In this paper, we study quorum sensing in Pseudomonas aeruginosa biofilms. Quorum sensing is a process where bacteria monitor their population density through the release of extra-cellular signalling molecules. The presence of these molecules affects gene modulation leading to changes in behaviour such as the release of virulence factors. Here, we use numerical methods to approximate a 2-D model of quorum sensing. It is observed that the shape of the biofilm can have a profound effect on the onset of quorum sensing. This has serious repercussions for experimental observations since biofilms of the same biomass but different shapes can produce quite different results.