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International Review of Chemical Engineering (Rapid Communications) - November 2011 (Vol. 3 N. 6) - Papers









International Review of Chemical Engineering (Rapid Communications) - Papers



go to top   Editorial

         by Jordan Hristov

         Vol. 3. n. 6, pp. 627



go to top   Comparative Study of Friction Factor by Prediction of Frictional Pressure Drop per Unit Length Using Empirical Correlation and ANN for Gas-non-Newtonian Liquid Flow Through 180° Circular Bend
         by Nirjhar Bar, Sudip Kumar Das

          Vol. 3. n. 6, pp. 628-643 


Abstract - An empirical correlation for the prediction of friction factor is developed from the experimental data obtained from our earlier study on the frictional pressure drop per unit length for gas-non-Newtonian liquid flow through 180° bend. Applicability of Artificial Neural Networks (ANN) methodology was investigated. This approach proved its worth when rigorous fluid mechanics treatment based on the solution of first principle equations is not tractable. The prediction of the frictional pressure drop per unit length is done using Multilayer Perceptrons (MLP) trained with five different algorithms, namely: Backpropagation (BP), Scaled Conjugate gradient (SCG), Delta-Bar-Delta (DBD), Levenberg-Marquardt (LM), Quick-Prop (QP). Four different transfer functions were used in a single hidden layer for all algorithms. The Chi-square test confirms that the best network for prediction of frictional pressure drop per unit length is when it is trained with Backpropagation algorithm in the hidden and output layer with the transfer function 1 in hidden layer having 6 processing elements. The friction factor calculated from the predicted values of frictional pressure drop per unit length using ANN gives better results than that calculated from empirical correlation.

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Keywords: Frictional Pressure Drop, Gas-Non-Newtonian Liquid Flow, Backpropagation, Scaled Conjugate Gradient, Delta-Bar-Delta, Levenberg-Marquardt, Quick-Prop.



go to top   Research Note on Power-Series Expression of Mass Concentration Profile in Nonlinear Diffusion-Reaction Processes
         by L. T. Villa, R. O. Grossi, G. Ryan

         Vol. 3. n. 6, pp. 644-649


Abstract - In this paper, a steady state one-dimensional diffusion-reaction process is considered. As a descriptive mathematical model for such processes, a high nonlinear boundary value problem (BVP) for a second order ordinary differential equation is associated. By using an opportune integral representation for the solution of such BVP, fundamentals aspects are provided in order to support the existence and uniqueness of a power series expression as solution of the BVP. So that, a contribution has been reached, leading to provide information of practical significance regarding to the mass concentration profile of the key reactant component in the process.

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Keywords: Concentration Profile, Diffusion-Reaction.



go to top   Study by Adsorption Calorimetry in Supported Catalyst: Adsorption Structure Sensitivity on Ru/γ-Al2O3
         by Liliana Giraldo, Juan Carlos Moreno-Piraján

         Vol. 3. n. 6, pp. 650-655


Abstract - In this study, the structure sensitivity of hydrogen, oxygen and carbon monoxide adsorption was investigated by changing the metal particle size of Ru/ γ-Al2O3 catalysts. The 3,5% Ru/ γ-Al2O3 catalysts were prepared by incipient wetness method; the particle size of the catalysts was modified by calcining at different temperatures. The differential heats of adsorption of hydrogen, carbon monoxide and oxygen were measured using a Tian-Calvet micro calorimeter specially constructed for this research. Hydrogen chemisorption sites with low and intermediate heats were lost when the particle size increased consistent with the previous reports in the literature. A structure dependency slight was observed for hydrogen, carbon monoxide and for the oxygen initial heats of adsorption. The adsorbate: total metal stoichiometries at saturation systematically decreased with increasing particle size. The hydrogen site energy distribution changed with increasing particle size, as well as for the oxygen and carbon monoxide adsorption site energy distributions did not change appreciably with the metal particle size.

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Keywords: Catalyst, Structure Sensitivity, Heat of Adsorption, Hydrogen, Oxygen, Carbon Monoxide, Adsorption Calorimetry.



go to top   Effect of Surface Properties on Spouted Bed Particle Coating
         by M. B. Braga, S. C. S. Rocha

         Vol. 3. n. 6, pp. 656-662


Abstract - The objective of this study was to analyze the spouted bed coating process in terms of solid’s surface tension and wettability and adhesion characteristics before and after the formation of the first layer of coating on the particle. Testing of coating in spouted bed were conducted employing five aqueous polymeric suspensions with different physical properties and, as nucleus, particles of glass and ABS® with different surface energies, generating systems with different characteristics of wettability and adhesion evaluated by contact angle and work of adhesion. Relative growth and growth kinetics of particles were determined and related to surface characteristics. It was found that the high surface energy of the glass had a great influence on the studied systems, resulting in low values of contact angle and consequently good wettability. Due to the lower surface energy of ABS®, the contact angles were higher when compared to glass. Although adhesive forces decreased with increasing film thickness, growth kinetics of particles showed no difference after the formation of the first covering layer, as could be expected by the change in wettability after film formation on the particle.

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Keywords: Spouted Bed, Wettability, Surface Energy, Contact Angle, Adhesion .



go to top   Liquid-Liquid Equilibria for the Ternary System Eugenol+Ethanol+Water at Temperatures 303.15, 313.15 and 323.15 K
         by Kuswandi, E. Naryono

         Vol. 3. n. 6, pp. 663-667


Abstract - The liquid-liquid equilibria (LLE) for the ternary syatem eugenol + ethanol + water are presented. The LLE of the system have been measured at atmospheric pressure and at temperatures 303.15, 313.15 and 323.15 K. The experimental data presented are correlated using UNIQUAC and NRTL activity coefficient models. The reliability of the models is tested by comparison with experimental data in terms of root mean square deviations (RMSD). The NRTL model with a value of the non-randomness parameter at 0.2 fits the experimental data satisfactorily. The correlation with the UNIQUAC equation gives better results than the NRTL equation. The simultaneous correlation of the three isothermal data sets gives a unique set of parameters in the range of the temperature investigated.

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Keywords: Ethanol, Eugenol, Liquid-liquid equilibria, NRTL, UNIQUAC, Water.



go to top   Spreading Pressure in Activated Carbons with Different Surface Properties and Its Relation with the Immersion Enthalpy
         by L. Giraldo, J. C. Moreno-Piraján

         Vol. 3. n. 6, pp. 668-673


Abstract - For three activated carbons obtained from African palm stone for physical activation with CO2 to 900 °C for activation times between 4 and 10 hours, adsorption isotherms of nitrogen are determined from which the spreading pressure is calculated. The activated carbons are microporous with micropore volumes between 0.36 and 0.48 cm3g-1. The immersion enthalpies of the activated carbons in benzene are determined, with results between 96 and 130 Jg-1, with the intention of establishing their relation with the spreading pressure. The activated carbon with the highest values of surface area and immersion enthalpy presents the smallest value for the spreading pressure.

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Keywords: Activated Carbons, Nitrogen Isotherm, Spreading Pressure, Immersion Enthalpy, Surface Area.






go to top   Nano Methods in Polymer Synthesis and Processing: Carboxyl/Anhydride Functionalized Copolymers for Nanoengineering Applications
         by Zakir M. O. Rzayev

         Vol. 3. n. 6, pp. 674-732

Abstract - This review summarizes recent advances in the different synthetic routes to polymer silicate layered nanocomposites and polymer/silica (metal oxides, functionalized carbon nanotubes, etc.) hybrids including (a) interlamellar (co)polymerization and controlled/living copolymerization of various functional monomers using the concept of ‘nano-reactor’, (b) macromolecular reactions between anhydride-containing copolymers and organosilanes to produce polymer/silica hybrid materials (sol-gel method), and (c) intercalation/exfoliation of copolymers and grafts of maleic anhydride between silicate galleries through compounding of various polymer blends in melt by reactive extrusion systems. Special attention is devoted to the mechanism of in situ grafting reactions and H-bonding effect in the reactive blend processing and nano-structure formation. The role of functionaized organo-nanofillers and their preintercalated complexes with carboxyl/ anhydride containing monomers in the preparation of important polymer nanomaterials is also highlighted. The structural details, unique properties and application areas of these new class nonocomposites and high performance engineering polymer materials have also been described.

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Keywords: İnterlamellar Copolymerization, Organoclays, Sol-Gel, Reactive Extrusion, Polymer/Silica Hybrids, Nanocomposites.



go to top   MHPC vs. HEC as Rheological Modifiers in Coating Colors for Paper Applications: a Comparative Analysis
         by J. Velho

         Vol. 3. n. 6, pp. 733-737


Abstract - The main goal of this research is to compare the behaviour of two co-binders, MHPC and HEC, in order to improve rheology of PCC suspensions for paper applications. Two PCC pigments were selected: one, with scalenohedral habit, calcitic (PCC-C); the other, with acicular particles, aragonitic (PCC-A). The results show a clear difference between rheological characteristics of PCC-C and PCC-A slurries due, essentially, to particle shape effects. Rheological properties of coating colours with added MHPC or HEC show interesting results which confer to these additives an high potential for paper coating applications.

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Keywords: MHPC, HEC, Rheology, Coating Colors, PCC.



go to top   A CFD Simulation to Study Changing Conventional Trays to Revamp Trays
         by Ehsan Askari, Mitra Dadvar1, Aliasghar Mahjoobi

         Vol. 3. n. 6, pp. 738-743


Abstract - Using high performance trays is desired in the separation processes of chemical industries. Revamp trays are used to improve the performance of conventional trays. The size of the downcomer clearance affects the revamp trays performance. A CFD analysis is used for modelling and simulation of conventional sieve trays. The results are compared with an experimental data. The agreement of the results indicates the validity of the model. The model is used to study the hydrodynamics of the flow on the revamp tray by changing the geometry of the conventional sieve tray. The simulation results specify the dependence of the liquid height in the downcomer on the size of the downcomer clearance which directly affects the tower performance. This method can be used for estimating the best size for the downcomer clearance.

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Keywords: Sieve Trays-Revamp Tray-Downcomer Clearance-CFD.



go to top   Derivation of the Discriminated Dimensionless Numbers that Rule the Forced Mass Convection
         by M. Conesa, F. Alhama, C. N. Madrid

         Vol. 3. n. 6, pp. 744-749


Abstract - Discriminated dimensional analysis (DDA, hereinafter), a fundamental extension of classical dimensional analysis (CDA, hereinafter), assumes as independent quantities or physical characteristics of vector character such as length, surface, velocity, viscosity, diffusivity… As a consequence, the dimensional equations of these quantities depend on the spatial direction they are influencing on the physical phenomenon. This causes that the resulting re-grouping of variables to form the dimensionless independent groups are different according to the use of DDA or CDA. The mass transfer problem between a horizontal plate and a forced surrounding fluid is studied assuming two type of boundary conditions, isoconcentration (Diritchlet) and prescribed mass flow at the plate (Neumann). The application of the -theorem to the set of relevant variables provides an only dimensionless group, the Schmidt number (Sc, hereinafter). To determine the unknowns (thickness of the velocity and concentration boundary layers, as well as the mass transfer coefficient) it is enough to separately introduce these variables in the relevant list of quantities. The two dimensionless groups that emerge for the three unknowns reduce to only one for the limit cases Sc<<1 and Sc>>1, providing for these scenarios the order of magnitude of the unknowns, a result not given by CDA.

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Keywords: Dimensional Analysis, Discrimination, Forced Convection, Mass Transfer.



go to top   Solid State Synthesis of Magnesium Borates at 800oC from Periclase and Sassolite
         by A. S. Kipcak, F. T. Senberber, E. M. Derun, S. Piskin

         Vol. 3. n. 6, pp. 750-754


Abstract - IIn this study, solid state method is investigated at 800oC with using periclase and sassolite. Molar ratios of periclase to sassolite mineral are selected as 1:1, 1:2, 1:4, 1:6, and 1:8. Produced magnesium borate compounds are found as; Mg3(BO3)2 known as “Kotoite”, Mg2(B2O5) also known as “Suanite” and MgB4O7. Synthesized products are characterized by X-Ray Diffraction (XRD) for identification analyses, Fourier Transform Infrared Spectroscopy (FT-IR) and Raman Spectroscopy techniques for identification analyses.

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Keywords: Magnesium Borates, Solid State, Periclase, Sassolite.



go to top   Estimation of Magnetic Field Intensity for the Magnetic Packed Beds Using Artificial Neural Networks
         by T. Abbasov, M. Yuceer, Z. Yildiz

         Vol. 3. n. 6, pp. 755-759


Abstract - Magnetizing properties of the packed beds that are constructed from the stainless steel balls of various sizes are investigated in order to determine the effect of packing fraction factor, filter length, magnetic strength and diameter of the ball on the magnetizing properties of the bed. In this study, we have investigated the effect of the volumetric packing factor on the magnetizing properties of the magnetic packed bed using artificial neural networks. An ANN model was developed to predict the magnetic intensity. The back-propagation algorithm was employed for training and testing of the network, and the Levenberg Marquardt algorithm was utilized for optimization. The MATLAB 7.0 environment with Neural Network Toolbox was used for coding. Given the associated input parameters such as the external magnetic field strength (H), diameter of the balls (d), filter length (L) and packing fraction factor (), the model estimates the effect of the variation of the magnetic field intensity.

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Keywords: ANN, Magnetized Packed Bed, Magnetic Field Intensity.



go to top   Gas-Solid Suspension with Chemical Reaction: Evolution of Weak Perturbations
         by O. V. Sharypov, I. S. Anufriev

         Vol. 3. n. 6, pp. 760-764


Abstract - Dynamics of weak finite-amplitude perturbations in two-phase homogeneous medium (gas + solid particles) with non-equilibrium chemical reaction in gas is studied theoretically. Non-linear model of plane perturbation evolution is substantiated. The model takes into account wave-kinetic interaction and dissipation effects, including inter-phase heat and momentum transfer. Conditions for uniform state of the system are analyzed. Non-linear equation describing evolution of plane perturbation is derived under weak dispersion and dissipation effects. The obtained results demonstrate self-organization in the homogeneous system: steady-state periodic structure arises, its period, amplitude and velocity depends on the features of the medium. The dependencies of these parameters on dissipation and chemical kinetics are analyzed.

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Keywords: Instability, Gas-Solid Suspension, Chemical Reaction, Non-Linear Wave-Kinetic Interaction, Inter-Phase Transfer, Numerical Calculation.



go to top   Wind Energy Use to Hydrogen Storage
         by S. Urrejola, A. Sanchez, A. Cancela, R. Maceiras, J. E. Dans

         Vol. 3. n. 6, pp. 765-768


Abstract - In this work, a combined system of wind energy and hydrogen storage is presented with the aim to give service to a passenger ship. The goal of this research is to replace the traditional diesel fuel by hydrogen using a storage system of energy remaining of an eolic plant. This energy could be used in the ship daily routines, allowing a reduction of polluting gases into the atmosphere and a form of energy management that will provide a more sustainability to global system.

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Keywords: Wind Energy, Hydrogen, Ship, Electrolyser.



go to top   Polymers as Phase Change Materials
         by Eva Günther, Stefan Hiebler

         Vol. 3. n. 6, pp. 769-773


Abstract - Phase change materials (PCM) are used for thermal energy storage because of their high storage density. Polymeric phase change materials offer some key advantages compared to the currently most popular PCM based on simple organic materials or salt hydrates. However, there are also new problems to be expected. In this paper, we discuss which properties of polymeric materials are relevant for their possible application as PCM. This theoretic part is followed by a discussion of new measurement data on poly-ethyleneglycole (PEG) as one example polymeric PCM.

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Keywords: Phase Change Material, Polymer, Material Development, Calorimetry, Microscopy.



go to top   Control of Metal Dispersion, Chemical Composition and Texture of Palladium-Zinc Catalysts on Mesoporous Titania
         by Lyudmila B. Okhlopkova, Mikhail A. Kerzhentsev, Zinfer R. Ismagilov

         Vol. 3. n. 6, pp. 774-783


Abstract - Nanoparticle-doped mesoporous titania coatings were synthesized by incorporation of PdZn nanoparticles into support sol and deposition of the resulting sol on the inner surface of a fused silica capillary. This method allows controlling the chemical nature of the film, the porosity, metal dispersion and loading with an active species. The structural properties, chemical composition and morphology of the active component and the support were studied by means of TEM, EDS, ICP AES, X-ray diffraction and N2 adsorption. Monodispersed PdZn bimetallic colloidal particles were prepared by polyol method in the presence of polyvinylpyrrolidone. The average particle size ranging from 1.8-4.3 nm was found to depend on the amount of PVP added and NaOH concentration. The bulk composition of nanoparticles depends on concentrations of the precursors and NaOH. The reaction mechanism is shown to involve the oxidation of ethylene glycol to mainly glyoxal and glycolic acid, while the metal Pd salts are reduced to form catalysts for Zn2+ ions reduction. Palladium-zinc-incorporated mesoporous TiO2 films were synthesized by a sol-gel method using a nonionic structure-directing agent Pluronic F127. The control of the pore size of the mesoporous titania was achieved by adding co-surfactants, such as n-butanol. The influence of the activation conditions on crystallite size and composition of metal particles was investigated.

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Keywords: PdZn Colloids, PdZn Nanoparticles, Polyol Method, Mesoporous Titania Coating.



go to top   Functional Copolymer/Organo-MMT Nanoarchitectures. XII. Polypropylene/Poly(MA-alt-1-octadecene)/Organoclay Based Biaxially Oriented Nanofilms Through Reactive Extrusion
         by Eren Altungöz, Zakir M. O. Rzayev, Erdoğan Alper

         Vol. 3. n. 6, pp. 784-795


Abstract - This work is an approach to develop a green technological process for the preparation of polyolefin (especially i-PP) biaxially oriented nanofilms without utilization of toxic and volatile monomers as grafting agents. Intercalated and exfoliated polymer layered silicate micro-composites (masterbachs) and nano-composite films were prepared in melt by reactive extrusion (21 mm Rondol twin-screw compounding line supported with biaxially oriented film-forming unit or granulator, and plasmatron) using isotactic polypropylene (i-PP) as a matrix polymer, poly(maleic anhydride-alt-1-octadecene) (poly(MA-alt-OD) and PP-g-MA as compatibilizers, octadecyl amine-montmorillonite (ODA-MMT) and dimethyldidodecyl ammonium-MMT (DMDA-MMT) as reactive and non-reactive nano-fillers, respectively, as well as PP-g-MA/organoclay masterbaths (5, 10 and 20 wt.%). To design and synthesize i-PP based silicate layered nanocomposites we have been developed two approaches involve the following formulations: (1) i-PP/ PP-g-MA–O-MMT clay masterbaths and (2) i-PP/PP-g-MA/poly(MA-alt-1-octadecene)/O-MMT clay nanocomposite. A first approach involves synthesis and characterization of PP based micro- and nano-composites prepared by two step melt compounding using twin-screw extrusion system supported with biaxially oriented film-forming unit. A first step includes preparation of PP-g-MA–DMDA-MMT clay blends (masterbaths) with different compositions. A second approach involves melt compounding the various mixtures of i-PP/PP-g-MA-DMDA-MMT blend. The structure–properties (MFI, thermal behavior and morphology) relationships and effect of organoclay origin and content of internal plasticizer-compatibilizer were investigated by FTIR, XRD, DSC-TGA and SEM analysis methods. It was demonstrated that the intercalation/exfoliatıon of functional copolymer between silicate layers proceeds through complex-formation and amidization reactions of anhydride units with ammonium cation and primary amine groups of organoclays, respectively; long alkyl groups of functional copolymer-compatibilizer also play a role internal plasticization in the processing and formation of nanofilms. Obtained thermal behavior, XRD parameters and surface morphology of nanofilms are showed that these important characteristics strongly depend on the composition of reactive polymer blends and chemical structure of organoclays and functional copolymer-reactive compatibilizer.

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Keywords: Polypropylene, PP-g-MA, Alternating Copolymer, Organoclays, Reactive Extrusion, Composites, Nanofilms.



go to top   The Influence of PH on the Synthesis of Hyaluronic Acid Nanoparticles by Precipitation
         by Rafaela C. S. Bicudo, Maria Helena A. Santana

         Vol. 3. n. 6, pp. 796-800


Abstract - This paper presents the influence of pH on the production process and on hyaluronic acid (HA) nanoparticles morphology. HA nanoparticles were produced in a bulk process by precipitation, as water (solvent) diffused towards acetone (non-solvent), and followed by chemical crosslinking. The pH was varied in the whole process by additions of hydrochloric acid or sodium hydroxide. It was found that the acid medium on the precipitation step leads to smaller coil globules, as well as it leads to larger particles on the crosslinking reaction step. Such results indicate the possibility of adjusting the pH in different stages of the process for the production of HA nanoparticles with different sizes for specific applications.

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Keywords: Hyaluronic Acid, Nanoparticles, PH, Precipitation.





go to top   Preface

         by Jordan Hristov

         Vol. 3. n. 6, pp. 801


A Brief Note From the Editor to the Collection on Fractional Calculus Applications.



go to top   Transient Flow OF A Generalized Second Grade Fluid Due to a Constant Surface Shear Stress: an approximate Integral-Balance Solution
         by Jordan Hristov

         Vol. 3. n. 6, pp. 802-809


Abstract - Integral balance solution to start-up problem of a second grade viscoelastic fluid caused by a constant surface stress at the surface has been developed by an entire-domain parabolic profile with an unspecified exponent. The closed form solution explicitly defines two dimensionless similarity variables ξ and , D0 responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed, as well comparison with the existing exact solutions have been performed. Numerical test with variable exponent of the approximate profile have been performed as a step improving the approximate solution.

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Keywords: Start-Up Problem, Surface Shear Stress, Viscoelastic, Integral-Balance Solution.



go to top   A Research Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives
         by Ruslan Meilanov, Muminat Shabanova, Enver Akhmedov

         Vol. 3. n. 6, pp. 810-813


Abstract - Stefan problem based on nonlocal heat conduction equation with fractional-time derivatives has been solved. The approach suggests a generalized time-dependent Stefan boundary condition defined by expression θ (α, β, τ) = δ (α, β)·τα/β. The solution developed shows that the phase change boundary co-ordinate θ depends on time τ and the parameters (0 < α ≤ 1) and β,(1 < β ≤ 2) which are the fractional orders with respect to the time and the space co-ordinate, respectively. A practical example with ice-water system was used to exemplify the solution with both α and β near to α = 1 and β = 1 (the classical problem).

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Keywords: Fractional Derivative, Nonlocal Heat Conduction Equation, Stefan Problem.



go to top   Development of Heavy Metal Sorption Isotherm Using Fractional Calculus
         by Márcio C. dos Santos, ErvimLenzi, Enrico M. Gomes, Marcelo K. Lenzi,Ervin K. Lenzi

         Vol. 3. n. 6, pp. 814-817


Abstract - Lead is a heavy metal effluent pollutant, which can be generated by different chemical plants. Literature reports different approaches for lead removal, however, great attention has been given to water hyacinths. Mathematical modeling of heavy metal sorption represents an important tool for in-depth process studies. This work proposes a new approach for modeling heavy metal isotherm sorption by using fractional calculus formalism. A novel isotherm based on Mittag-Leffler function is developed for lead sorption experimental data equilibrium modeling, in order to provide more accurate equilibrium information for sorption dynamic modeling. Experimental data were obtained using Eicchorniacrassipes as the hyacinth. Simulation results were compared to classical equilibrium sorption models. It was shown that the proposed isotherm, Epslon, provides better results when compared to classical models.

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Keywords: Isotherm, Fractional Calculus, Lead, Hyacinth, Sorption.



go to top   Modeling of Granular Material Mixing Using Fractional Calculus
         by RodrigoA. Pfaffenzeller, Marcelo K. Lenzi,Ervin K. Lenzi

         Vol. 3. n. 6, pp. 818-821


Abstract - Particulate and granular materials are found in different chemical processes. Measuring and characterizing the mixing degree remains a challenge, s it is an important variable for process performance. The availability of reliable sensors for real time control is still incipient or expensive, an alternative remains on the development of mathematical models for mixing prediction.The most commonly used approach for solid mixing concern on either diffusive or advective/convective processes. Fractional calculus represents a novel approach and a growing research field for process modeling, being based on derivates of arbitrary order. Therefore, it represents an important and alternative tool for mixing process modeling. This work study the use of a fractional diffusion model to describe granular mixing in a rotary cylinder, considering finite type of boundary conditions. Experimental data previously reported were used for validation purposes. The proposed approach could successfully describe the experimental data, thus, can be used as an alternative tool for mixing evaluation.

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Keywords: Granular material, Mixing, Fractional Calculus, Diffusion, Modeling.



go to top   Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall
         by I. Siddique, D. Vieru

         Vol. 3. n. 6, pp. 822-826


Abstract - Stokes flows of a Newtonian fluid with fractional derivatives produced by the motion of a flat plate are analyzed under the slip condition at boundary. The plate motion is assumed to have a translation in its plane with a given velocity and the relative velocity between the velocity of the fluid at the wall and the speed of the wall is assumed to be proportional to the shear rate at the wall. The exact expressions for the velocity and the shear stress are determined by means of the Laplace transform. The velocity fields corresponding to both cases with slip and non-slip conditions, for fractional Newtonian and Newtonian fluids are obtained. The particular case, namely sine oscillations of the wall is studied. Results for fractional Newtonian fluids are compared with those of viscous Newtonian fluids in both cases of the flow with slip and non-slip conditions. In addition the influence of the slip coefficient on the relative velocity is studied.

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Keywords: Newtonian Fluid, Fractional Derivative, Velocity Field.



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