Page 554 - Bird R.B. Transport phenomena

534 Chapter 17 Diffusivity and the Mechanisms of Mass Transport

Table 17.7-1 Notation for Concentrations
Basic definitions:
p = mass concentration of species a (A)
a
N
(B)
P = 2 Pa = mass density of solution
(C)
°>a = PalP = mass fraction of species a
c a = molar concentration of species a (D)
N
c
c = 2 a = molar density of solution (E)
a = \
x a = c /c = mole fraction of species a (F)
a
M = р/с = molar mean molecular weight of solution (G)
Algebraic relations:
с а = р /М а (Н) Ра = С а М а (I)
а
N N
(J) (К)
N N
у Д/f =
у 1У1
л
/LA а а l v ДЛ l (L) (М)
х М
0>а/М а а а
Y Х « — N (N) (О)
2 (о)р/Мр)
/з=1 /3=1
Differential relations:
(Р) я

N
M
= ~ 2 2 Ш - MJ]Vx y (Q)"
y=\
у Фа
"Equations (P) and (Q), simplified for binary ystems, are

М А М В M A M B Vx A
(Q')
+ х в М в ) 2
(х А М А
MA

Note that pv is the local rate at which mass passes through a unit cross section placed
perpendicular to the velocity v. This is the local velocity one could measure by means of
a Pitot tube or by laser-Doppler velocimetry, and corresponds to the v used in the equa-
tion of motion and in the energy equation in the preceding chapters for pure fluids.
Similarly, one may define a local molar average velocity v* by

(17.7-2)
x v
1 а
Note that cv* is the local rate at which moles pass through a unit cross section placed
perpendicular to the molar velocity v*. Both the mass average velocity and the molar
average velocity will be used extensively throughout the remainder of this book. Still