# Diffusion Mass Transfer

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## Content

Diffusion Mass Transfer Chapter 14 Sections 14.1 through 14.7

General Considerations

General Considerations •  Mass transfer refers to mass in transit due to a species concentration gradient in a mixture. mixture. !

Must have a mixture of two or more species for mass transfer to occur occur.. !  The species concentration gradient is the driving potential for transfer.

Mass transfer by diffusion is analogous to heat transfer by conduction.

•  Physical Origins of Diffusion: !

Transfer Trans fer is due to t o random molecular motion.

Consider two species A and B at the same T  and  and p,  but initially separated by a partition.

–   –  Diffusion in the direction of decreasing concentration dictates net transport of A molecules molecules to the right and B molecules to the left.

–   –  In time, uniform concentrations of A and B are achieved.

Definitions

Definitions

( kmol/m ) of species i. 3

C i

:

Molar  concentration  concentration

! i

:

Mass density (kg/m density (kg/m3) of species i.

M i :

Molecular  weight (kg/kmol) weight (kg/kmol) of species i.  ! i

*

J i :

Molar  flux flux   !

N i  !!

:

=

M  iC i

kmol ol/s /s ! m ) of species i due to diffusion diffusion.. ( km 2

Transport Transpo rt of i relative to molar average velocity (v*) of mixture.

Absolute molar flux  flux  !

ji

kmol ol/s /s ! m ) of species i. ( km 2

Transport Trans port of i relative to a fixed reference frame.

(

)

2 flux  kg/s! m Mass flux  of species i due to diffusion diffusion.. !  Transp Transport ort of i relative relati ve to mass-average velocity (v) of mixture.

:

(

!! !!

)

flux  kg/s! m 2 of species i. ni   :   Absolute mass flux  !   xi : i

m

Transport Transp ort of i relative relati ve to a fixed reference frame.

fraction of  of species i Mole fraction :

( x

i

=

)

Ci / C  .

=

fraction of  of species i ( mi   !i / ! ). Mass fraction

Property Relations

Property Relations •  Mixture Concentration Concentration:: C

! C i ! " xi

=

=

1

i

i

•  Mixture Density: Density:  !

" ! i !  " mi

=

i

i

•  Mixture of Ideal Gases: Gases: C i  ! i

p

=

pi !iT

pi

=

=

RiT  ! pi i

xi

=

Ci C

=

pi p

=

1

Diffusion Fluxes

Molar and Mass Fluxes of Species A due to Diffusion in a Binary Mixture of Species A and B •  Molar Flux of Species A: !  By definition:

(

!

J A v

!

C A   v A

=

=  x

A

vA

+

"

v

!

)

xB v B

law (mass transfer analog to Fourier  s law): From Fick  s law (mass ’

!

J A

=

" CDAB#x A

Binary diffusion coefficient coefficient or  or mass diffusivity (m diffusivity (m2/s)

•  Mass Flux of Species A: !

By definition:  j A   ! A (  vA " v ) =

v = m A vA

+

mB v B

From Fick  s law: ’

j A

=

" ! DAB#mA

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