质量传递Ch09-Mass-Transport

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ρ A = c A M A , ρ B = cB M B
cA M A ρA ρA = = ρ ρ A + ρ B c A M A + cB M B
xAM A x A M A + xB M B
(9.2-9)
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Molecular mass transfer
wAy ω −0 = ρDAB A0 A Y ⇒ j Ay = − ρDAB dω A dρ = − DAB A dy dy (9.1 - 1)
Fick’s Law of Diffusion
jAy: mass flux of component A through medium B
⎡ [ jAy ] = ⎢ kg ⎤ ⎦ ⎣ m2 • s ⎥
c Au A = −CDAB dx A + x A ( c Au A + c B u B ) dz
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(9.2-22) where NA is molar flux of component A relative to the steady plane z=constant. Comparison: JA is the molar flux of component A relative to the average molar velocity of mixture uM.
Molecular mass transfer
ρ A = c A M A , ρ B = cB M B
(9.2-7)
ρA ωA
(9.2-5)
ω A ,ω B mass fractions of species of A and B
x A , xB mole fractions of species of A and B
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(9.2-15) Where uM is the average molar velocity of mixture relative to the steady plane z=constant.
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Molecular mass transfer
PART III MASS TRASNPORT
Chapter 9 Introduction To Mass Transport
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Fick’s Law of Diffusion
wA=0 Y t<0
9.1 Fick’s Law of Binary Diffusion (Molecular Mass Transport)
∴ N A = −CDAB
dx A + xA ( N A + N B ) dz
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Molecular mass transfer
NA includes two parts: one is molecular diffusion component, the other is convective (bulk flow) component. In the same way we can derive
J A = − DAB dc A dz
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Molecular mass transfer
Where JA is the molar flux (mol/m2 s) of species A as it diffuses at a diffusion velocity of (uA-uM), and c=constant. DAB: mass diffusivity of component A through medium B. Fick’s law of diffusion in terms of mass flux is given by: dρ A (9.2-16) j = −D
2
⎣
⎦
ρ: the density of mixture of A and B
[ρ A ] = ⎡ kg ⎤ ⎢ 3⎥
⎣m ⎦
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Two basic forms of mass transfer: Molecular mass transfer Mass transfer: Convectional mass transfer Molecular mass transfer: mass transfer caused by molecular diffusion. For a binary mixture of species A and B Fick’s law (concentration form) is:
c cA MA MA (9.2-8) xA = A = = = ω A ωB C c A + cB ρ A + ρ B + MA MB MA MB
ωA =
=
(9.2-6) Where MA and MB are mole molecular weight of species of A and B.
c Au A + c B u B c c A ( c Au A + c B u B ) ∴ c AuM = c = x A ( c Au A + c B u B )
Q uM =
Molecular mass transfer
Q N A = c Au A , N B = cBu B
Eq.(9.2-21)
N N u A = A , uB = B cB cA
Molecular mass transfer
N = Cu M = N A + N B = c Au A + cBu B CuM = c Au A + cBu B uM = c Au A + c B u B C
(9.2-13)
Total molar flux of the mixture N is given by: N = N A + N B = c Au A + cBuB (9.2-14)
uA =
Molecular mass transfer
Total mass flux of mixture relative to the steady plane z=constant n is given by: n = n A + nB = ρ Au A + ρ Bu B (9.2-11) u is defined as mass average velocity of mixture relative to the steady plane z=constant, and we have:
y x
t=0
ωA=ωA0
ωA(y, t)
Small t
ωA(y)
Large t
ωA=0
ωA=ωA0
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Fick’s Law of Diffusion
At steady state, For the binary mixture A and B systems we can obtain
(9.1 - 2)
Eq. (9.1-2) is the Fick’s Law of Diffusion
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Fick’s Law of Diffusion
DAB: mass diffusivity of component A through medium B.
For the binary mixture, mass fluxes of species A and B relative to a steady plane z=constant are nA and nB(kg/m2 s), and relative velocity of A and B to the steady plane z=constant are uA and uB (m/s), and then we have:
n A = − ρDAB dω A + ω A ( n A + nB ) dz
J AZ = − DAB dC A dz
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Convectional mass transfer: mass transfer caused by macromixing of fluid.
N A = k c Δc A
(9.1-4)
(9.1-3)
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dz dω A j A = − ρDAB dz
Molecular mass transfer
If u and uM are constant, we have: (9.2-19) (9.2-20) j A = ρ A (u A − u ) Combining Eqs.(9.2-17) and (9.2-19) we can obtain:
9.2 Flux and Velocity of Molecular Mass Transfer
(9.2-3) (9.2-4)
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Molecular mass transfer
c c x A = A , xB = A C C x A + xB = 1