| Microporosity is one of the major defects in casting. In this thesis, a phase-field model is developed for the simulation of the transport processes in microporosity formation during solidification. Alloy solidification, bubble growth and dynamics, shrinkage flow, chemical reaction at the gas-liquid interface, coexistence of the solid, liquid, and gas phases, and triple junction motion are all taken into consideration.; A diffuse interface model for two-phase flows is introduced that assumes the two phases coexist inside the diffuse interface. A separate momentum equation is used to calculate the slip velocity between the phases within the diffuse interface. This two-phase approach is coupled with a phase-field equation for implicit interface tracking to study the buoyancy-driven Hele-Shaw flows with Rayleigh-Taylor instability for two fluids of large property contrasts.; As the first step toward modeling porosity in solidification, bubble growth and flow are studied in a supersaturated liquid. A phase-field model is derived that accounts for the pressure dependent equilibrium concentration at the gas-liquid interface. Flows in both gas and liquid are solved using a diffuse interface model with surface tension and phase change. An anti-trapping current is included in the species equation and the resulting model reduces to the sharp-interface equations in a thin-interface limit. Simulations are performed for the growth of a spherical bubble, bubble merging, and coarsening.; Solidification with density change flow is then considered. The dependence of the interface temperature on the density difference between phases, interface kinetics, and pressure and stresses are considered at a solid-liquid interface. Phase-field models are derived to simulate the density change flow normal to a planar solidification front. The operating state of a growing two-dimensional dendrite with density change flow is then examined.; Finally, a multiphase-field model is constructed for the solid-liquid-gas system present in porosity formation during solidification. The model allows for an arbitrary contact angle at the triple junction and reduces to the quantitative model for alloy solidification at the solid-liquid interface. Simulations are conducted for the formation of single-component bubbles in directional solidification of pure substances and alloys. The pore growth and final shape of the pores are investigated as a function of the initial gas concentration, nucleation supersaturation, and important solidification parameters. The interactions of the pores with planar and dendritic solidification microstructures are examined in detail. |
