Page 557 - Bird R.B. Transport phenomena

§17.8 Summary of Mass and Molar Fluxes 537

Table 17.8-1 Notation for Mass and Molar Fluxes*

With respect to With respect to mass With respect to molar
Quantity stationary axes average velocity v average velocity v*
Velocity of species a v u (A) v — v (B) v — v* (C)
* a v
(cm/s)
Mass flux of species a n.. = A,v a (D) !. = P.<v.-v) (E) j* = Р (У - v*) (F)
а
а
2
(g/cm s)
С
Molar flux of species a 4 , = c av a (G) L = а&а ~ V) (H) J: = c (v - v*> (I)
2 o B
(g-moles/cm s)
N N
Sums of mass fluxes 2 n« = pv (J) 2 I = о (K) 2 & = P(v - v*) (L)
« -=1
N N A/
V
Sums of molar fluxes 2 N ft = cv* (M) 2 Ja = ^( * ~ V) (N) .?,'•*"° (O)
Relations between mass n (f = M £rN tr (P) (Q) (R)
and molar fluxes
N
Interrelations among ,. = ь. + , . (S) a (T) f = n -x 2—n, (U)
a
o
mass fluxes /3=i
Interrelations among N = J* + c v* (V) (W) (X)
(t tt
molar fluxes
* Entries in the shaded boxes, involving the "hybrid fluxes" j* and J are seldom needed; they are included only for the sake of
a/
completeness.

Table 17.8-2 Equivalent Forms of Fick's (First) Law of Binary Diffusion
Flux Gradient Form of Fick's Law

¥а, (A)
)A л U = -f^AB^A
n Vx /( J* A = ~c% AB Vx A (B)
¥а>л П А = ^>л( Л + Ь') ~~ P^AB^ * ^ — p v — рЯЬ ^<л) А (C)
0
П
П
A
АВ
N A = x (N A + N ) - (3) Ъ 10 ~~ С AV* C2) Л D^X Л (D)
B
АВ
A
Р^лв ^
p(v -v ) t ч (E)
A B
с2) ^ ^
civ л -v ) Vx A х х лв (F)
B
л в