Page 23 - Valve Selection Handbook

10 Valve Selection Handbook

and the Reynolds number decreases below its critical value, the leakage
flow becomes laminar, and the leakage flow will, from Poisuille's equa-
tion, vary inversely with the viscosity of the gas and the length of the
capillary, and proportionally to the driving force and the diameter of the
capillary. As the diameter of the capillary decreases still further until it is
of the same order of magnitude as the free mean path of the gas mole-
cules, the flow loses its mass character and becomes diffusive, that is, the
gas molecules flow through the capillaries by random thermal motion.
The size of the capillary may decrease finally below the molecular size
of the gas, but even then, flow will not strictly cease, since gases are
known to be capable of diffusing through solid metal walls.

Mechanism for Closing Leakage Passages

Machined surfaces have two components making up their texture: a
waviness with a comparatively wide distance between peaks, and a
roughness consisting of very small irregularities superimposed on the
wavy pattern. Even for the finest surface finish, these irregularities are
large compared with the size of a molecule.
If the material of one of the mating bodies has a high enough yield
strain, the leakage passages formed by the surface irregularities can be
closed by elastic deformation alone. Rubber, which has a yield strain of
approximately 1,000 times that of mild steel, provides a fluid-tight seal
without being stressed above its elastic limit. Most materials, however,
have a considerably lower elastic strain, so the material must be stressed
above its elastic limit to close the leakage passages.
If both surfaces are metallic, only the summits of the surface irregular-
ities meet initially, and small loads are sufficient to deform the summits
plastically. As the area of real contact grows, the deformation of the sur-
face irregularities becomes plastic-elastic. When the gaps formed by the
surface waviness are closed, only the surface roughness in the valleys
remains. To close these remaining channels, very high loads must be
applied that may cause severe plastic deformation of the underlying
material. However, the intimate contact between the two faces needs to
extend only along a continuous line or ribbon to produce a fluid-tight
seal. Radially directed asperities are difficult or impossible to seal.