## 3 Results and Discussion
### Flow Field and Particle Trajectories  
For the rigid and flexible duct models, the flow field is shown for 18 and 21 generations in Figure 4. The computed flow field is represented by separation streamlines. The obtained flow fields have similar streamlines for both simulated generations. Figure 4 demonstrates the flow field and pattern 2.5 s after the start of a 5 s inspiration. Figure 4a,b shows the flow field predicted for the 18 th generation of rigid and realistic models, respectively, with flow directed from left to right. Similarly, the flow field is characterized by curvilinear streamlines at alveolar openings for the 21 st generation in Figure 4c,d. For the rigid model, no bulk convective exchange is observed between the surrounding alveoli and the central part of model; rather, a separation streamline exists at the mouth of the alveoli. In addition, the recirculating flows, which have a velocity several orders of magnitude smaller than the mean lumen velocity, are positioned in the centre of each alveoli segment. Similar flow regimes were determined in previous studies with low Reynolds number flow and rigid boundaries [12; 18; 19]. To satisfy mass conservation, a significant portion of the flow in the central of duct enters the alveoli in the flexible realistic model. Therefore, compared to the rigid model the flow pattern differs, these differences become more tangible with increasing generation number. A comparison of the recirculating flow velocities in the alveoli for rigid and flexible models shows that the velocity of air flows during the moving boundary model is less than in the non-moving case. Figure 3: Particle deposition percentages for 1–5 \(\upmu\)m range particles as a function of: (**a**) one-way particle number rate (when the number rate reaches 4000, the deposition percentage becomes stable and the difference between the two steps for increasing of number rate are reasonable and converged to zero); and (**b**) two-way particles number rate (when the number rate reaches 1500, the deposition percentage becomes stable). In addition, the high velocity region positioned closer to the centreline of the lumen was affected more significantly by the pressure gradient for low generations than high generations. Indeed the streamlines in our model having deformable walls are expected to analyse faraway situations of proximal regions in the acinus accurately. Figure 5a,b shows the 1 and 5 \(\upmu\)m one-way particle trajectories (coloured black), superimposed on the fluid streamlines (coloured with flow velocity magnitude) for the 21 st generation and orientation [0, 0, \(-\)1] (This means that the gravity acceleration acts on z-direction for the rigid model). It is seen that the 1 \(\upmu\)m particle trajectories with small sedimentation velocities are more accurately agree with the flow pathways. In other words, the curvilinear trajectories of 1 \(\upmu\)m particles are observed to have better conformity with the fluid streamlines than the 5 \(\upmu\)m particles, which diverge from the fluid streamlines. It is clear that 5 \(\upmu\)m particles cannot follow the airflow streamlines at the 21 st generation. The physical reason of this phenomenon is the large sedimentation velocity of the 5 \(\upmu\)m particles relative to the 1 \(\upmu\)m particles. Normally inhaled suspension particles due to dilution of concentration have negligible collisions and interactions between particles. Therefore, the use of Euler-Lagrange or Euler-Euler methods can be satisfactory for simulating nano- or micro-particle deposition and transport in the human respiratory systems. If the high velocity gradient, pressure differences and intense particle collisions are challenging conditions, the numerical analysis must be modified to alternative approaches that investigate the fluid-particle interactions. No experimental study is available for investigating one- and two-way coupling of the particle-fluid interaction of micron-scale particulates inhaled into the lung and respiratory system.