We discuss modeling, analysis, and simulation of a free boundary problem arising in one of two applications of current interest. First, we consider methane gas is mixed with water under low temperatures and high pressure conditions, leading to the presence of dissolved gas, free gas, and hydrate crystals. Second, we describe biofilm growth at the poreescale around the grains of porous medium. Depending on the time and spatial scale of interest, the model(s) can be of equilibrium (variational inequality) or kinetic type, and can be described with a phase field model. This is joint work with many students and collaborators to be named in the talk.