mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
This is because unit vector dot products: 1 and
0 . Using the equations of continuity and
i i i j
equation of motion:
v
0
(74)
Dv
2
p v g
(75)
Dt
With some rearranging, the following is arrived at:
g
*
Dv * * *2 * gD
p v
* 2
Dt Dv v g
(76)
The terms in brackets are reciprocals of the Reynolds (Re) number and Froude (Fr) number respectively.
If in two different systems the scale factors are such that the Re and the Fr are the same, then both
systems are described by identical dimensionless differential equations (Placeholder1). In addition, if the
initial and boundary conditions are the same, they are mathematically identical. Such systems are
geometrically and dynamically similar and scale-up is easily done in that case.
Another method used to elucidate dimensionless numbers. This is the Buckingham Pi method of
dimensional similarity. In the case of local liquid mass transfer as a function of its variables rose to
different powers:
k K v D d
(77)
L
1
AB
Now by inserting the appropriate dimensions within this assumed equation:
2
L L M M L
K1 3
t t L Lt t
L
(78)
There are three equations in L, M, and t respectively:
1 3 2
(79)
0
(80)
1
(81)
Eliminating some of the constant exponents and inserting back into the original equation for local mass
transfer:
48