4.5 Evaporation and Diffusion
4.5.4 Evaporation and Diffusion through Quiescent Air
(page 286)
z
y
a,1
, y
j,1
or P
a,1
, P
j,1
volatile liquid (species j)
z
1
y
a,2
, y
j,2
or P
a,2
, P
j,2
z
2
diffusion of
contaminant
(j)
diffusion of air
(a)
bulk motion of air and j
Figure 4.10
Evaporation of a volatile liquid (species j) from a container open at the top, partially
filled with the volatile liquid.
The
evaporation mass flow rate
(mass per time) is given in all cases by
evap,j
j
j
mN
M
=
±
A
(4-46)
A
log mean mol fraction
(y
am
) and a
log mean partial pressure ratio
(P
am
) are defined as
a,2
a,1
am
a,1
yy
y
y
ln
y
−
=
(4-53)
and
( )
a,1
am
a,1
PP
P
P
ln
P
−
=
(4-54)
The
mass transfer coefficient
is defined as k
G
. For pure diffusion, k
G
is
()
ja
G
u21
a
k
RTz
z y
=
−
D
m
(4-59)
or,
ja
G
a
m
P
k
z P
=
−
D
(4-60)
The molar flux (N
j
) can be expressed as
( )
jG j
,
1j
,
2
Nk
P
y y
=−
(4-61)
Alternatively, the molar flux (N
j
) can be written instead as
( ) ( )
j
G
u
molar,j,1
molar,j,2
G
j,1
j,2
N
kRTc
c
k P
P
=
−
(4-62)
Usually, points 1 and 2 correspond to the liquid-gas interface (subscript i) and the top of the
container or tank (subscript 2 in Figure 4.10) respectively.