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For precise prediction of the free settling velocities of the solid particle in the quiescent, the Newtonian fluid has been used for different liquid-particle systems, e.g., mineral processing, slurry pipelines, solid-liquid separation, and drilling. This study determined terminal settling velocity (TSV) from the fluidized bed experiments for binary particle mixture of the irregularly shaped particle and water as fluid. The influence of the particle diameter of the binary mixture on TSV was explored. Finally, a simple correlation was proposed to estimate the TSV for a binary mixture of irregular-shaped particles compared with the previously reported correlation in literature. TSV was also predicted with the help of a hybrid of genetic algorithm and artificial neural network (GAANN) model.

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... 19 The hybrid of GA and artificial neural network (ANN) was employed as an optimization technique over the past few years. 20,21 This work uses GA-ANN to speculate the percentage removal of Cu(II). ...

... A similar process was used by researchers in the past. 20,21,57,58 Variation of generation number with respect to the generation error was described in Figure 16. Table 8 gave the result of GA analysis. ...

The present study comprises the preparation of chitosan‐nTiO2 nanocomposites and their characterization with the help of scanning electron microscopy (SEM), Brunauer–Emmett–Teller (BET), Fourier transform infrared spectroscopy (FTIR), X‐ray diffraction (XRD), and thermogravimetric analysis (TGA). Various adsorbent samples are prepared with different weight ratios of chitosan to nTiO2. The adsorption capacity of the prepared adsorbents towards Cu(II) in an aqueous solution is also tested. The adsorption experiment is performed in batch mode under varying experimental conditions. Several isotherm and kinetic models are analyzed with the experimental data, and thermodynamic conditions required for adsorption are also determined. The highest elimination of Cu(II) was 39.19% with the adsorbent chitosan without nTiO2 (CWT) with 20 mg L⁻¹ initial Cu (II) concentration at adsorbent dosage 3 gL⁻¹ and 98.5% with the adsorbent CTNC1‐1 (chitosan/nTiO2 nanocomposite with the mass proportions of chitosan:nTiO2 = 1:1) and 93% with CTNC2‐1 (chitosan/nTiO2 nanocomposite with the mass proportions of chitosan:nTiO2 = 2:1) with 10 mg L⁻¹ initial Cu(II) concentration at adsorbent dosage 5 g L⁻¹. The isotherm model confirmed the monolayer adsorption. Maximum Langmuir adsorption capacities (qL) of the adsorbents for Cu(II) were given as CTNC1‐1 > CTNC2‐1 > CWT. The pseudo‐second‐order model excellently depicted the kinetic process with good correlation for all adsorbents. The statistical (R‐square is more than 0.99) and genetic algorithm (GA) model (R‐square is more than 0.99) effectively predicted the percentage removal of Cu(II).

... There are two main approaches to predicting the terminal velocity of non-spherical particles. One approach is to explore the independent effects of various shape factors (e.g., Corey shape factor [23,30,32,40], sphericity [17,42,43], and roundness [23,44,45]) on the particle terminal velocity. For instance, Dietrich [23] proposed a prediction model that accounted for the independent effects of the Corey shape factor and roundness. ...

The prediction of the terminal velocity of non-spherical particles, such as sediments and microplastics, is essential for understanding their transport processes in rivers or marine environments. However, most of the existing models have been proposed based on specific particle materials, and there is a lack of systematic research on the effects of different shape factors on terminal velocity. In this study, super-ellipsoidal particles were selected as test particles for settling experiments, and a particle–velocity tracking code was developed to measure their terminal velocities during falling through glycerin–water mixtures. A terminal–velocity model for super-ellipsoidal particles was proposed based on the measured data. Owing to the new model, multivalued predictions of the terminal velocity based on a single shape factor, such as sphericity and Corey shape factor, were disclosed, and the prediction errors were evaluated. The results of this study can provide a basis for establishing a general terminal–velocity model that considers the influence of particle shape.

Heavy metals and organic dyes in water in concentrations exceeding the tolerable limit are unsafe for aquatic life and humans. Chitosan nanocomposites show a potential adsorption capacity to organic dyes. The present study encompasses the preparation of chitosan‐ n SiO 2 nanocomposites (CSNC) with different weight ratios of chitosan to n SiO 2 and its application in the methylene blue (MB) dye adsorption. The nanocomposites were characterized with the help of SEM, BET, FTIR, XRD, and TGA. The adsorption experimentation was executed in batch mode under varying experimental conditions. Several isotherm and kinetic models were analyzed with the experimental data, and thermodynamic conditions required for adsorption were also determined. Maximum Langmuir adsorption capacities ( q L ) of the adsorbents for MB varied in the range of 21.32–31.34 mg g ⁻¹ . The pseudo‐second‐order model was the best‐fitted kinetic model concerning all three adsorbents. The statistical modeling using multiple polynomial regression (MPR) for CWS CSNC1‐1 and CSNC2‐1 yielded the equations with R‐square ranging from 0.984 to 0.996. For GA modeling, it is more than 0.999. So, the efficient employment of statistical modeling, and genetic algorithms has also been achieved.

Fluidization of non-spherical binary particle beds with non-Newtonian power-law liquid was investigated. The influence of parameters such as particle diameter, column diameter, and rheological property of liquid on minimum fluidization velocity (Umf) was studied. It reveals that Umf decreases with the increasing concentration of non-Newtonian fluid due to the change in effective viscosity. The higher the weight fraction of the larger diameter particle in a binary mixture, the higher the minimum fluidization velocity. An empirical correlation was proposed to estimate Umf. The applicability of the proposed correlation was compared with existing documented correlations and with the assistance of a genetic algorithm (GA).

The solid-water fluidized bed was investigated with a binary mixture of irregularly shaped sand particles. A binary mixture was produced by mixing particles of sand for different weight ratios. The influence of various operating parameters on minimum elutriation velocity was investigated. It was observed that the Ume decreases with the increase of the lighter particles in the binary mixture, and the Ume increases with the increase of column diameter. A simplified empirical correlation has been developed to predict minimum elutriation velocity with acceptable statistical parameters. Application concerning a hybrid of artificial neural network (ANN), and genetic algorithm (GA), is successfully predicted.

This investigation aims to implement the fixed bed column method to eliminate methylene blue (MB) by H3PO4 treated eucalyptus leaves (PEUL). PEUL is characterized using SEM, XRD, FTIR, solid-state NMR, and BET surface areas. Initially, the batch experiments revealed that the maximum percentage removal of MB is obtained at pH 8. The column experiments are performed at pH 8 and 25 °C with a varying bed height (5–9 cm), rate of flow (10–20 ml min−1), and MB concentration (10–50 mg L−1). The column experimentation shows that the breakthrough and exhaustion times rise with the bed's height but decrease with the increasing rate of flow and MB concentration. Different well-known kinetic models are tested with the experimental results, which display that the Thomas model (R2 = 0.9969, χ2 = 0.0005) fits better than others, so it is appropriate for the scale-up design. The Langmuir isotherm model (R2 = 0.9949) is superior to the Freundlich model (R2 = 0.9516). The Langmuir maximum adsorption capacity is 52.18 mg g−1, which suggests monolayer adsorption. Desorption of MB from used adsorbents with CH3COOH solution (0.4 N) suggests 55.10% regeneration efficiency. The used adsorbents are safely disposable after incineration at 800 °C. This innovative study suggests that the inexpensive H3PO4 treated eucalyptus leaves feasible to use effectively for MB removal from the wastewater. The modeling using multiple linear regressions shows a statistically good result. The applicability of GA-ANN modeling is also tested.

The traditional procedure of predicting the settling velocity of a spherical particle is inconvenient as it involves iterations, complex correlations, and an unpredictable degree of uncertainty. The limitations can be addressed efficiently with artificial intelligence-based machine-learning algorithms (MLAs). The limited number of isolated studies conducted to date were constricted to specific fluid rheology, a particular MLA, and insufficient data. In the current study, the generalized application of ML was comprehensively investigated for Newtonian and three varieties of non-Newtonian fluids such as Power-law, Bingham, and Herschel Bulkley. A diverse set of nine MLAs were trained and tested using a large dataset of 967 samples. The ranges of generalized particle Reynolds number (ReG) and drag coefficient (CD) for the dataset were 10−3 < ReG (-) < 104 and 10−1 < CD (-) < 105, respectively. The performances of the models were statistically evaluated using an evaluation metric of the coefficient-of-determination (R2), root-mean-square-error (RMSE), mean-squared-error (MSE), and mean-absolute-error (MAE). The support vector regression with polynomial kernel demonstrated the optimum performance with R2 = 0.92, RMSE = 0.066, MSE = 0.0044, and MAE = 0.044. Its generalization capability was validated using the ten-fold-cross-validation technique, leave-one-feature-out experiment, and leave-one-data-set-out validation. The outcome of the current investigation was a generalized approach to modeling the settling velocity.

The accurate prediction of terminal settling velocity of solid spheres in non-Newtonian liquids is important for various fluid-particle systems such as slurry pipelines, separation processes, hole-cleaning in drilling operations, and mineral processing. The standard practice for the prediction involves an implicit procedure that requires repeated iterations using Newtonian correlations. Wilson et al. developed an explicit method that allows direct (noniterative) prediction of the velocity in non-Newtonian liquids. Although very useful, the original Wilson model has an empirical constraint that limits its application. In this study, experiments are performed to measure the terminal settling velocity of precision spheres in Newtonian liquid (water) and non-Newtonian drilling fluids (Flowzan solutions). The Herschel–Bulkley three parameter model satisfactorily modeled the non-Newtonian rheology. Experimental data and similar measurements available in the literature are presented in this paper. The data exhibited the standard relationship between the drag coefficient and the Reynolds number. The original Wilson model was tested for these data points and was modified in this study to address its limitations. Consequently, it was observed that the modified version yielded more accurate results than the original model. Its prediction was especially better when the value of corresponding Reynolds number was more than 10.

Long-term exposure of Cr(VI) causes severe health effects to the living beings. A continuous fixed bed experimental study is carried out by using pistachio shell as green and eco-friendly adsorbent for Cr(VI) adsorption. Effects of several operating parameters on Cr(VI) removal were investigated using the breakthrough curves (CtC0 versus time) and determination of saturation time (CtC0≤1). Cr(VI) adsorption equilibrium was illustrated by Langmuir isotherm. Different kinetic models like Yan et al. (2001), Thomas (1944), Yoon-Nelson (1984), and Bohart-Adams model(1920) were applied to study the dynamics of the adsorption process.Yan et al. model was found more effective compare to other kinetic models.This studyshowed that the pistachio shells, green adsorbent, have potential adsorption capacity for Cr(VI) ions. Applicability of GA-ANN hybrid model has been tested to predict the percentage removal of Cr(VI).

In order to obtain best solutions, we need a measure for differentiating best solutions from worst solutions. The measure
could be an objective one that is a statistical model or a simulation, or it can be a subjective one where we choose better solutions
over worst ones. Apart from this the fitness function determines a best solution for a given problem, which is subsequently used by
the GA to guide the evolution of best solutions. This paper shows how GA is combined with various other methods and technique to
derive optimal solution, increase the computation time of retrieval system the applications of genetic algorithms in various fields.

An accurate model for the drag coefficient (CD) of a falling sphere is presented in terms of a non-linear rational fractional transform of the series of Goldstein (Proc. Roy. Soc. London A, 123, 225-235, 1929) to Oseen's equation. The coefficients of the six polynomial terms are improved through a direct fit to the experimental data of Roos and Willmarth (AIAA J., 9:285-290, 1971). The model predicts CD up to Reynolds number 100,000 with a standard deviation of 0.04. Results are compared with eight different formulations of other authors.

This work presents a new empirical relationship between Reynolds number Ret and Archimedes number Ar. From this relationship it is possible to calculate the free settling (terminal) velocity of irregularly shaped (e.g. crushed) solids in water. Experimental terminal velocities for various size fractions from earlier works were correlated with the new equation. The data refer to crushed quartz and galena particles.The new relationship gives for a very wide range of Archimedes numbers (flow regimes) a good correlation between experimental and calculated terminal velocities. Comparisons with the Ganguly relationship also showed a good agreement for the prediction of the terminal velocities. The current work shows that the terminal velocities in water can be calculated with a single equation for various irregularly shaped solids and for various size fractions.

Explicit equations are developed for the drag coefficient and for the terminal velocity of falling spherical and nonspherical particles. The goodness of fit of these equations to the reported experimental data is evaluated and is compared with that of other recently proposed equations.Accurate design charts for CD and ut are prepared and displayed for all particle sphericities.

A new and simplified formula for predicting the settling velocity of natural sediment particles is developed. The formula proposes an explicit relationship between the particle Reynolds number and a dimensionless particle parameter. It is applicable to a wide range of Reynolds numbers from the Stokes flow to the turbulent regime. The proposed formula has the highest degree of prediction accuracy when compared with other published formulas. It also agrees well with the widely used diagrams and tables proposed by the U.S. Inter-Agency Committee in 1957.

Experimental investigation of the fluidization behavior in single and binary solid-liquid fluidized beds of non-spherical particles (as solid phase) and water as the liquid phase was performed using a Perspex column of diameter 0.072 m 0.054 m, respectively. Different particle sizes ranging from 3.057×10⁻³ m. to 7.74×10⁻³ m were used to prepare the single and binary mixture. The mixture had different weight ratio depending upon the percentage of 0%, 20%, 40%, 60%, 80%, and 100%for fluidization. Minimum fluidization velocity increased with the increase in average particle size and reduced sphericity for the binary mixture. An empirical correlation was developed to predict the minimum fluidization velocity. GA-ANN was applied to predict Umf for single and binary component solid-liquid fluidized bed. The applicability of GA-ANN analysis leads to designing the binary solid-liquid fluidization system without going through experimentation.

The terminal settling velocity (TSV) of solid particles is experimentally determined in fluidizing columns. In monodispersed (single component) systems, the bed expansion behavior has been experimented with using pseudoplastic liquids. The terminal velocity is calculated from the plot of bed voidage (ε) vs. liquid velocity and extrapolating to ε = 1.0. An empirical correlation is developed for determining the TVS with acceptable statistical accuracy. Successful applicability of ANN modeling has been reported. After comparing with existing literature, it was found that the present work yielded better results (based on the statistical error parameters) than the previous literature.

Terminal Settling velocity (Vts) is a significant phenomenon for two-phase solid-liquid flows in various process units, such as slurry pipeline, annular drillpipe, fluidized bed reactor, drier, and gasifier. A two-phase system operated below Vts encounters several technical issues, such as solid accumulation, surface wear, erosion, flow irregularity, increased energy requirement, and backflow or, even, bursting. Measuring and predicting the Vts of spherical and non-spherical particles in rheologically different fluids are of interest to the concerned research community. Although many empirical models with limited boundary conditions were proposed earlier, the application of artificial intelligence (AI) for such modeling is still in infancy. In the current study, we attempt to address the shortcomings of the previous methods of predicting Vts by using a generalized machine learning (ML) approach. The training and testing of the ML models were conducted using an extensive dataset including various particle shapes and fluid rheologies. The current dataset is substantially larger compared to the similar datasets used for previous studies. We investigated several state-of-the-art ML algorithms, including ensemble learning and multi-stage regression models to find out the most optimum model for predicting Vts. The proposed model is applicable to spherical and non-spherical particles in both Newtonian and non-Newtonian fluids. This new application of AI-based modeling in the field of engineering can be used for industrial-scale design and operation with much needed reliability in a cost-effective manner.

Coconut coir (Cocos nucifera L.), particle size 300–850 μm, has been identified as an adsorbent for safranin-O dye removal from aqueous solution. Bioadsorption efficiency is improved by modifying untreated coconut coir (UCC) with 1 N phosphoric acid (PCC) and 1 N sulphuric acid (SCC). The acid treatment enhances the surface area of adsorbents and accelerates more dye uptake. The adsorption process is optimized by varying the physicochemical conditions like initial pH, adsorbent amount, contact time, initial dye concentration, and temperatures. The adsorption process’s optimum pH is 4, 6, and 6, respectively, using UCC, PCC, and SCC adsorbents.
In contrast, more than 98% of dye removal has been observed at the lower concentration of dyes up to 200 mg/L at 303 K. Maximum dye removal is possible at 75 mg/L of dye concentration. UCC, PCC, and SCC adsorbents’ adsorption capacity is 80.32 mg/g, 96.81 mg/g, and 89.53 mg/g, respectively, at 303 K temperature. Langmuir and Tempkin model and the pseudo-second-order model are the best-fitted models for isotherm and kinetic study. Thermodynamic parameters indicate the adsorption process is viable, pontaneous, exothermic. 75% glacial acetic acid is the most potent solvent for safranin-O dye extraction from dye loaded biomass. The functional groups and different interactions are identified to establish the adsorption mechanism. The PCC adsorbent has been used for scale-up design. The multiple polynomial regression (MPR) successfully predicts the dye removal efficiency for individual adsorbents. The modeling of the Genetic Algorithm has also been done successfully.

The aim of this investigation concerns the elimination by batch adsorption method of a primary (cationic) textile dye (Crystal Violet) from the synthetic medium, using raw and acid-modified eucalyptus leaves. Parametric studies, such as pH (2–10), unmodified and acid-modified eucalyptus leaves dose (1–10 g L⁻¹), time (5–300 min), and initial strength of CV (10–300 mg L⁻¹) are performed on the elimination of Crystal Violet from the Synthetic Medium. The R–P model gives the maximum coefficient of correlation (R² = 0.99), which denotes the best fitting isotherms with the investigational data from the other isotherms. The maximal capacity of adsorption is 141 mg g⁻¹ for Crystal Violet (CV) on PEUL at 25 °C and pH7. The kinetics study of the CV elimination signifies the pseudo 2nd order kinetics model gives the acceptable fitting rate equation (R² = 0.99) with the investigational data. Intraparticle diffusion model, IPD implies it's not only the rate-limiting step. The overall outcome recommends eucalyptus leaves probably utilized as a low-cost environment-friendly adsorbent for the de-pollution of effluents laden with basic (cationic) textile dye (CV). MPR and GA application on experimental data correctly predicted the removal percentage.

This research aims to experiment with the potential of neem (Azadirachta indica) leaves for phenol adsorption. Morphology, functional groups, etc. characterize the adsorbent. Batch studies are conducted at pH (2–7), dose (7–12 g/L), time (60–360 min), initial concentration (100–500 mg/L), and temperature (30–50 °C). Maximum 97.5% phenol is removed when pH, dose, time, temperature, and phenol concentration is 3, 10 g/L, 240 min, 30 °C and 100 mg/L, respectively. Experimental results are supported by pseudo-second-order (r² = 0.99999). Kinetic testing is supported by adsorption mechanisms developed by Elovich, Reichenberg, Boyd, Furusawa and Smith, and Fick models. Freundlich model (r² = 0.99648) is fitted well compare to other models. Sorption energy (0.5288 kJ/mol) supports physical adsorption. Thermodynamics has suggested for a non-random, exothermic, and spontaneous process. The multiple linear progressing (MLR) modeling has successfully predicted the removal percentage. Desorption with ethanol has revealed 58.5% phenol removal potential. Safe disposal of the used adsorbent is recommended by incineration. The scale-up design has demonstrated that 27.925 kg adsorbent is required for 1000 L wastewater to reduce phenol from 100 ppm to 0.06 ppm in two stages. The novel study concludes that the natural, low-cost bio-adsorbent neem leaves can suitably be used in the refineries and other allied chemical industries for phenol remediation.

In this paper, agricultural waste nutshells, such as walnut and almond shell, were utilized to treat Pb(II) containing aqueous solution. Lead(II) is a typical poisonous, commercial, water-pollutant, having multiple awful effects on the environment. The effluent of the different industrial wastewater cans is treated by using leftover and excess green waste. This finding is focused on the utilization of walnut and almond shells for Pb(II) removal. These green adsorbents are characterized using SEM, FTIR, pHpzc, and BET analyzer. The operating parameters are first optimized. The pseudo-2nd order kinetic, as well as the Langmuir isotherm model, have better applicability for both nutshells. Chemical sorption processes have been reported at higher temperatures, whereas at a lower temperature, it follows the physical sorption process. Elevated temperature helps to remove the metal ion more efficiently. The sorption process is spontaneous and endothermic for both nutshells. The desorption study shows that adsorbents can be used several times. Deadly effects of Pb(II) have been reported by the RBC count of Gallus gallus domesticus. It’s been observed that the treated solution is somewhat less harmful. Application study using industrial effluent is successfully demonstrated. The scale-up design operation has been investigated. Statistical modeling has also been very successfully implemented using the data collected from the experiment. The study indicates that both nutshells have the potential for the removal of Pb(II).

Mango, jackfruit, and rubber leaves showed potential for Cr(VI) elimination in a batch mode. The present study was performed in fixed bed downflow columns at multiple flow rates, bed depths, and influent concentrations for Cr(VI) elimination using the above green adsorbents. The experiments were performed at influent flow rates of 5 to 25 ml.min⁻¹, concentrations of 5 to 80 ml.L⁻¹, and bed depths of 3 to 9 cm. The adsorption capacity for reduced flow rates and concentrations were more effective. Well-known kinetic models had been used to fit the experimental data to determine their associated parameters. Thomas model was the best fit, especially for the mango leaf. The Thomas maximum adsorption capacity of mango, jackfruit, and rubber leaves was 69.52, 22.45, and 15.79 mg.g⁻¹, respectively.
The multiple linear regression and GA-ANN technique predicted Cr(VI) removal efficiency successfully with a high cross-correlation coefficient.

Maiti, Samit BikasBar, NirjharDas, Sudip Kumar expansion characteristics in non-Newtonian fluid–solid two-phase fluidized bed have been examined. Bed expansion measurements are carried with irregular shaped sized particles and non-Newtonian liquids (aqueous solutions of carboxymethyl cellulose). The bed voidage is found to be increasing with the increasing superficial liquid velocity. It has also been noticed that the value of this increase has been smaller as the particle size increases. Also, increase in the viscous non-Newtonian type flow behaviour has increased in bed voidage. A multilayer perceptron neural network trained with the backpropagation as well as the Levenberg-Marquardt algorithm has been attempted for the proposed analysis. Four types of common transfer functions are used with the use of a single hidden layer. The best performing ANN model has been the Levenberg-Marquardt algorithm applied with transfer function 4 having 11 processing elements within the hidden layer for the predictability related to the bed height ratio.

In the present batch study, eucalyptus leaves (EUL), H2SO4‐treated eucalyptus leaves (SEUL), and H3PO4‐treated eucalyptus leaves (PEUL) are used as bio‐adsorbents for the removal of methylene blue (MB). The bio‐adsorption is executed to inspect the results of the variation between different experimental variables such as pH (2–10), adsorbent dose (1–10 g/L), contact time (5–360 min), and temperature (298–318 K) on the bio‐adsorption of MB. The Langmuir isotherm (R² = 0.99) fitted adequately to the bio‐adsorption data for the initial MB concentrations of 10–300 mg/L. It is also necessary to mention that the MB bio‐adsorption occurred in the order of a monolayer on the EUL, SEUL, and PEUL. The bio‐adsorption kinetics have been fitted by the pseudo‐second‐order model (R² ≥ 0.99) for various MB concentrations. The maximum bio‐adsorption capacity was 194.34 mg/g and was achieved for the H3PO4‐treated eucalyptus leaves (PEUL). These results showed that EUL, SEUL, and PEUL may be utilized as a favorable low‐cost bio‐adsorbent to eliminate MB from aqueous solutions. With safe disposal methods in mind, this investigation has revealed the eco‐friendliness of the bio‐adsorbents. A prediction of the removal percentage of methylene blue using a genetic algorithm (GA) from the data collected from the experiment has also been tested. The results related to the prediction using the GA‐ANN are accurate.
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This paper is continuation of our earlier paper in batch studies (Nag et al., 2018) and aims to deliver efficient and affordable solution for Cd(II) remotion from their wastewater of small to medium scale industries operating in India and worldwide. Three biowaste materials, jackfruit, mango and rubber leaves are used for Cd(II) bioremediation from synthetic wastewater in continuous down flow in packed bed columns. The influence of influent concentration (20–80 mg L⁻¹), flow rate (10–25 ml min⁻¹) and bed depth (3–9 cm) on Cd(II) removal has been examined at pH 6. Rise in bed height favoured the adsorption process whereas the decrease in bio-sorption efficiency was recorded at high influent flow rate and concentration. 98.26% Cd(II) was removed at breakthrough by jackfruit leaves at a flow rate of 10 ml min⁻¹ when the influent concentration was 20 mg L⁻¹ and 5 cm bed height. Different kinetic models were evaluated for their comparative applicability. Applicability of hybrid artificial intelligence GA-ANN was attempted as a tool for simulation and optimization of Cd(II) removal efficiency prediction as a function of influent variables. The network performed appreciably well in terms of cross-correlation coefficient (R) value (between 0.997 to 0.999) and minimization of errors.

The paper aims to provide efficient and affordable means for pollution abatement to MSME sector. In this work, the performance of some naturally available bio-waste materials, viz., leaves of jackfruit, mango and rubber plants have been attempted as biosorbents for remediation of toxic Cd(II) from aqueous solution. The biomasses have been characterised to find out the surface morphology, active surface area, presence of characteristic surface groups etc. which facilitate the biosorption process. Batch experiments are conducted to see the effects of operating parameters, viz., aqueous phase pH, initial Cd(II) concentration, adsorbent dose, time, temperature for Cd(II) ion removal onto these green biomaterials. The bioremediation mechanism was strongly pH dependent, spontaneous and followed second-order kinetics. Mass transfer, intra-particle diffusion and chemical adsorption controlled the process. Jackfruit leaf showed the best sorption performance by removing 98.72% Cd(II) from 20 mg L⁻¹ aqueous solution at a dose of 5 g L⁻¹ and the equilibrium adsorption capacity of 20.37 mg g⁻¹.The bio-sorbents performed satisfactory when tested against the industrial wastewater. The toxicity effect of the cadmium ion was analyzed on living animal cell and they showed morphological alteration of RBC along with clumped appearance. The cell alteration intensity reduced with the treated effluent. The natural adsorbents have comparable adsorption capacity of other green adsorbents used by different researchers. Modelling of the complex sorption process has been performed using hybrid artificial intelligence (GA-ANN) technique to predict the metal ion removal efficiency accurately and obtained results have good agreement with the experimental data with correlation coefficient (R) ranging from 0.97-0.99. All these findings have manifested application of jackfruit, rubber and mango leaves for removal of Cd(II) ions in an environmentally sustainable and friendly way.

The difficulty associated with the prediction of the settling velocity of a single particle in a non-Newtonian fluid seems to be an academic problem; yet, this parameter plays an important role in the design of slurry pipelines and handling equipment. Wilson et al. (Int. J. Min. Process. 71(2003) 17-30) presented a direct method that was able to provide reasonably accurate estimations for the terminal settling velocity of spheres in fluids with yield stresses. The application of this method is limited. The current study presents measurements of terminal settling velocities of metal spheres in clay-water suspensions. These experimental results, along with data taken from the literature, have been used to modify existing methods for prediction of settling velocity in viscoplastic fluids.

The rheological behaviour of power plant ash samples collected from JSPL (M/s Jindal Steel & Power Limited, Raigarh), India was carried out using a HAAKE Rotational Rheometer (Model: RheoStress 1, Thermo Fisher Scientific). The ash slurry indicated non-Newtonian behavior in the solids concentration range of 50-60% by mass. The rheological data were best fitted by Bingham Plastic model in the studied ranges of concentrations and shear rates. Two selective additives namely; sodium silicate and Ghadi detergent were applied in small quantities (0-0.6% of total solids) and their effect on rheological parameters were evaluated. It was indicated that the small dosage of sodium silicate substantially influenced the Bingham parameters of the ash slurry than the Ghadi detergent. The percentage reduction in Yield stress at a slurry concentration of 60% by weight were found to be 59.3% and 46.23% for sodium silicate and Ghadi detergent respectively at a maximum dosage of 0.6% additives. More importantly, the plastic viscosity reduced by 37.6% and 16.3% respectively with the same dosage of sodium silicate and Ghadi detergent at same slurry concentration.

Prediction of the terminal velocity of solid spheres falling through Newtonian and non-Newtonian fluids is required in several applications like mineral processing, oil well drilling, geothermal drilling and transportation of non-Newtonian slurries. An artificial neural network (ANN) is proposed which predicts directly the terminal velocity of solid spheres falling through Newtonian and non-Newtonian power law liquids from the knowledge of the properties of the spherical particle (density and diameter) and of the surrounding liquid (density and rheological parameters). With a combination of non-Newtonian data with Newtonian data taken from published data giving a database of 88 sets, an artificial neural network is designed. Analysis of the predictions shows that the artificial neural network could be used with good engineering accuracy to directly predict the terminal velocity of solid spheres falling through Newtonian and non-Newtonian power law liquids covering an extended range of power law values from 1.0 down to 0.06.

Influence of particle shape on hydrocyclone classification was investigated. Classification tests using hydrocyclone and cyclosizer showed that coarse fractions of plate-like particles such as PTFE and glass flake used here were not necessarily recovered as underflow product, especially at relatively high inlet velocity. Settling velocity of the glass flake particles in centrifugal field was estimated using a centrifugal particle size analyzer, and it was revealed that differences in settling velocity between coarse and fine glass flake particles became smaller with increases in angular velocity. Moreover, settling test of glass plate in water or glycerin solution was conducted to know relationship between particle Reynolds number (Re) and settling velocity of the plate. At smaller Re condition, the glass plate settled straight and stably, and larger plate settled faster than smaller plate. However, oscillating motion of the plate occurred in the region of high Re, and settling velocities of the large plate became smaller than that of the small plate in such conditions. Drag coefficient (C) calculated based on the settling velocity of the glass plate is similar to that of glass spheres below Re of about 50, above which it became larger than that of glass sphere. Approximation formula of correlaton between Re and C suggests that the influence of the Re on C can be neglected in the region of high Re, and C increases with increases in the ratio of the particle diameter to thickness (D/T).The decrease of the difference in settling velocity recognized in the centrifugal settling test and the effect of the particle shape (D/T) on C at high Re region are considered to be able to affect the hydrocyclone classification. The misplacement of coarse plate-like particles in the hydrocyclone and cyclosizer tests could be ascribed to the particle shape effects.

Knowledge of the settling velocity of spherical particles in non-Newtonian power law liquids is required in design calculations for hydraulic conveying systems, using dense media, thickening and fluidization equipment, etc. In this work, an empirical formula has been developed which is explicit in velocity and reproduces a vast amount of data available in the literature. The scheme presented herein reproduces the results of nearly 400 individual sphere fall tests with an average error of 14% over wide ranges of rheological conditions and Reynolds numbers from 1 to 104.

Graphical relations have been developed from data on the fall of spherical particles in Bingham fluids available in literature for predicting terminal settling velocity and drag coefficient. It has been found that the relations fit the data extremely well.

The settling velocity of solids has been determined experimentally in a fluidizing column. The bed expansion characteristics of monodispersed (single component) systems have been noted using water as the fluid. The experimentally determined bed voidages have been plotted against particle Reynolds number, Rep on a log-log graph paper. The settling velocity, ut, has been obtained by extrapolating the resulting straight line to ϵ=1.0. Close-cut size fractions of coal, graphite, sand, limestone, chalcopyrite and magnetite have been used as different solids. Water has been used as the fluidizing fluid throughout the experiment.The experimental values of Ret have been empirically correlated with the relevant system properties, e.g., particle diameter, its shape, density of liquid and solid, liquid viscosity—all of these being represented by Archimedes number and shape factor, φs. The correlation proposed is: Ret=0.103(Ar0.804(φs)0.745 The standard deviation of the proposed correlation has been calculated to be ±15.2%. The ranges of Ar and φs are: 53≤Ar≤3761; 0.5000≤φs≤0.9740The present correlation has been compared with existing equations for monodispersed systems whereby a fair agreement is obtained. This is also found to be reasonably accurate for polydispersed systems when the calculated ut values, based on average bed properties, are compared with those calculated theoretically after being multiplied with the Pettyjohn-Christiansen sphericity correction factor.

Sphere drag data from throughout the twentieth century are available in tabular form. However, much of the data arose from experiments in small diameter cylindrical vessels, where the results might have been influenced by the wall effect. Wall effect corrections developed by others were applied to 178 of the 480 data points collected. This corrected data set is believed to be free of the influence of wall effects. Existing drag and settling velocity correlations were compared to this data set. In addition, new correlations of the same forms were developed using the corrected data. Two new correlations of sphere terminal velocity are proposed, one applicable for all Reynolds numbers less than 2 X 10(5), and the other designed to predict settling velocities with exceptional accuracy for terminal Reynolds numbers less than 4,000, a region that contains almost all applications of interest in environmental engineering. The trial and error solution for settling velocity using the Fair and Geyer equation for drag should be retired in favor of the direct calculation available from these new correlations.

The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplasticity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations. This work is pertinent to ore processing, ceramics manufacture, and sewage treatment.

The published correlations for the drag force on a sphere moving in a fluid have been critically examined and their limitations have been identified. A series of new correlations has been proposed, each covering a wide range of particle Reynolds number Re(10< Re < 3 × 10) by choice of the appropriate form iterative calculations can be avoided.

New correlations have been developed to estimate the steady-state free-fall conditions of isolated, nonspherical, isometric particles moving in Newtonian fluids. The proposed relationships cover the Stokes, the Newton, and the transitional flow regions. Their explicit forms enable the direct computation of the particle size corresponding to a chosen terminal velocity and the straightforward calculation of the terminal velocity of a given nonspherical particle. The terminal velocities of crushed particles of limestone and lime have been measured and compared to the values predicted by the proposed formulas.

Bed expansion of liquid-solid fluidized beds has been correlated empirically in terms of particle Reynolds number and particle Galileo number. The proposed correlation is shown to be applicable from the onset of fluidization to the dilute phase fluidized bed with large voidage. The range of Galileo number covered is from 18 to 3 × 108.

In der vorliegenden Arbeit werden Aufströmungseigenschaften und hydrodynamische Zustände mit Luft aufgewirbelter Partikelschichten untersucht. Anschliεßend wird eine Versuchsanordnung und Methode für Wärmeübergangs-Messungen in solchen Schichten im Vergleich zu ruhenden Schüttungen behandelt und eine Deutung der Versuchsergebnisse gegeben.

The terminal settling velocity of several cylinders (of stainless steel, perspex and glass), needles (of steel) and rectangular prisms (of perspex) falling with their major axis parallel to the direction of motion has been measured in three Newtonian liquids. The measurements have been carried out in three to four fall tubes of different diameters to correct the measured terminal velocity for wall effects. The experimental results reported herein embrace the following ranges of conditions: particle to fall tube diameter ratio: 3.17 × 10−2 to 0.776; length to diameter ratio for cylinders and needles: 5 to 50; the sphericity of particles: 0.35 to 0.7 and particle Reynolds number: 0.095 to 400.Terminal velocity data (corrected for wall effects) have been correlated using two approaches, namely, the usual drag coefficient-Reynolds number relationship, and in terms of a dimensionless velocity factor denoting the departure from the behaviour of an equivalent sphere. Predictive expressions have been developed using both schemes. Finally, the paper is concluded by presenting detailed comparisons between the present results and the prior investigations available in the iterature.

Prediction of the terminal velocity of solid spheres falling through stagnant pseudoplastic fluids is required in several applications like oil well drilling, geothermal drilling, transportation of non-Newtonian slurries and mineral processing. Prior attempts utilized various Newtonian correlations to predict the drag coefficient and from this the terminal velocity with varying degrees of success. We report here carefully derived experimental data for solid spheres falling through non-Newtonian liquids and present them together with measurements reported in the literature, for a total of 80 pairs of Re–CD, and show that the data fall along the same curve. Through nonlinear regression, an equation is derived, similar to the most accurate, simple, five-constant equation proposed for Newtonian liquids, which has not yet been tested for non-Newtonian liquids. The predictions compare favorably with the measurements both for the proposed equation and for the Newtonian equation. With a combination of non-Newtonian data with Newtonian data, from this work and work from other investigators, giving a database of 148 pairs, an improved equation is derived. Analysis of the predictions shows that the Newtonian equation describes extremely well the Newtonian data and furthermore it could be used with good engineering accuracy to predict the terminal velocity of solid spheres falling through stagnant non-Newtonian liquids.

Velocity voidage relationship in fluidizing and sedimenting beds

- J Basu