mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
Pr Prandtl r number Ratio of molecular and momentum heat
transfer
µc p /
Re
Reynolds s
number
Ratio of inertia and viscous forces
ρdv/µ
Sc
Schmidt t
number
Ratio of molecular and momentum mass
transfer
µ/ρD AB
Sh
Sherwood u
number
Ratio of total and molecular mass
transfer
kd/D AB
v
Some of the more difficult elucidation of dimensionless numbers stems from non-dimensionalizing of the
governing partial differential equations. The following is one of the more illustrative in fluid mechanics
using the references nomenclature (Bird 1960):
* v * p
p0
* tv
v , p , t (70)
2
v v D
* x * y * z
x , y , z (71)
D D D
D (usually diameter), v (usually average velocity), and p 0 is a convenient reference pressure (e.g.,
standard pressure = 1 atmosphere).
x y z
*
D1 * 2
* 3 *
x y z
*2 2 2
D
*2 * 2 *3
(72)
(73)
r Ludwig Prandtl was a German scientist. He was a pioneer in the development of rigorous systematic mathematical analyses
which he used to underlay the science of aerodynamics, which have come to form the basis of the applied science of aeronautical
engineering.
s Osborne Reynolds was a prominent innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer
between solids and fluids brought improvements in boiler and condenser design.
t Ernst Schmidt was a German scientist and pioneer in the field of Engineering Thermodynamics, especially in Heat and Mass
Transfer.
u Thomas Kilgore Sherwood was a noted American chemical engineer and a founding member of the National Academy of
Engineering.
v Diffusivity based on binary A and B components
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