Planar flow casting (PFC) is a single-stage rapid solidification technique for the production of thin, metallic ribbons. Liquid metal flowing through a small nozzle contacts a copper wheel, serving as a heat sink and encouraging heating rates in excess of 10^5 K/s. Proximity of this nozzle to the wheel recruits capillary forces, holding the liquid metal above the wheel and creating a solidification zone referred to as the puddle. Solidification in the puddle occurs either as crystallization or vitrification (glass formation). Utilized for its ability to produce rapidly solidified glassy alloys in the industrial sector, the academic study of PFC has traditionally focused largely on the production of crystalline metals. The results presented in this work will focus on the processing of an aluminumsilicon crystalline alloy (Al-7Si) and the processing of a noncrystalline nickelphosphorus based alloy (MBF61), elucidating fundamental similarities and differences between the two families of materials. The work in this thesis will highlight the study of crystalline and noncrystalline materials in the PFC process, drawing parallels and differences between these two systems. While crystallization occurs instantaneously at the continuum scale and a clear difference between the solid and liquid phases exists, the vitrification process occurs continuously and the solid and liquid phases are indistinct. Although these processes are fundamentally different, it will be shown in this work (chapter 2) that the formation of glassy and crystalline solids are governed by the same macroscopic physics and exist on the same growth curve. This was determined through knowledge of the heat flow in the casting process, assuming the growth of a solid planar interface. Chapter 3 will show that, despite these processing similarities, fundamental differences in the processing of crystalline and noncrystalline materials exist. Performed through a fluid-flow analysis of the process it is shown that the physics governing fluid flow of the glass former differs from that of a glass former, despite the similarities shown in chapter 2. The knowledge garnered from these chapters was used to develop a computational model for the casting system using the OpenFOAM software package. Chapter 4 will highlight our attempts to utilize the OpenFOAM software package to simulate solidification processes. Although the results are preliminary, chapters 3 and 5 show promise in the ability to simulate the casting process and provide guidance in the production of augmenting the current casting process for the continuous casting of wire directly from the melt. Additional chapters are provided to highlight additional investigations (chapter 6), changes made to the lab (chapter 7), and how to customize an OpenFOAM package for use in the PFC process (appendix B).