• NUMERICAL MODELLING OF FLOWS ALONG THE NANOSTRUCTURED SURFACE

    Materials Science. Non-Equilibrium Phase Transformations., Vol. 4 (2018), Issue 4, pg(s) 129-132

    Not all the properties of structured surfaces can be predicted just through using stationary solutions. Hydrophilic and hydrophobic qualities distinctly manifest themselves when surface contacts with mobile liquid; besides, shape of surface projections could variously influence flow velocity in different directions forming turbulences behind projections (even cavitation zones if flow is very fast). The following properties of liquids are particularly important for these processes: dynamic and kinematic viscosity, density, flow velocity and characteristic flow size, which represents itself contact surface relation to cross-sectional area. Relationships between these parameters characterize flowability of the particular substance and can be expressed as Reynolds number. Solutions of kinetic equations could be helpful to develop understanding on particular fluid’s flowability in the close vicinity of the surface.
    Examples discussed in this paper can be used not only in nano- and microstructures related research but also for high school and university students training in physics and natural sciences. Comprehension development about flow rate diferences in various distances from tube walls should be considered as one of problems for successful acquiring of hydrodynamics topics. Even use of transparent tubes is not helpful enough for appropriate demonstration of tinted liquid speed distribution in flow’s cross-sectional area – laminar flow when Reynolds number value is low and turbulent flow when it is high.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    SOFTWARE DEVELOPMENT FOR NUMERICAL SIMULATION OF FORMATTING THE PERIODIC NANOSTRUCTURES AFTER LASER IRRADIATION

    Mathematical Modeling, Vol. 2 (2018), Issue 1, pg(s) 3-7

    Nano-level surface processing is becoming increasingly important in the development of modern materials. Laser technology allows to change the processing parameters in a wide range and achieve the desired surface properties – hydrophilic and hydrophobic for various fluids. In such circumstances, the benefit of any researcher would be to provide software that can quickly and visibly see and measure the shape, size and configuration of nano and microstructures to be obtained. It is especially important that the obtained results in the form of 3D graphs allow us to see the evolutionary trends of surface nanostructures and help to decide on changes in the processing parameters. The researcher would be given the opportunity to input a wide variety of parameters – laser wavelength, pulse power, polarization angle, pulse frequency, pulse duration, processing time or number of impulses per coordinate – and the result obtained in a short time would serve to better understand common trends and help to make an informed decision for the actual processing parameters to be used in the experiment.

  • TECHNOLOGIES

    ON A MATHEMATICAL MODEL DESCRIBING THE MOTION OF SOLID PARTICLES OF MICRO- AND NANO-SIZE IN GAS FLOW

    Machines. Technologies. Materials., Vol. 10 (2016), Issue 11, pg(s) 23-32

    In the present article, a mathematical model is developed to describe the motion of solid particles of micro- and nano-size in a gaseous medium. The model is represented by certain integro-differential equation with appropriate initial and boundary conditions. A probabilistic interpretation of the model is provided and its solvability is studied. We find that unique solution exists at certain sufficient condition. It is shown that the Fokker-Planck equation can be obtained from the integro-differential equation. Finally, a generalization to the 2D case is performed.