A phase-field method for interface resolving numerical simulations of two-phase flows with OpenFOAM (R) is validated for the buoyancy-driven rise of a single air bubble through a viscous stagnant liquid using experimental data from literature. The validation encompasses the terminal bubble rise velocity and the instantaneous cutting of the bubble by a solid horizontal cylinder. In the latter process, the numerical method takes into account the equilibrium contact angle of the three-phase system. The numerical method is then used to study the behavior of a single air bubble rising through a representative subdomain of a periodic open cellular structure (POCS) with cubic cell geometry filled with stagnant water. The results indicate that the bubble shape and path do significantly depend on the structure wettability. In the industrial application of POCS for enhancing mass transfer and as catalytic supports, the utilization of structures with high wettability (low contact angles) is expected to be beneficial. (C) 2016 Elsevier B.V. All rights reserved.