Sedimentation of Fibers from Laminar Flows in a Horizontal Circular Duct

Abstract

An analysis is presented to describe the motion of a fiber under gravity in laminar flows within a horizontal circular duct. The trajectory and orientation of the fiber were determined by simultaneously solving three equations for translations and two equations for rotation. Neglecting fiber inertia and the effect of Brownian diffusion, the limiting trajectories of the fiber for which the fiber just penetrates the duct without being collected were obtained for a variety of conditions of fiber size, flow pattern and velocity, and duct dimension. The limiting trajectories were then used to calculate the deposition efficiency of a fibrous aerosol passing through the duct. Assuming a uniform fiber concentration and a random fiber orientation at the duct entrance, numerical results and empirical expressions were obtained for deposition efficiency in terms of the fiber aspect ratio, the aspect ratio of the duct, and a sedimentation aprameter which represents the ratio of the mean residence time of the fiber in the duct, L/U, to the mean settling time of an equivalent volume sphere, R/u_s , where L and R are, respectively, the length and radius of the duct, U is the average velocity of the flow, and u_s is the particle settling velocity.