Movement and Deposition of Fibers in an Airway with Steady Viscous Flow

Abstract

Deposition of fibrous particles in lung airways is drastically different from deposition of spherical particles because of aerodynamic differences. In the past, assessment of fibrous particle deposition in airways used appropriate modifications of the analytical expressions for deposition efficiency for spherical particles. Recently, Chen and Yu (1991a) presented an analysis of fiber deposition by sedimentation for a parabolic flow through a circular tube. Fiber orientation in the flow was obtained from Jeffery's equations (1922) adapted to the case of parabolic flow. Deposition efficiency was then found from the solution of equations of motion for fibers. A more general approach has been taken in this study, in which the flow field is arbitrary but at a low Reynolds number. Inertial effects on both rotation and translation of the fiber are neglected. Equations for fiber orientation are derived in terms of Euler angles π and θ, and flow variables. The behavior of fiber orientation is found to be a function of the aspect ratio and initial orientation of the fiber, as well as the fluid strain and vorticity. A set of equations is obtained that describes translation of fibers in the flow field. Unlike the case of spherical particles, motion of a fiber due to gravitational force can have a nonzero component in all three coordinate directions. Fiber translation is a function of its geometry, its initial location and orientation, and a dimensionless parameters τ₁ representing sedimentation. The differential equations of translation and rotation, which are coupled through the dependence of fiber drag on its orientation in the flow field, are simultaneously solved numerically using a predictor-corrector method. For parabolic flow, the simulation results show that a for a given diameter, deposition by sedimentation decreases as the aspect ratio increases. A semiemperical expression is presented for τ₁ ≪ 1, which relates fiber deposition efficiency to τ₁ fiber aspect ratio, and airway inclination angle.