ROTATING-DISK-SAMPLER MEASUREMENT OF AEROSOLS
N(r) =f- n(r) dr
223
(1)
For this work it is convenient to divide the size spectrum into two
regions: the upper end for particles larger than 0.2 » in diameter and
the lower end for those smaller than 0.2 , in diameter. A simple new
method was used to sample the lower end of the distribution, Particles
were collected from room air by Brownian diffusion to an electron-
microscope grid placed at the center of a l-in. stainless-steel disk
rotated about the axis normal to its face. The results of the rotatingdisk study are reported in this paper.
THEORY
The theory of convective diffusion to a rotating disk has been
worked out for the laminar flow regimeby Levich’ based on the velocity
distribution derived from the theory of von Karman, This velocity dis-
tribution represents one of the few exact solutions of the Navier—Stokes
equations of fluid motion. A striking result of the theory of the fluid
motion is that the component of the velocity normal to the disk is a
function only of distance from the disk surface and not of distance from
the axis of rotation or angular position, As a result, Levich noted, there
exists a solution to the equation of convective diffusion in which the
concentration is a function only of distance from the disk surface.
Moreover, the diffusion flux is uniform over the surface of the disk
and is given by the following expression:
oe = 0.62 v-"D4we
(2)
where J = flux of matter, moles or particles/cm?/sec
C,, concentration at infinity
C, concentration at disk surface
v = kinematic viscosity
D = diffusion coefficient of the species with flux J
wW = rotational speed of the disk
This expression is derived for the limiting-case Schmidt number =
v/D— , but Eq. 2 is accurate® to within 7% of a more exact solution
whenv/D is greater than 100. This limit corresponds to particles
larger than about 0.0035 u in radius under ordinary atmospheric conditions. The theory is also limited to the laminar flow regime, which
has been found by experiment to exist below a Reynolds number, wR,
of 10‘ or 10°, where R is the disk radius.
The theory has been checked experimentally by several investigators. Litt and Serad* rotated disks of various materials in water and