Diffusion Mass Transfer
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
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
