mass transfer in multiphase systems - Greenleaf University

MASS TRANSFER IN MULTIPHASE SYSTEMS: VOLATILE ORGANIC COMPOUND
REMOVAL IN THREE-PHASE SYSTEMS
Mass transfer is unique in terms of units. It is similar to heat transfer except that when there is inter-phase
mass transfer, different bulk quantities are used. The transport of mass, heat, and momentum are
analogous. After applying the usual assumptions (Bird 1960) for illustration of this and applying to a
single dimension for the partial differential equations (PDE) of motion, energy, and mass:
v
y
vx
y
v
y
2
x
2
(45)
v
y
T
y
2
T
2
y
(46)
v
y
C
y
A
D
AB
2
C
y
A
2
(47)
It is immediately obvious that analogies are relevant. In fact, many correlations use analogies to
determine properties from one system and apply to the other in similar systems say knowledge of heat
transfer applied to mass transfer. The constants that are needed are also analogous in that they reflect the
diffusion magnitude of momentum, heat, and mass:
ν = µ/ρ
α = k/ρc p
D AB
Known as the kinematic viscosity (dynamic viscosity/density) and is the resistance of a
fluid sliding between two surfaces. It can be envisioned as momentum diffusivity. The
usual units are the same for all of these diffusivity constants, cm 2 /s.
Known as the thermal diffusivity. It is the ratio of thermal conductivity of a material to
density and heat capacity.
This is the mass diffusivity between two components A and B as in two different gases
or, as in this papers case, a volatile solute into a liquid.
The units of mass transfer can vary widely from the units of heat transfer even though the
analogies still hold true. While temperature is the chief dependent variable in heat transfer, mass transfer
units can be liquid concentrations, gas concentration, partial gas pressures, mole fractions, solid
concentrations, and other less well known. This is evident in the mathematical manipulations used within,
e.g., the solid mass transfer flux is:
i
A s A A
N k X X
(48)
For the flux to have the correct units of moles or mass per time per unit area,
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