Phase transition, and more specifically bubble formation, plays an important role in many industrial applications, where bubbles are formed as a consequence of reaction such as in electrolytic processes or fermentation. Predictive tools, such as numerical models, are thus required to study, design or optimize these processes. This paper aims at providing a meso-scale modelling description of gas–liquid bubbly flows including heterogeneous bubble nucleation using a Discrete Bubble Model (DBM), which tracks each bubble individually and which has been extended to include phase transition. The model is able to initialize gas pockets (as spherical bubbles) representing randomly generated conical nucleation sites, which can host, grow and detach a bubble. To demonstrate its capabilities, the model was used to study the formation of bubbles on a surface as a result of supersaturation. A higher supersaturation results in a faster rate of nucleation, which means more bubbles in the column. A clear depletion effect could be observed during the initial growth of the bubbles, due to insufficient mixing.