis was conducted on reaction kinetic parameters, axial dispersion coefficient, external mass transfer coefficient, and activated carbon particle porosity, which indicated negligible effects of external mass transfer and porosity variations.

A novel method for fabrication of a binary oxide biochar composite for oxidative adsorption of arsenite: Characterization, adsorption mechanism and mass transfer modeling

Arsenite [As(III)] is more mobile and toxic than arsenate [As(V)], making it more difficult and more critical to remove from water. The oxidative adsorption of As(III) is preferred due to its cost and time effectiveness. The chemical mixing process is a common method for preparation of biochar composites, but it is not time-efficient for homogeneous metal impregnation and is challenging to achieve consistent and reproducible physicochemical properties of the composite. The mixing method is even more challenging if two metal oxides are utilized in preparing engineered biochars. The current study proposes a novel microwave- and electrochemical-assisted technique to overcome the shortcomings of the mixing method and create a binary-oxide biochar composite with oxidation and adsorption capabilities. In addition, a new procedure was used to develop a diffusional mass transfer model combined with a genetic algorithm to characterize the adsorption process. Characterization of the fabricated biochar indicated that the deposited Fe and Mn oxides on the biochar surface included a mixture of Mn(II,III,IV) oxides and poorly crystalline α-FeOOH, respectively. The adsorption results suggested a hybrid adsorption mechanism with a high probability of a homogeneous monolayer adsorption process. Based on XANES analyses, no reduction to As(III) was observed for the As(V) adsorbed onto adsorbent, while 79% of the adsorbed As(III) was oxidized to As(V). The intraparticle diffusion and external mass transfer coefficients were estimated using a diffusional mass transfer model. Based on the modeling results, the adsorption of As onto the fabricated adsorbent was mainly controlled by external mass transfer. Overall the As(III) adsorption capacity of untreated biomass increased from 62 to 21,426 μg/g through the modification, indicating the high potential of the proposed procedure for preparation of adsorbents with improved oxidation and adsorption performance.

Modeling of anthocyanins adsorption onto chitosan films: An approach using the pore volume and surface diffusion model

The use of smart packaging is a global trend, and several works are being reported in this sense. Special attention is given to biodegradable materials like chitosan and natural pigments like anthocyanins. For example, previous studies report that it is possible to produce smart packaging by extracting anthocyanins from red cabbage and adsorbing it into chitosan films. This work elucidates for the first time the mass transfer aspects in the anthocyanins adsorption on chitosan films (CFS). Anthocyanins were extracted from red cabbage and subsequently adsorbed from the leach liquor using chitosan films. The Freundlich model well represented the adsorption isotherms of anthocyanins on CFS. In addition, the PVSDM (pore volume and surface diffusion model) model was implemented to represent the adsorption data and to elucidate the mass transfer. This model was suitable to represent the adsorption data, with a coefficient of determination (R2) higher than 0.95 and an average relative error (ARE) lower than 2.00%. The surface diffusion coefficient values (DS) ranged from 3.70 × 10−10 cm2 s−1 to 1.16 × 10−9 cm2 s−1. The external mass transfer coefficient (kF) was in the range of 10−2 cm s−1. Finally, the Biot number (Bi) revealed that mechanisms inside the particle controlled the anthocyanin's adsorption onto CFS.

Experimental and modeling investigation on char combustion and char-nitrogen evolution characteristics under different conditions

The proper description of char combustion and char-nitrogen (char-N) evolution characteristics are imperative to analyze the operating performance of decoupling combustion systems. The char-O2 combustion and char-CO2 gasification reactivity of three typical coal chars, including lignite, bituminous, and anthracite, was tested in a lab-scale fixed-bed reactor in the temperature range of 1023 K–1223 K. The relevant chemical kinetic parameters were determined by applying a one-dimensional packed-bed reactor model embedded with a lumped particle model. Meanwhile, a 1-dimensional spherical particle model is necessary for describing the char-N conversion behaviors. Experimental results show that the conversion rate of char-N in the entire bed to NO (XNO, bed) gradually decreases with increasing temperature, and the decrease of coal rank leads to a decline in the NOx emission. Further simulation results indicate that for a single char particle in the initial combustion stage, if the char particle size increases (0–1000 μm), the external gas mass transfer coefficient decreases (0–5 m·s−1), or the oxygen content decreases (0–20%), the char-N conversion to NO (XNO, p) will gradually decrease. However, due to the complicated effects of temperature on multiple factors, involving reactivity, CO/CO2 ratio in products, and dual nature of CO influence on char-NO reaction, the relationship between char-N conversion and temperature for a single particle is not fixed. When the oxygen concentration is low, the XNO, p increases as temperature rising; while, an opposite trend may be formed under high oxygen conditions.

Continuous Production of DHA and EPA Ethyl Esters via Lipase-Catalyzed Transesterification in an Ultrasonic Packed-Bed Bioreactor

Ethyl esters of omega-3 fatty acids are active pharmaceutical ingredients used for the reduction in triglycerides in the treatment of hyperlipidemia. Herein, an ultrasonic packed-bed bioreactor was developed for continuous production of docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA) ethyl esters from DHA+EPA concentrate and ethyl acetate (EA) using an immobilized lipase, Novozym® 435, as a biocatalyst. A three-level–two-factor central composite design combined with a response surface methodology (RSM) was employed to evaluate the packed-bed bioreactor with or without ultrasonication on the conversion of DHA + EPA ethyl ester. The highest conversion of 99% was achieved with ultrasonication at the condition of 1 mL min−1 flow rate and 100 mM DHA + EPA concentration. Our results also showed that the ultrasonic packed-bed bioreactor has a higher external mass transfer coefficient and a lower external substrate concentration on the surface of the immobilized enzyme. The effect of ultrasound was also demonstrated by a kinetic model in the batch reaction that the specificity constant (V′max/K2) in the ultrasonic bath was 8.9 times higher than that of the shaking bath, indicating the ultrasonication increased the affinity between enzymes and substrates and, therefore, increasing reaction rate. An experiment performed under the highest conversion conditions showed that the enzyme in the bioreactor remained stable at least for 5 days and maintained a 98% conversion.

A comprehensive investigation of external mass transfer and intraparticle diffusion for batch and continuous adsorption of heavy metals using pore volume and surface diffusion model

Separation of heavy metals from water bodies is a need of hour, to protect human kind, marine life, and the environment. In this context, adsorptive separation of heavy metal over cheap and environmental friendly biosorbent remains promising. Numerous studies have been carried out to characterize the adsorption of heavy metal ions through isotherms, kinetics, and simple mathematical models. However, such studies lacked in detailed mass transfer models evaluating heavy metal adsorption in batch and continuous modes. This work reports the application of pore volume and surface diffusion (PVSD) model investigating mass transfer processes of Cu (II), Cd (II), and Pb (II) adsorptions over alkali-treated Caryotaurens seeds, chemically modified Albizia lebbeck pods, and Schleichera oleosa bark, respectively, in batch and continuous modes. Heavy metal-biosorbent systems are represented by Freundlich, Temkin, and Langmuir isotherms, respectively. PVSD model equations (algebraic, ordinary, and partial differential equations) for batch and continuous modes are solved in gPROMS (General Process Modelling System). For validation, concentration decay and breakthrough curves concerning batch and continuous modes, respectively, are predicted and matched excellently with in-house experimental data and justified with R2 and RMSE values. In batch mode, external mass transfer coefficient suggested no constraint for heavy metal external transport, whereas, surface and pore volume diffusion coefficients were found to control the adsorption process. For continuous mode, breakthrough curves are predicted concerning metal solution flowrate, initial metal concentration, and bed height, and parameters viz. breakthrough time, exhaustion time, adsorption column capacity, and mass transfer zone are calculated. Axial dispersion and mass transfer coefficients signify negligible resistance for metal ions' bulk transport within the column. Surface and pore volume diffusions affected continuous adsorption process, with surface diffusion being dominant. The current PVSD model may represent other metal-biosorbent systems to estimate transport parameters suitable for continuous adsorber operation.

Effect of mixing intensity on biodegradation of phenol in a moving bed biofilm reactor: Process optimization and external mass transfer study

In this work, an effort has been made to design the process variables and to analyse the impact of mixing intensity on mass transfer diffusion in a moving bed biofilm reactor (MBBR). A lab-scale MBBR, filled with Bacillus cereus GS2 IIT (BHU) immobilized-polyethylene biocarriers, was employed to optimize the process variables, including mixing intensity (60–140 rpm), phenol concentration (50–200 mg/L), and hydraulic retention time (HRT) (4–24 h) using response surface methodology. The optimum phenol removal of 87.64 % was found at 100 rpm of mixing intensity, 200 mg/L of phenol concentration, and 24 h of HRT. The higher mixing intensity improved the substrate diffusion between the liquid phase and the surface of the biofilm. The external mass transfer coefficients were found in the range of 1.431 × 10-5-1.845 × 10-5 m/s. Moreover, the detection of catechol and 2-hydroxymuconic semialdehyde revealed that the Bacillus sp. followed the meta-cleavage pathway during the biodegradation of phenol.