Densification of non-reactive viscous liquids containing solid inclusion

Theoretical models are developed for processes involved in non-reactive liquid phase densification. Results of these theoretical analyses are used to examine the densification behavior at 700$rmspcirc C$ of a model system containing spherical monosized copper powder as the inclusion phase and monosized lead-aluminoborate glass spheres as the liquid forming phase. It is shown that when the volume fraction of the inclusions exceeds the rigidity percolation threshold, densification is constrained by a rigid network of inclusions. When the volume fraction of the inclusions is below the rigidity percolation threshold, densification is controlled by buoyancy rise and by diffusion-controlled dissolution of pores (Ostwald dissolution). Elimination of large pores is controlled by buoyancy rise of pores assisted by pore coalescence. Small pores are eliminated by pore shrinkage controlled by Ostwald dissolution. It is shown that complete densification was not achieved after heat-treatment for up to 24 hours in helium for all samples except for the sample without inclusions. The main causes for incomplete densification of copper-lead aluminoborate system are (1) rigid network formation for samples with volume fraction of inclusions exceeding the rigidity percolation threshold, (2) settling of pores due to pore-inclusion attachment when the pore coordination number n is larger than a critical value n$rmsb{b}$*, (3) stabilization of pores when n is larger than a critical value n$sb{rm s}$*, (4) reduced rise velocities of pores due to hindered rise, increased effective viscosity and pore-inclusion attachment, and (5) settling of copper inclusions in the melt.