2 9 2 D O C . 2 9 0 T H E O R Y O F R A D I O M E T E R F O R C E S
For, in the interior of the gas let a fine vane lie perpendicularly to a heat flow,
whose dimensions are large compared to the free path length λ. Likewise, let the
distances of the vessel walls from the edges of the vane be large compared to λ. Far
enough away from the edge of the vane, a pressure equilibrium will then prevail;
far enough beyond the vane, however, the conditions studied in § 1 will prevail,
which have the effect that a body small as against λ experiences the pressure
force .
At the edge of the plate a gradual transition will take place between these two
states of the gas, the width of which is of the order of magnitude λ. Hence, a force
of order of magnitude
(11)
will act on the unit of length of the plate edge as long as the dimensions of the vane
are large against the free path length.
The case of the vane heated on one side is similar insofar as there, too, a marginal
zone of the indicated width λ will be present in which the pressure equality on both
sides of the vane is not satisfied. In this case, which is ill-suited to a quantitative
test, however, I find for the force acting on the unit length along the edge the ex-
pression
, (11a)
which, of course, likewise only claims validity in order of magnitude.
Another cause of radiometer forces lies in the slippage velocity that a wall gives
the gas at a tangential temperature gradient. This phenomenon, which Maxwell has
already covered theoretically and Knudsen has rediscovered independently, is cur-
rently being worked on by Messrs. Hettner and
Czerni.[8]
σf
u
-----
K
fλ
u
---- -
1
2
-
λ2∂T
T ∂x
–--p----- = =
K pλ-----------
Δ T ⋅
T
–=
[p. 6]