We present a review of recent technical developments in Lattice Boltzmann Equations, as applied to single-phase flows with and without slip lenghts at the wall and for multi-phase flows in presence of hydrophobic walls. The interplay between roughness and hydrophobicity is discussed for microfluidics application. The issue of finite Knudsen effects is also addressed.

In the present research, we used molecular dynamics simulation to determine the effect of cutting parameters on micro-grain boundary structures and Burgers vector distribution in single crystal iron and polycrystalline iron materials. The result showed that the destruction of the lattice in polycrystalline iron caused by the cutting tool was restricted to the contact surface area. In addition, in the precision machining process, a higher refining grain was observed on the iron surface. During the cutting process of single crystal iron, large-scale slip occurred along the <111> crystal direction on the {110} crystal plane. And the slip presented an annular shape.

Results of the ab initio molecular dynamics calculations of silicon crystals are presented by means of analysis of the velocity autocorrelation function and determination of mean phonon relaxation time. The mean phonon relaxation time is crucial for prediction of the phonon-associated coefficient of thermal conductivity of materials. A clear correlation between the velocity autocorrelation function relaxation time and the coefficient of thermal diffusivity has been found. The analysis of the results obtained has indicated a decrease of the velocity autocorrelation function relaxation time t with increase of temperature. The method proposed may be used to estimate the coefficient of ther-mal diffusivity and thermal conductivity of the materials based on silicon and of other wide-bandgap semiconductors. The correlation between kinetic energy fluctuations and relaxation time of the velocity autocorrelation function has been calculated with the relatively high coefficient of determination R2 = 0.9396. The correlation obtained and the corresponding approach substantiate the use of kinetic energy fluctuations for the calculation of values related to heat conductivity in silicon-based semiconductors (coefficients of thermal conductivity and diffusivity).

The molecular dynamics of the well-known nematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl geometrically restricted in Anopore and Synpor porous membranes with various pore structure and treated by different surfactants (namely decanoic acid and lecithin) is compared. In the Anopore membrane the chosen surfactants induce the homeotropic orientation of the molecules on the walls of the cylindrical pores and observed corresponding relaxation processes (librational modes) are practically the same. The dielectric measurements of lecithin treated Synpor membranes reveals the reorientation of the molecules from planar to homeotropic on the complex multilayer structure present in their volume. The dielectric strengths of the observed two molecular processes (δ-process and librational mode) are inversed in the ratio compared to the untreated membranes. The observed differences in molecular dynamics results from the orientation of the liquid crystal molecules in untreated and treated membranes and the structure of the membranes themselves.