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.
Steel is a versatile material that has found widespread use because of its mechanical properties, its relatively low cost, and the ease with which it can be used in manufacturing process such as forming, welding and machining. Regarding to mechanical properties are strongly affected by grain size and chemical composition variations. Many industrial developments have been carried out both from the point of view of composition variation and grain size in order to exploit the effect of these variables to improve the mechanical proprieties of steels. It is also evident that grain growth are relevant to the mechanical properties of steels, thus suggesting the necessity of mathematical models able to predict the microstructural evolution after thermo cycles. It is therefore of primary importance to study microstructural changes, such as grain size variations of steels during isothermal treatments through the application of a mathematical model, able in general to describe the grain growth in metals. This paper deals with the grain growth modelling of steels based on the statistical theory of grain growth originally developed by Lücke  and here integrated to take into account the Zener drag effect and is therefore focused on the process description for the determination of the kinetics of grain growth curves temperature dependence.
The growth kinetics of the zinc coating formed on the surface of casting made from ductile iron grade EN-GJS-500-3 was investigated. To produce homogenous metal matrix in test samples, the normalising and ferritising annealing was carried out. Studies showed a heterogeneous structure of cast iron with varying content of the phases formed. This was followed by hot dip galvanising treatment at 450°C to capture the growth kinetics of the zinc coating (the time of the treatment ranged from 60 to 600 seconds). Nonlinear estimation of the determined growth kinetics of the alloyed layer of a zinc coating was made and an equation of the zinc coating growth was derived. Based on the results of the investigations it was concluded that thickness of the zinc coating formed on the surface of casting with a 100% pearlitic matrix makes 55% of the thickness of coating formed on the surface in 100% ferritic.