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.

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.

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.

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.

A kinetic model to describe lovastatin biosynthesis by Aspergillus terreus ATCC 20542 in a batch culture with the simultaneous use of lactose and glycerol as carbon sources was developed. In order to do this the kinetics of the process was first studied. Then, the model consisting of five ordinary differential equations to balance lactose, glycerol, organic nitrogen, lovastatin and biomass was proposed. A set of batch experiments with a varying lactose to glycerol ratio was used to finally establish the form of this model and find its parameters. The parameters were either directly determined from the experimental data (maximum biomass specific growth rate, yield coefficients) or identified with the use of the optimisation software. In the next step the model was verified with the use of the independent sets of data obtained from the bioreactor cultivations. In the end the parameters of the model were thoroughly discussed with regard to their biological sense. The fit of the model to the experimental data proved to be satisfactory and gave a new insight to develop various strategies of cultivation of A. terreus with the use of two substrates.

The studies showed that alkaline lipase from Pseudomonas fluorescens enables an irreversible transesterification of vinyl esters to give enantiomeric excess (eeR) of about 80% using vinyl butyrate as acyl donor and diisopropyl ether as a solvent, at partially optimized conditions. For the native lipase the process was adequately described by a five-parameter Ping-Pong Bi Bi model for both enantiomers plus expression accounting for the formation of enzyme-acyl donor complex, but for the same lipase supported on mesoporous materials of SBA-15-Oc type, R-product inhibition also had to be taken into account. The use of hydrophobic support increased by more than two-fold the rate of the S-solketal conversion but even more that of R-solketal. Thus the immobilization of lipase had very positive effect on the process kinetics but decreased its enantioselectivity.

The aim of the present theme issue was to study the influence of ultrasound enhancement on the kinetics of osmotic dehydration and the effect of convective drying from the point of view of drying time and quality of dried products. Apple fruit was used as the experimental material. The kinetics of osmotic dehydration with (UAOD) and without (OD) ultrasound enhancement were examined for 40% fructose and sorbitol solutions. The effective dehydration time of osmotic process was determined. Preliminary dehydrated samples with OD and UAOD were next dried convectively with (CVUS) and without (CV) ultrasound assistance. The influence of OD and UAOD on the kinetics of CV and CVUS drying was analysed. The parameters of water activity and colour change were measured for the assessment of product quality after drying process.

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.