The effect of packing mickostructure on the effective conductivity of random sphere packing for sintering applications

Sintering is a thermally activated solid diffusion process. Study of the heat transfer process is one of the key elements for the improvement of sintering technology. Within sphere packings, the three-dimensional interconnected network of spheres and the interconnected pore structures are very complex. In order to bypass this complexity, typically, the porous medium approach has been used for applications allow relative coarse resolution. However, for sintering studies, the traditional effective conductivity determination may not be directly applicable. Firstly, the porosity variation may be very rigorous due to the non-uniform densification process with a stiff temperature gradient. Furthermore, a fine control volume is required for the fine temperature resolution for studying the effect on unbalance densification rate within packings. Therefore, it is necessary to investigate the dependence of the effective conductivity of the small packing on the detailed packing parameters, such as coordination number and the contact radius ratio. Indeed, this study was one of the first attempts to investigate such effect. A numerical study was performed. The results showed that porosity is indeed not the unique parameter for describing the packing structure while the mean coordination number and the mean contact radius ratio are more appropriate for small population size of spheres. With the developed correlation, the effective conductivity can be directly determined for any packing with the known mean coordination number and the known contact radius ratio without requiring any empirical determination