K n. III. Gas flow. 1. The nature of the gas : Knudsen s number. 2. Relative flow : Reynold s number R = ( dimensionless )

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Marsha Jackson
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1 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 > viscous : R< < 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)

2 - 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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4 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

5 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

6 Parallel onductance L Series onductance 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

7 IV. Gas release from solids Vaporization Γ ( molecules s ) / P A M T Γ nν 4 Γ n k T 2 π m / 2 7

8 ( 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

9 Pressure limits Behaves like a small leak ( hours) ( hours) (days) (years) - Stimulated desorption due to incident of photons, electrons, ions on solid surfaces can also limit the ultimate pressure in a vacuum chamber. 9

10 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

11 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.

Conductance of an aperture

Conductance of an aperture n Vacuum φ 4 How many molecules travel through in a time t? P P onductance of an aperture q φ.64 0 ( T / M) n Volume of gas passing through? Q Q dv/dt q/n.64 0 ( T / M) Q P Q / ΔP.64 (T / M ) l/s.64 0