mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
m / t dxdydz
(104)
t
u v w
dxdydz dxdydz
x y z t
(105)
or
t
v
0
(106)
Case IV, Infinitesimally small element moving with the flow
m V
(107)
Since the derivative of the mass is zero everywhere (no change in mass):
D
m DV
(108)
Dt Dt
By the multiplication rule of calculus:
DV
Dt
D
V
0
(109)
Dt
The divergence of the velocity vector is the volume rate of change per unit volume:
1 DV
v
V
Dt
D
v
0
Dt
(110)
(111)
Show that case III is the same as case I (Path C in Figure 18)
S
vdS dV
t
V
(112)
Using the divergence theorem on the left side
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