Ever-more stringent legislative regulations on harmful emissions and fuel efficiency have driven researchers to develop cleaner and more efficient internal combustion engines. Research studies have shown that low temperature combustion can produce very low NOx and soot emissions while obtaining diesel-like high thermal efficiency. One strategy is reactivity controlled compression ignition (RCCI) combustion, which has been shown to be more practical and applicable than homogeneous charge compression ignition (HCCI) by providing extra controllability on the combustion processes, including for the combustion phasing and duration. However, recent experimental work has shown that more than 95% of the particulate matter from RCCI combustion consists of organic species, which is drastically different from conventional diesel combustion (CDC), which mainly produces carbonaceous soot. This distinctive character is believed to be related to condensation processes of large hydrocarbon species that cannot stably exist in the gas phase. Rather, under certain conditions the heavy gaseous species can condense and they become responsible for the organic fraction of the particulate matter. To investigate this physical phenomenon, a thermodynamically consistent, robust and efficient phase equilibrium solver, which performs rigorous phase stability tests and phase splitting calculations with advanced numerical algorithms, was developed. This is a first step forward modeling condensation processes in engines. Potential phase separation and combination are considered using Gibbs free energy minimization and entropy maximization. The numerical solver was well validated on a number of mixtures in two- and three-phase equilibria with available data. It was also applied to study the complex phase behavior of mixtures, including multiphase dynamic flash calculations, supercritical fluid behavior, condensation and evaporation, PVT analysis and critical point behavior. In addition, the developed model was coupled with an open-source CFD code, KIVA, widely used for multi-dimensional engine spray and combustion simulations, thus enabling a consistent treatment of both the fluid dynamics and thermodynamics. The model was used to investigate a number of two-phase flow problems, including regular condensation in a nozzle, retrograde condensation in a shock tube, condensation processes during supercritical fuel injection, and condensation in an engine combustion chamber. The simulations were validated using available experiments for both pure species and mixtures, ranging from subcritical to supercritical flows. The thermodynamic equilibrium analysis was also applied to study engine fuel condensation processes under non-reacting conditions. First, simulations were performed for Sandia optical combustion vessels and engines with direct injection of a diesel jet into a pure nitrogen environment. Consistent with experiments, the simulations show that condensation of previously evaporated fuel takes place during the expansion stroke. For high-pressure fuel injection of an n-alkane fuel, there are local sub-critical conditions under which phase separation can take place. This is because of the significant reduction of the mixture temperature caused by vaporization and cooling of the cold liquid fuel. Therefore, even though the ambient conditions during injection are supercritical relative to the fuel, the actual mixture temperature can be much lower so that the mixture enters into the two-phase region. The phase equilibrium model was finally applied to study fuel condensation processes in a RCCI combustion engine. Condensation was predicted during the late stages of the expansion stroke, when the continuous expansion sends the local fluid into the two-phase region again. The condensed fuel is shown to affect emission predictions, including engine-out particulate matter and unburned hydrocarbons. Consistent with experiments, the organic fraction mass from the condensed fuel is predicted to be the majority (more than 99%) of the total particulate matter. Also, as the engine operation changes from low to high load, fuel condensation is significantly reduced due to the higher temperatures and pressures, and the engine-out PM is predicted to be mainly composed of solid carbonaceous soot particles.