Vacuum Technology - Thin Film Materials Processing - Lecture Slides, Slides of Material Engineering

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Vacuum Technology

Page 2

Gas Flow

• Flow Regimes

– Nature of the Gas (Knudsen’s Number)– Relative Quantity (Reynolds’ Number)– Turbulent– Laminar– Viscous– Molecular– Transition

Vacuum Technology

Page 3

Knudsen’s Number (Kn)

d

Kn

d d d

Kn < 0.01 Viscous Flow - gas flowdetermined by gas-gas collisions

Kn > 1.0 Molecular Flow - gas flowdetermined by gas-wall collisions

1 > Kn > 0.01 Transition Flow

Vacuum Technology

Page 5

Flow Regimes

Laminar Viscous Flow - Ordered flow of gas in streamlines.Dominated by gas-gas collisions

Kn < 0.01, R < 1200

Molecular Flow - Dominated by gas-wall collisions. Assume diffusereflection at surfaces (molecules are re-emitted in a directionindependent of the incident direction). Gas molecules do not collidewith eachother.

Kn > 1, R < 1200

Turbulent Flow -

Kn < 0.01, R > 2200

Transition Flow - Gas is neither viscous nor molecular. Flow isdominated by both gas-gas collisions and gas-wall collisions

1 > Kn > 0.

Vacuum Technology

Page 6

Definitions

Throughput (Q) - Quantity of gas (the volume of gas at a knownpressure) that passes a plane in a known time. Units = Pa-m

3

/s or

Watts (energy flow -- energy it takes to transport the molecules acrossa plane)

Q = P(dV/dt) where: P=pressure and dV/dt = volumetric flow rate

Mass Flow - The quantity of a substance (kg) that passes a plane in aknown time. Units = kg/s

Molecular Flow - The quantity of a substance (number of moleculesN) that passes a plane in a known time. Units = N/s

Conductance - The ability of an object to transport gas between twopressures regimes. Units = m

3

/s

Analogous to ohms law -- 1/R= I/V

1

2

P

P

Q

C

Vacuum Technology

Page 8

Viscous Flow -- Orifice

contracta"

vena "

flow

gas

of

speed

high

the

of

because

area

sectional

cross

the

reduces

ch

factor whi a

is

(triatomic

and , )

(monatomic

for

species),

(diatomic (^4). 1

'

1

2 1

1 2

1

2 1

1

2 1

1 2

'

1

−

−

C

C C

where

P P

for

P P

P P

kT m

C

AP

Q

P V

γ

γ

γ γ

γ

Docsity.com

Vacuum Technology

Page 9

Viscous Flow -- Orifices

P

of t

independen

is

Flow

air

for

1 1

1 2

'

1

1

(^21)

−

−

γ

γ

γ

kT^ m

C

AP

Q

P P

for^ Flow is said to be “critical” or “choked” –

limited by gas stream traveling at

the speed of sound

P2/P

Q/A

choked

Vacuum Technology

Page 11

Viscous Flow – Long Round Tubes

P

P

l

d

)

(

2

128

2

1

2

1

4

P P P P l d Q

−

=

η

π

For Air at Room Temperature

(

)

2

)

(

10

38 . 1

2

1

4

6

Pascals

P

P

l

meters

d

x

l s

C

=

  

  

Hagan-Poiseuille Equation

Vacuum Technology

Page 12

Viscous Flow – Long Round Tubes

• Assumptions for Hagan-Poiseuille Equation
  • Fully developed flow – ie velocity profile is

not position dependent

• Laminar flow– Zero wall velocity– Incompressible gas – U(mach number) =

U/U

sound

< 1/3 (ie non-choked flow)

Viscous flow, R<

Vacuum Technology

Page 14

Molecular Flow – Long Round Tube

l d

v

C

3

π 12

=

For Air at Room Temperature

)

(

)

(

121

m

l

m

d

s m

C

=

  

  