In this work, airflow and particle transport are studied using mathematical and image-based models of pulmonary acinus. Numerical results predict that airflow in the presence of wall motion in a three-dimensional honey-comb like geometry is characterized by the presence of a recirculation region within the alveolar cavity and a weak entraining flow between alveolar duct and cavity. Alveolar flow in distal generations is characterized by higher alveolar flow rates, larger entrainment of ductal flow and absence of recirculatory flow inside alveoli. The study of transport constitutes assessment of mixing visualized by the tracking of massless particles and the study of transport and deposition of aerosols. The phenomenon of steady streaming is found to hold the key to the origin of kinematic mixing in the alveolus, the alveolar mouth and the alveolated duct. This mechanism provides the explanation for observed folding of material lines and increases in material surface area, and has no bearing on whether the geometry is expanding or if flow separates within the cavity or not. Streaming results in non-zero drift of particles between the beginning and end of a breathing cycle. Based on flow conditions and resultant convective mixing measures, we conclude that significant convective mixing in the duct and within an alveolus could originate only in the first few generations of the acinar tree as a result of non-zero inertia, flow asymmetry and large KC number. Evidence of streaming and related Lagrangian drift is also observed in image-based acinar models. Finally, particle deposition calculations are performed on the models of pulmonary acinus considered in this study.