III. Gas flow. The nature of the gas : Knudsen s number K n λ d 2. Relative flow : U ρ d η U : stream velocity ρ : mass density Reynold s number R ( dimensionless ) 3. Flow regions - turbulent : R > 2200 - viscous : R< 200-200 < R < 2200 : turbulent or viscous depending on the geometry of the inlet and outlet - laminar viscous flow : ordered flow of a gas in stream lines (R < 200, K n < 0.0)
- Molecular flow range : molecular gas K n >, R < 200 The nature of molecular flow is very different from laminar viscous flow. Gas-wall collisions predominate and the concept of viscosity is meaningless. For most surfaces diffusion reflection at the wall is a good approximation. (Diffusion reflection at the wall : arrive, sticks, rattles and reemitted in a direction independent of its incident velocity. If λ d, there is a chance to be returned to entrance. Back streaming -Transition flow (slip flow) range not well understand 0.0 < K n <, d is several times larger than λ The velocity at the wall is not zero as in viscous flow Reflection is not diffuse as in free-molecular flow 2
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Throughput, Mass flow, and onductance Throughput is the quantity of gas that passes a plane in a known time, d dt ( PV ) Q SI unit (System International ) Pa m 3 /s W Pa N/m 2, J N m Throughput is the energy required to transport the molecules across a plane. Temperature change can alter the Q. Mass flow (molar or molecular flow) is the quantity of substance that passes a plane in a known time. Relationship of molar flow and Q Q N ( moles / sec ) N k T 0 Q R T Molar flow T should be defined for N to be related to Q 4
onductance 3 Q Pa m / sec : P2 P Pa 3 [ m / sec ] Pressure drops across a tube Similar to transportation of e P P 2 Large tubes(conducting wire) Pumping speed S Q P unit : m 3 /sec 5
Parallel onductance + 2 + 3 + L Series onductance + 2 + 3 Monte arlo simulation of molecular flow Input side : higher pressure decrease the conductance - need to have two large reservoir of the end of component -components should be connected by the shortest possible length of pipe 6
IV. Gas release from solids Vaporization Γ ( molecules s ) / 2.63 24 0 P A M T Γ nν 4 Γ n k T 2 π m / 2 7
( average) Desorption st order desorption 2 nd order desorption mean velocity ν ( t) 8 k T π m d k dt d( t) 2 k2 dt () t / 2 () t 27 hours 0 9 years 8
Pressure limits Behaves like a small leak 2.8 0 3 ( hours) 2.8 0 8 ( hours).2 0 7 (days) 3.2 0 4 (years) - Stimulated desorption due to incident of photons, electrons, ions on solid surfaces can also limit the ultimate pressure in a vacuum chamber. 9
Permeation is a three step process. d : thickness of wall D : diffusion constant desorption from interior wall Hydrogen : metal walls Helium : glass walls Adsorption on outer wall diffusion through wall 0
Vacuum Baking [ E / kt ]: diffusion of gas in the solid D D exp d constant 0 P D f P d D2 T < T 2 -The net effects of baking are the reduction in the outgassing rate and the reduction of the time required to remove the initial concentration of gas dissolved in the solid. -Vacuum baking also reduces the surface desorption time in the same manner as it reduces the out-diffusion time.