7 0 D O C . 7 2 P O R E S I Z E O F F I LT E R S
72. “Experimental Determination of the Pore Size of
Filters”
[Einstein and Mühsam 1923]
Completed before 2 July 1923
Published 3 August 1923
In: Deutsche medizinische Wochenschrift 49, no. 31 (1923): 1012–1013.
There is, up to now, no exact method yet to determine the permeability of filters.
Membrane filters
(Bechhold,[1]
de Haën) are calibrated by the water’s speed of pas-
sage, hard filters (Chamberland, Berkefeld, Pukal, etc.) by their permeability for
colloids of approximately known size. These determinations are very rough, of
course, because adsorption produces errors that cannot be overlooked and because
the true measurements of comparison substances (serum albumin, hemoglobin,
etc.) are unknown.
The consideration presented in the following leads to a secure and easily execut-
able method for determining the largest dimensions that an organized or inanimate
substance passing through the filter can have. Filters made out of porous materials
can be regarded as walls riddled with numerous little channels of various widths.
The narrowest spot of each small channel is decisive for its permeability. The cross
section of the narrowest spot of a small narrow channel is easily determined, how-
ever, by means of capillarity. For, if the channel is originally filled with liquid and
one seeks to drive the liquid out by means of compressed air, the capillary force has
to be overcome, provided the liquid moistens the channel wall. For a circular cross
section, the excess pressure required to overcome the capillary forces is equal to
, where σ signifies the capillarity constant, r the channel radius. In order to
drain the liquid completely out, a pressure of is necessary, where means
the radius of the channel at the narrowest spot. If a plate is riddled orthogonally
with many channels that are initially filled with liquid, air enters into the plate only
at a pressure at which air penetrates through the widest channel bottleneck. If is
[p. 1012]
[p. 1013]
2σ
r
------
2σ
rmin
-------- - rmin
r0