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<p>Grain structure and secondary phases play a critical role in determining the mechanical properties of industrial alloys. The spatial variation of such phases is very closely correlated to the liquid pooling established during late stage solidification and grain boundary coalescence. Obtaining a theory that correlates the evolution of length scales during grain boundary coalescence is a critical step toward the optimization of commercial alloys. This thesis highlights various phenomena that enter such a theory. They include coarsening and coalescence of dendrites, nucleation mechanisms and changes in composition of inter-dendritic liquid where second phases tend to initially form. Quantitative phase field models of solidification to simulate casting conditions and microstructure evolution are used in combination with characterization techniques to illustrate the connection between number, size, and distribution of liquid pools. Characterization techniques include spectral analysis, and clustering analysis by way of the Hoshen-Kopleman algorithm. By characterizing late-stage liquid pools, this thesis aims to be a first step towards developing a statistical scaling theory of length scale of liquid pooling.</p> / Master of Applied Science (MASc)