Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Kinetic model for selective cultivation of microfungi in a microscreen process for food processing wastewater treatment and biomass production

The research was aimed at developing a technology to combine the production of useful microfungi with the treatment of wastewater from food processing. A recycle bioreactor equipped with a micro-screen was developed as a wastewater treatment system on a laboratory scale to contain a Rhizopus culture and maintain its dominance under non-aseptic conditions. Competitive growth of bacteria was observed, but this was minimised by manipulation of the solids retention time and the hydraulic retention time. Removal of about 90% of the waste organic material (as BOD) from the wastewater was achieved simultaneously. Since essentially all fungi are retained behind the 100 mum aperture screen, the solids retention time could be controlled by the rate of harvesting. The hydraulic retention time was employed to control the bacterial growth as the bacteria were washed through the screen at a short HRT. A steady state model was developed to determine these two parameters. This model predicts the effluent quality. Experimental work is still needed to determine the growth characteristics of the selected fungal species under optimum conditions (pH and temperature).

Adsorption of food dyes onto chitosan: Optimization process and kinetic

Adsorption of food dyes acid blue 9 and food yellow 3 onto chitosan was optimized. Chitosan was obtained from shrimp wastes and characterized.Afull factorial design was used to analyze the effects of pH, stirring rate and contact time in adsorption capacity. In the optimal conditions, adsorption kinetics was studied and the experimental data were fitted with three kinetic models. The produced chitosan showed good characteristics for dye adsorption. The optimal conditions were: pH 3, 150rpm and 60 min for acid blue 9 and pH 3, 50rpm and 60 min for food yellow 3. In these conditions, the adsorption capacities values were 210mgg−1 and 295mgg−1 for acid blue 9 and food yellow 3, respectively. The Elovich kinetic model was the best fit for experimental data and it showed the chemical nature of dyes adsorption onto chitosan.

Adsorption of anionic dyes on chitosan grafted poly(alkyl methacrylate)s

Chitosan grafted poly(alkyl methacrylate)s (namely chitosan grafted poly(methyl methacrylate) (ChgPMMA), chitosan grafted poly(ethyl methacrylate)(ChgPEMA), chitosan grafted poly(butyl methacrylate) (ChgPBMA) and chitosan grafted poly(hexyl methacrylate) (ChgPHMA)) were synthesized and characterized by using FT-IR and C-13 NMR techniques. The adsorption batch experiments on these grafted copolymers were conducted by using an anionic sulfonated dye. Orange-G. A pseudo-second-order kinetic model was used to determine the kinetics of adsorption. The effect of grafting, effect of process variables and the effect of different sulfonated anionic dyes (Orange-C, Congo Red, Remazol Brill Blue R and Methyl Blue) on the adsorption kinetics was determined. The Langmuir and Freundlich models were used to fit the adsorption isotherms and from the values of correlation coefficients (R-2), it was observed that the experimental data fits very well to the Langmuir model. The values of the maximum adsorption capacity of the adsorbents follow the order: ChgPMMA > ChgPEMA > ChgPBMA > ChgPHMA > chitosan. (C) 2010 Elsevier B.V. All rights reserved.

Studies on the adsorption equilibrium and kinetics of pentachlorophenol on suspended particulate matter of Donghu Lake water

In this paper, the adsorption equilibrium and kinetic behaviors of pentachlorophenol (PCP) on suspended particulate matter (SPM) in Donghu Lake water were investigated. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and their constants were evaluated. The results indicated that the adsorption of PCP on Donghu Lake SPM followed the Freundlich isotherm. Furthermore, the first order Lagergren rate equation and the pseudo-second order rate equation were used to describe the kinetic behaviors of PCP adsorption on Donghu Lake SPM, the rate constants were determined, and the kinetic process of the adsorption of PCP on Donghu Lake SPM followed the second order kinetic model.

Studies on the adsorption and kinetics of photodegradation of a model compound for heterogeneous photocatalysis onto TiO2

An investigation was made on the adsorption and kinetics of photodegradation of potassium hydrogenphthalate in an aqueous suspension of TiO2. Two models, Langmuir and Freundlich, were used to describe the adsorption process and the model proposed by Langmuir-Hinshelwood (L-H) was employed to describe the kinetics of the photodecomposition reactions of hydrogenphthalate. The results of the adsorptions were fitted to the models proposed by Langmuir and Freundlich. Adsorption was found to be a function of the temperature, with adsorption capacity increasing from 2.4 to 4.5 mg/g when the temperature rose from 20 to 30 degrees C. The kinetic model indicates that the rate constant, k, of the first order reaction, is high in the 10.0 to 100 mg/l interval, which is coherent with the low value of the adsorption constant, K. The results fitted to the L-H model led to an equation that, within the range of concentrations studied here, theoretically allows one to evaluate the photodegradation rate. (c) 2005 Elsevier Ltd. All rights reserved.

Remediation of phenol-contaminated water by adsorption using poly(methyl methacrylate) (PMMA)

Recently polymeric adsorbents have been emerging as highly effective alternatives to activated carbons for pollutant removal from industrial effluents. Poly(methyl methacrylate) (PMMA), polymerized using the atom transfer radical polymerization (ATRP) technique has been investigated for its feasibility to remove phenol from aqueous solution. Adsorption equilibrium and kinetic investigations were undertaken to evaluate the effect of contact time, initial concentration (10-90 mg/L), and temperature (25-55 degrees C). Phenol uptake was found to increase with increase in initial concentration and agitation time. The adsorption kinetics were found to follow the pseudo-second-order kinetic model. The intra-particle diffusion analysis indicated that film diffusion may be the rate controlling step in the removal process. Experimental equilibrium data were fitted to five different isotherm models namely Langmuir, Freundlich, Dubinin-Radushkevich, Temkin and Redlich-Peterson by non-linear least square regression and their goodness-of-fit evaluated in terms of mean relative error (MRE) and standard error of estimate (SEE). The adsorption equilibrium data were best represented by Freundlich and Redlich-Peterson isotherms. Thermodynamic parameters such as Delta G degrees and Delta H degrees indicated that the sorption process is exothermic and spontaneous in nature and that higher ambient temperature results in more favourable adsorption. (C) 2011 Elsevier B.V. All rights reserved.

Study of biosorption of rare earth metals (La, Nd, Eu, Gd) by Sargassum sp. biomass in batch systems: Physicochemical evaluation of kinetics and adsorption models

This work evaluated kinetic and adsorption physicochemical models for the biosorption process of lanthanum, neodymium, europium, and gadolinium by Sargassum sp. in batch systems. The results showed: (a) the pseudo-second order kinetic model was the best approximation for the experimental data with the metal adsorption initial velocity parameter in 0.042-0.055 mmol.g -1.min-1 (La < Nd < Gd < Eu); (b) the Langmuir adsorption model presented adequate correlation with maximum metal uptake at 0.60-0.70 mmol g-1 (Eu < La < Gd < Nd) and the metal-biomass affinity parameter showed distinct values (Gd < Nd < Eu < La: 183.1, 192.5, 678.3, and 837.3 L g-1, respectively); and (c) preliminarily, the kinetics and adsorption evaluation did not reveal a well-defined metal selectivity behavior for the RE biosorption in Sargassum sp., but they indicate a possible partition among RE studied. © (2009) Trans Tech Publications.

Adsorption/desorption of arsenic by tropical peat: influence of organic matter, iron and aluminium

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multilayer adsorption of Cu(II) and Cd(II) over Brazilian Orchid Tree (Pata-de-vaca) and its adsorptive properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Removal of antibiotic compounds by adsorption using glycerol-based carbon materials

This study is focused on the synthesis and application of glycerol-based carbon materials (GBCM200, GBCM300 and GBCM350) as adsorbents for the removal of the antibiotic compounds flumequine and tetracycline from aqueous solution. The synthesis enrolled the partial carbonization of a glycerol-sulfuric acid mixture, followed by thermal treatments under inert conditions and further thermal activation under oxidative atmosphere. The textural properties were investigated through N2 adsorption–desorption isotherms, and the presence of oxygenated groups was discussed based on zeta potential and Fourier transform infrared (FTIR) data. The kinetic data revealed that the equilibrium time for flumequine adsorption was achieved within 96 h, while for tetracycline, it was reached after 120 h. Several kinetic models, i.e., pseudo-first order, pseudo-second order, fractional power, Elovich and Weber–Morris models, were applied, finding that the pseudo-second order model was the most suitable for the fitting of the experimental kinetic data. The estimated surface diffusion coefficient values, Ds, of 3.88 and 5.06 10 14 m2 s 1, suggests that the pore diffusion is the rate limiting step of the adsorption process. Finally, as it is based on SSE values, Sips model well-fitted the experimental FLQ and TCN adsorption isotherm data, followed by Freundlich equation. The maximum adsorption capacities for flumequine and tetracycline was of 41.5 and 58.2 mg g 1 by GBCM350 activated carbon.

Mean-field results of a lattice-gas model of multilayer adsorption

A lattice-gas model of multilayer adsorption has been solved in the mean-field approximation by a different numerical method. Earlier workers obtained a single solution for all values of temperature and pressure. In the present work, multiple solutions have been obtained in certain regions of temperature and pressure which give rise to bysteresis in the adsorption isotherm. In addition, we have obtained a parameter which behaves like an order parameter for the transition. The potential-energy function shows a double minimum in the region of bysteresis and a single maximum elsewhere.

A surface kinetics model for the growth of Si1-xGex by UHV/CVD using SiH4/CeH4

The surface reaction mechanism of Si1-xGex/Si growth using SiH4 and GeH4 in UHV/CVD system was studied. The saturated adsorption and desorption of SiH4 from Si(1 0 0) surface was investigated with the help of TPD and RHEED, and it was found that all the 4 hydrogen atoms of one SiH4 molecule were adsorbed to the Si surface, which meant that the dissociated adsorption ratio was proportional to 4 power of surface vacancies. The analysis of the reaction of GeH4 was also done. A new surface reaction kinetic model on Si1-xGex/Si epitaxial growth under UHV conditions by SiH4/GeH4 was proposed based on these studies. The predictions of the model were verified by the experimental results. (C) 2000 Elsevier Science B.V. All rights reserved.

Adsorption of Ni(SO4) on Malaysian rubber-wood ash

The possible use of wood ash as an adsorbent of nickel sulphate from dilute solutions and the effect of operating parameters were investigated in this study. The rate constants of adsorption were determined at different concentrations and temperatures. The applicability of the first-order reversible equation and an empirical kinetic model were tested to understand the kinetics of nickel sulphate removal at different concentrations. Pore diffusion was found as the rate-controlling step. The Langmuir and Freundlich isotherms were applied to find out the adsorption parameters. The activation energy of adsorption was -11.54 kJ mol-1. The value of the enthalpy change was ?H=-10.35 kcal mol-1.

Adsorption and photocatalysed destruction of cationic and anionic dyes on mesoporous titania films: Reactions at the air-solid interface

Cationic dyes, such as methylene blue (MB), Thionine (TH) and Basic Fuschin (BF), but not anionic dyes, such as Acid Orange 7 (AO7), Acid Blue 9 (AB9) and Acid Fuschin (AF), are readily adsorbed onto mesoporous titania films at high pH (pH 11), i.e. well above the pzc of titania (pH 6.5), due to electrostatic forces of attraction and repulsion, respectively. The same anionic dyes, but not the cationic dyes, are readily adsorbed on the same titania films at low pH (pH 3), i.e. well below titania's pzc. MB appears to adsorb on mesoporous titania films at pH 11 as the trimer (lambda(max) = 570 nm) but, upon drying, although the trimer still dominates, there is an absorption peak at 665 nm, especially notable at low [MB], which may be due to the monomer, but more likely MB J-aggregates. In contrast, the absorption spectrum of AO7 adsorbed onto the mesoporous titania film at low pH is very similar to the dye monomer. For both MB and AO7 the kinetics of adsorption are first order and yield high rate constants (3.71 and 1.481 g(-1) min(-1)), indicative of a strong adsorption process. Indeed, both MB and AO7 stained films retained much of their colour when left overnight in dye-free pH 11 and 3 solutions, respectively, indicating the strong nature of the adsorption. The kinetics of the photocatalytic bleaching of the MB-titania films at high pH are complex and not well-described by the Julson-Ollis kinetic model [A.J. Julson, D.F. Ollis, Appl. Catal. B. 65 (2006) 315]. Instead, there appears to be an initial fast but not simple demethylation step, followed by a zero-order bleaching and further demethylation steps. In contrast, the kinetics of photocatalytic bleaching of the AO7-titania film give a good fit to the Julson-Ollis kinetic model, yielding values for the various fitting parameters not too dissimilar to those reported for AO7 adsorbed on P25 titania powder. (C) 2008 Elsevier B.V. All rights reserved.