Understanding flow phenomena in the pulmonary acinus is important for predicting particle transport and deposition and hence, in designing effective drug delivery strategies for the lung. In the current study, a three-dimensional honeycomb-like geometry involving a central airspace and surrounding alveoli is used to represent an alveolar duct and sacs. Numerical results predict that flow in the presence of wall motion is characterized by the presence of a developing recirculation region within the cavity and by a flow entrainment region indicative of the weak nature of interaction between duct and cavity. Under the normal breathing condition (2.5 s) and volumetric expansion (approximately 25%) considered here, recirculation disappears for Re<0.6. Alveolar flow in higher generations (at lower Reynolds number) results from significantly higher entrainment of the ductal flow, and does not exhibit any recirculation. In an asymmetric arrangement of the alveolar cluster, topological differences in cavity result in significant differences in the size of recirculation and the size of entrainment region within the alveoli of the same acinar generation, indicative of a non-uniform alveolar ventilation. The flow in the terminal alveolar sac is non-recirculating and not affected by variation in geometrical features.