Low Reynolds number capture of small particles on cylinders by diffusion, interception, and inertia at subcritical Stokes numbers

We predict the capture fraction η(Pe, R, Stk, Re) for cylinders at subcritical Stokes numbers Stk < Stk*, at small values of: the Reynolds number (Re), the inverse Peclet number (1/Pe), and the particle/fiber radius ratio (R = ap/af). Inertial effects are described by matching an outer deterministic region with an inner near-wall region. In the first, Newtonian trajectory calculations along the stagnation streamline yield the particle concentration nw at the stagnation point, which may exceed the upstream value n∞ by a large enrichment ratio E(Stk) ≡ nw/n∞. At given Stk, all capturable particles originate very near the stagnation line, having approximately the same nw/n∞. Inertial effects decay greatly in the vicinity of the wall, whence the particle velocity for the inner problem is describable locally as a small perturbation of the fluid velocity. Furthermore, Friedlander's diffusion-interception similarity parameter Π∼Pe1/3R still applies at finite inertia, reducing the inner problem to the (numerical) solution of a linear second order parabolic partial differential equation with only Π and Stk as parameters. Normalizing η(Pe, R, Stk, Re) with its stagnation point value results in a function F(Π, S) taking values of order unity in the whole domain of its (only) two variables. F(Π, S) is computed in the limits Π = 0 (no interception) and Π = ∞ (no diffusion). Its determination at small or large Π is only sketched. Recasting into self-similar form prior calculations yields F(Π, 0) in the interesting range 0 < Π < 2. The universal function F(Π, S) remains to be computed at values of Π of order unity.Copyright © 2019 American Association for Aerosol Research