Ria Millati Jurusan Teknologi Pangan dan Hasil Pertanian
Fakultas Teknologi Pertanian Three principles of mechanism:
1. Molecular diffusion 2. Interphase mass transfer one-film theory
3. Interphase mass transfer two-film theory
1. Molecular Diffusion
Consider the following figure:
When the partition is removed, gas A is diffused into gas B.
General formula:
dz dx
D C
x N
N N
A AB
A B
A A
. .
where:
time area
in B ient of A
on coeffic or diffusi
y diffusivit
the D
B A
mol mol A
on mol fracti
X volume
mol ion
concentrat total
C time. area
mol A N
AB A
A
B A
Three special cases: 1. Diffusion through stagnant medium N
B
= 0
dz dx
D C
x N
N N
A AB
A B
A A
. .
dz dx
x D
C N
A A
AB A
. 1
.
Example: water evaporating into air, volatile oil evaporating into air
2. Equimolar counter diffusion N
A
= -N
B
Illustration:
A NB
NA B
dz dx
D C
x N
N N
A AB
A B
A A
. .
dz dx
D C
N
A AB
A
. .
Example: diffusion of vapor and liquid in the distillation column
3. Diffusion within dilute solution x
A
0, thus C is constant
dz dx
D C
x N
N N
A AB
A B
A A
. .
dz dx
D C
N
A AB
A
. .
dz x
C d
D N
A AB
A
. .
.
Ficks law dz
C d
D N
A AB
A
....... .
.
Note: Diffusion can occur in gases, liquids, and there is also diffusion in solids. For diffusion in solids, the the equiation follow Fick’s law.
2. Interphase mass transfer one-film theory for two immiscible phases
SystemPhase: Solid-liquid crystallization
Solid-gas sublimation, adsorption
Illustration:
As an approximation of the mass transfer rate of A, the following equation can be applied:
A S
A g
A AS
y A
AS x
A AS
c A
P P
k y
y k
x x
k C
C k
N
t A
A
P y
P .
where:
area.time mol A
sfer of A mass tran
N
A
ion of A concentrat
saturated C
AS
B gas
in or
liquid in
n fluid ion of A i
concentrat C
A
Solid A capable of
being dissolved
C
AS
•
C
A
Fluid B liquid or gas N
A
film
ce s
film resi oefficient
transfer c mass
k k
k k
g y
x c
tan ,
, ,
Contoh aplikasi: Suatu padatan A misal: kapur barus atau es kering berbentuk bola jari-jari R
= 0,8 cm berada di udara yang ventilasinya cukup
baik. Rapat massa A
3
1,1g cm
. Suhu
system T = 300 K. tekanan uap murni zat A pada 300 K adalah
4
1,14.10
AS
P atm
. Koefisien transfer massa A dari permukaan ke
udara 2000 cm
kc jam
. Ingin diperkirakan waktu yang diperlukan sampai zat A
tersebut habis menyublim. Diketahui berat molekul A, 128 g
M mol
.
Analisis : Neraca massa A padatan :
2 3
............................ 4
1 .4
. . .
3
AS A
rate of rate of
rate of massa A
input output
accumulation waktu
d kc
r C
C r
dt M
� � �
� � �
� � �
� � �
��� �
�
� �
� �
Dimana r = berubah sehingga :
2 3
4 1
.4 .
. . 3
AS A
d kc
r C
C r
M dt
Dimana :
3 3
2
. 3
d d
dr r
r dt
dr dt
dr r
dt
Sehingga :
2 2
4 .4
. .
3 3
.
AS A
AS A
dr kc
r C
C r
M dt
dr kc M
C C
dt
Karena ventilasi baik maka
A
C ≈ 0 Zat A padat
r
.
AS
dr kc M
C dt
AS AS
P C
RT
.
AS
P dr
kc M dt
RT
. . . .
t ts r
AS t
r R ts
R AS
RT dt
dr kc M P
RT t
dr kc M P
� �
. . .
. .
AS AS
RT ts
R kc M P
RTR kc M P
3 3
4
. 1,1
0,082 300
0,8 1
. 1000
24 2000
128 1,14.10
30,907 31 g
L atm x
x K x
cm cm
hari mol K
cm ts
x x
g L
jam cm
x x
atm jam
mol hari
�
3. Interphase mass transfer two-film theory for two immiscible phases
