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Dimensionless Groups

Shi ji j

i j

k d

,

,

,

Sc i ji j

,

,

Revd

Sherwood number

Reynolds number

Schmidt number

mass transfer

fluid flow

mixture property

diameter

film thickness

Re 1 laminarRe 1 turbulent

Sc 1 in gasesSc 103 in liquids

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Heat Transfer

mass transfer heat transfer

)Sc(Re,Sh f )Pr(Re,Nu f

k h

a

same as

replace thermal diffusivity

)( pca

by

by

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Tubes - laminar

z

d

vd

1

20

v

d

inlet zone fully developed

concentration of absorbing species

laminar Re 2000

Sh Sci j i j z

d, ,. Re

162 1 3 1 31 3

Shi j, .3 66

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Tubes - turbulent

v

d

turbulent

inlet zone(short) fully developed

Re 2000 Sh Sci j i j d

z, ,. . Re

0 027 1 0 7 4 5 1 3

inlet correction

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Membrane Spacer

d

zv

Sh Sci j i j d

z, ,. Re

19 1 2 1 3

1 2

membranes

spacer wires

300 2000 Re

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Packed Beds

superficial velocity v void fraction e particle diameter d

external (film) coefficient Sh Sci j i,j ,.

Re0 34 2 3 1 3

e

minimum value (chromatography) Shi j, 4

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Packing with Gas

and Liquid

liquid as a film

over the packing

gas through and

around the packing

liquid, superficial velocity vL

gas, superficial velocity vG

d

Sh Re Sc2 3

i,j

G G

i,j

G 0 9 1 1 3 1 3

. e

e void fraction

Sh Re Sc1 2

i,j

L L

i,j

L 19 1 3

liquid:

gas:

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outside Rigid Interfaces

k g i j i j , ,

/

.

0 3 21 3

, ,and i j are values in the fluid outside

for short times

for small particles

for large particles

boundary layer theory

k

ti j

i j

,

,. 113

k

di j

i j

,

,2

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surface active agents

swept to the back

these immobilise the

drop or bubble whend

f

g

1 2/

fis the fouling (fudge) factor

f0 2. in clean liquidsf 1 in dirty liquids

the transition is atd 1 mm

cause surface tension

gradients d

Mobile or Rigid?

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Bubbles with Mobile Interfaces

bubbles:

k g i j i j , ,

/

. 0 4

2 2

3

1 6

and are for the liquid (outside)

outside

k g i jd i jd, ,

/

. 0 4

2 23

1 6

inside (?)

i jd

,

i j,

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Mobile Drops in a Liquid

i jd

,

i j,

d

mobile drops in a liquid

calculate the rigid and mobile

(bubble) coefficients separately

interpolate using d

k k ki j i j mobile

i j

rigid

, , ,

.

.

.

1

1 0 3

0 3

1 0 3

(these differ for the outerand

innercoefficients)

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Drops in a Gas

dg

2

1 2

/

dg

4

1 2

/

rigid

sphere mobile oscillating drop drop shatters