In this post-graduate research, kinetic equations of the Boltzmann type were used to model and simulate two-phase flows with phase change. This work was aimed at two different applications where it is important to understand and finely analyze the mechanisms and dynamics of phase change. The first topic is related to the development of two-phase passive cooling devices for micro-electronics. The second application is the aggregation of colloidal particles that results in the formation of deposits on the surface of a membrane during the process of membrane filtration. For the colloid application, a two fluid model is proposed that adapts existing Lattice Boltzmann methods to solve the flow. Finally, in a more exploratory part, an original method is proposed to solve the Boltzmann-Enskog equation, to deal with flows with phase change including thermal effects.