The theoretical study of the efficiency of diffusion deposition of nanoaerosols in the extended range of the Peclet numbers

The efficiencies of the diffusion deposition of nanoaerosols for a single fiber for the models of aerosol filter and wire mesh screen are studied numerically in the extended range of the Peclet number Pe.The rectangular periodic cell model for fluid flow and convective-diffusive transport of small aerosol particles is used.Most of the previous theoretical and experimental studies of single fiber diffusion deposition efficiency were for the case of Pe>1.The array with uniform square or chess grid of fibers and of a row of circular cylindrical fibers are considered as the filter and wire mesh screen models.The flow and particles transport equations are solved numerically using the Boundary Element Method.The obtained numerical data are used to derive the approximate formulas for the deposition efficiency in the entire range of the Peclet number for the various porosities of the filter medium or distances between fibers in a wire mesh screen.The derived dependencies take into account nonlinearity of the deposition efficiency at the low Peclet numbers.The obtained analytical dependencies compare well with the numerical and experimental data.

DEM SIMULATION OF LIQUEFACTION FOR GRANULAR MEDIA UNDER UNDRAINED AXISYMMETRIC COMPRESSION AND PLANE STRAIN CONDITIONS

Based on three dimensional （3D） Discrete Element Method （DEM）, the paper presents simulation results of undrained tests on loose assemblies of polydisperse spheres under axisymmet- ric compression and plane strain conditions using a periodic cell. In the present work, undrained tests were modelled by deforming the samples under constant volume conditions. The undrained （effective） stress paths are shown to be qualitatively similar to experimental results in literature. A microscopic parameter in terms of redundancy factor （RF） is used to identify the onset of lique- faction （or temporary liquefaction）, with the condition of RF equal to unity defining the transition from ＇solid-like＇ to ＇liquid-like＇ behaviour. It is found that the undrained behaviour is governed by the evolution of redundancy factor under both undrained axisymmetric compression and plane strain conditions, and a reversal of deviatoric stress in stress path for medium loose systems oc- curs due to the fact that the system becomes a structural mechanism （RF 〈 1） transiently at the microscopic level during the evolution.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.