Space fractional-order modeling for the sintering process of metal fibers via Lattice Boltzmann method

Considering the abnormal diffusion phenomena in the forming process of the sintered junction of metal fibers, a spatial fraction-order differential model is proposed based on the geometrical model and the integer-order differential model in this work. Lattice Boltzmann method(LBM) is applied to numerically analyze the established fractional model. And the growth process of sintered junctions dominated by surface diffusion mechanism at different fiber angles and sections is characterized by numerical simulation. Besides, the effects of fractional order, diffusion coefficient, and skewing parameters on the sintered process of metal fibers are presented and discussed. The developed model is valid by comparing the outcomes of numerical simulations with those obtained from the scanning electron microscope(SEM). It is also demonstrated that the fraction-order model can accurately depict the sintering process of metal fibers, and the anisotropy of metal bars can be characterized via the proposed model during sintering.