An asymptotic model of particle deposition at an airway bifurcation

Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at the carina of an airway bifurcation during inspiration. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge that considers the viscous boundary layer near the wedge and the outer inviscid region and is then used to solve the particle transport equations. Sometimes particle impaction on the wedge is prevented due to the boundary layer. We call this boundary layer shielding (BLS). This effect can be broken down into different types: rejection, trapping and deflection that are described by what happens to the particle's initial negative velocity normal to the wall either changing sign, reaching zero, or remaining negative in the boundary layer region. The deposition efficiency depends on the critical Stokes number but exhibits a weak dependence on Reynolds number. Deposition efficiency for S(c) in the range 0 < S(c) < 0.4 yields the following relationship De ≈ (1.867S(c)¹·⁷⁸-0.016) sin(βπ/2) at large Reynolds numbers, where βπ is the wedge angle. For a specific deposition efficiency, S(c) decreases as βπ increases. The distribution of impacted particles was also computed and revealed that particles primarily impact within one airway diameter of the carina, consistent with computational fluid dynamics approaches. This work provides a new insight that the BLS inherent to the wedge component of the structure is the dominant reason for the particle distribution. This finding is important in linking aerosol deposition to the location of airway disease as well as target sites for therapeutic deposition.