A mathematical model of a plane, steady state biofilm, with the use of a single substrate kinetics, was proposed. A set of differential equations was solved. In order to analyse the biofilm’s behaviour, a number of simulations were performed. The simulations included varying process parameters such as detachment coefficient and substrate loading. Two detachment models were taken into consideration: one describing the detachment ratio as proportional to the thickness of the biofilm, and the other one proportional to the thickness of the biofilm squared. The results provided information about substrate and live cell distribution in biofilm and the influence of certain parameters on biofilm behaviour.

The paper focuses on the modelling of bromate formation. An axial dispersion model was proposed to integrate the non-ideal mixing, mass-transfer and a kinetic model that links ozone decomposition reactions fromthe Tomiyasu, Fukutomi and Gordon (TFG) ozone decaymodelwith direct and indirect bromide oxidation reactions, oxidation of natural organicmatter and its reactionswith aqueous bromine. To elucidate the role of ammonia an additional set of reactions leading to bromamine formation, oxidation and disproportionation was incorporated in the kinetic model. Sensitivity analysis was conducted to obtain information on reliability of the reaction rate constants used and to simplify the model.

This paper presents an experimental study on Cochineal Red A dye adsorptive removal by yeast. Batch equilibrium and kinetic tests were conducted in constant temperature of 30 ◦C for the dye’s initial concentration range of 0.02–0.50 g/L (pH = 3 and 10) and 0.02–0.35 g/L (pH = 7:6). The equilibrium was reached after 105–120 min. Yeast demonstrated the adsorption capacity of 10.16 mg/g for acidic environment (pH = 3) and slightly lower values (8.13 mg/g and 8.38 mg/g respectively) for neutral (pH = 7:6) and alkaline environment (pH = 10). The experimental equilibrium results were fitted with Langmuir, Freundlich, Sips and Toth isotherm models. Most of them (Freundlich model being the exception) were proven sufficient for the experimental data correlation. The adsorption kinetic studies showed that the pseudo-second order model fits better the experimental data than the pseudo-first- order model. Results achieved from intra-particle diffusion model indicate that powdered yeast are a nonporous adsorbent. The percentage of solution discoloration reached a maximum value of 75% at pH = 3 for an initial dye concentration of 0.02 g/L.

In order to investigate the mechanism of adsorption of reactive dyes from the textile industry on ash from heating plant produced by brown coal combustion, some characteristic sorption constants are determined using Langergren adsorption equations for pseudo-fi rst and pseudo-second order. Combined kinetic models of pseudo-first order and pseudo-second order can provide a simple but satisfactory explanation of the adsorption process for a reactive dye. According to the characteristic diagrams and results of adsorption kinetic parameters of reactive dyes on ashes, for the applied amounts of the adsorbents and different initial dye concentrations, it can be concluded that the rate of sorption is fully functionally described by second order adsorption model. According to the results, the rate constant of pseudo-second order decreases with increasing initial dye concentration and increases with increasing amount of adsorbent – ash.

The cometabolic biodegradation of 4-Chlorophenol (4-CP) by the Stenotrophomonas maltophilia KB2 strain in the presence of phenol (P) was studied. In order to determine the kinetics of biodegradation of both substrates, present alone and in cometabolic systems, a series of tests was carried out in a batch reactor changing, in a wide range, the initial concentration of both substrates. The growth of the tested strain on phenol alone was described by Haldane kinetic model (mm = 0:9 1/h, Ksg = 48:97 gg/m3, KIg = 256:12 gg/m3, Yxg = 0:5715). The rate of 4-CP transformation by resting cells of KB2 strain was also described by Haldane equation and the estimated parameters of the model were: kc = 0:229 gc=gxh, Ksc = 0:696 gc=m3, KIc = 43:82 gc=m3. Cometabolic degradation of 4-CP in the presence of phenol was investigated for a wide range of initial 4-CP and phenol concentrations (22–66 gc/m3 and 67–280 gg/m3 respectively). The experimental database was exploited to verify the two kinetic models: CIModel taking only the competitive inhibition into consideration and a more universal CNIModel considering both competitive and non-competitive inhibition. CNIModel approximated experimental data better than CIModel.

The study analyses application possibilities of filtration and thickening models in evaluation of papermaking suspension drainage rate. The authors proposed their own method to estimate the drainage rate on the basis of an existing Ergun capillary model of liquid flow through a granular material. The proposed model was less sensitive to porosity changes than the Ergun model. An empirical verification proved robustness of the proposed approach. Taking into account discrepancies in the published data concerning how the drainage velocity of papermaking suspension is defined, this study examines which of the commonly applied models matches experimental results the best.

Analysis of granulation kinetics was carried out using a laboratory disc granulator with a diameter D of 0.5 m. A liquid binder was delivered to the tumbling bed at a constant flow rate with a nozzle generating droplets with a size of approx. 4-5 mm. Fine-grained chalk was used as a model of raw material and water or disaccharide solution with concentrations of 20 - 40% as a wetting liquid. Different times of droplet delivery ranging from 2 to 6 min were utilized. Granulometric composition of the bed for selected lengths of process, bed moisture and the moisture of individual size-fractions were assessed. Mass of granulated material, which was transferred from nuclei fraction to other size fractions was determined on the basis of mass balance analysis and the assessment of liquid migration between fractions. The influence of disaccharide concentration in wetting liquid on the aforementioned phenomena was also examined.

A mathematical model of waste tyre pyrolysis process is developed in this work. Tyre material decomposition based on a simplified reaction mechanism leads to main product lumps: noncondensable (gas), condensable (pyrolytic oil) and solid (char). The model takes into account kinetics of heat and mass transfer in the grain of the shredded rubber material as well as surrounding gas phase. The main reaction routes were modelled as the pseudo-first order reactions with a rate constant calculated from the Arrhenius type equation using literature values of activation energy determined for main tyre constituents based on TG/DTG measurements and tuned pre-exponential parameter values obtained by fitting theoretical predictions to the experimental results obtained in our laboratory reactor. The model was implemented within the CFD software (ANSYS Fluent). The results of numerical simulation of the pyrolysis process revealed non-uniformity of sample’s porosity and temperature. The simulation predictions were in satisfactory agreement with the experimentally measured mass loss of the tyre sample during pyrolysis process investigated in a laboratory reactor.

Ozonation is a heterogeneous process of chemical absorption often controlled by a gas-liquid mass transfer rate. This paper presents the results of kinetics in a reaction between phenylphenol isomers and ozone. The degradation of phenylphenol isomers during ozonation proceeds quite fast. In order to avoid the influence of mass transfer limitation the kinetics experiments were conducted in a homogenous liquid-liquid system. The second-order rate constants were determined using classical and competition methods, which are especially recommended for fast reactions. The determined rate constants at pH 2 using the two different methods are almost the same. The increase of pH causes an increase of rate constants for the reaction of phenylphenol isomers with ozone.

Validation results of a theoretical model that describes the formation of bromate during ozonation of bromide-containing natural waters are presented. An axial dispersion model integrating the nonideal mixing, mass-transfer and a kinetic model that links ozone decomposition reactions from the Tomiyasu, Fukutomi and Gordon ozone decay model with direct and indirect bromide oxidation reactions, oxidation of natural organicmatter and reactions of dissolved organics and aqueous bromine was verified. Themodel was successfully validated with results obtained both at a laboratory and a full scale. Its applicability to different water supply systems was approved.

In this study a group of selected transformation kinetics equations is applied to describe the isothermal ferritic transformation in austempered ductile iron (ADI). A series of dilatometric tests has been carried out on ADI at different temperatures. The obtained experimental data are utilized to determine the parameter values of the considered kinetic equations. It is found that the transformation kinetics models by Starink, Austin and Rickett are substantially more effective at describing the ferritic transformation in ADI than the much celebrated Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. Furthermore, it is demonstrated that evaluating the kinetic parameters using the least squares method instead of calculating them from vastly used formulas can significantly improve the accuracy of the JMAK model’s predictions.

In this work, the spectrophotometric studies on the kinetics of redox reaction between gold(III) bromide complexes and sodium nitrite, were carried out. From the kinetic curves collected under different conditions of reactants concentration, addition of bromide ions, temperature, pH and ionic strength, corresponding rate constants have been determined. The obtained results suggest the complex path of the [AuBr4]– reduction consisting of two parallel, bimolecular reactions where different reductant species (HNO2 and NO2–) take place and consecutive step with the metallic gold production. The second-order rate constants at 20oC are equal to 2.948 and 0.191 M–1·s–1, respectively. The values of activation enthalpy and activation entropy for the first and the second parallel step of the reaction were found to be ΔH‡ = 29.18 kJ·mol–1 and ΔS‡ = –13.95 J·mol–1·K, and ΔH‡ = 40.75 kJ·mol–1 and ΔS‡ = –31.06 ­J·mol–1·K, respectively. It was found that the reaction accelerates significantly with the increase of pH and is inhibited with the increase of Br– concentration. The substitutive, inner-sphere mechanism of electron transfer in the studied system was also suggested.