Deposition in the extrathoracic airways is typically described as a function of the Stokes number based on a reference flow timescale. However, this choice leads to significant scatter in deposition data since the velocity and length scales experienced by the particles as they are advected through the flow deviate considerably from the reference values in many sections of the airways. Therefore, an accurate model of extrathoracic deposition remains a challenge. 

In this work, we propose the use of an instantaneous Stokes number based on the local properties of the flow field. We define the effective Stokes number as the time-average of the instantaneous value. This effective Stokes number captures the flow history and geometric variability, inherently taking into account the effect of the flow field. 

Our results demonstrate that this average, or effective, Stokes number can deviate significantly from the reference value particularly in the intermediate Stokes number range where inter-subject variability is most pronounced. In addition, the effective Stokes number shows a very clear correlation with deposition efficiency, and is therefore a more appropriate parameter to describe aerosol transport.

effective Stokes number