Separations as unit operations - Principles of Chemical Separations with Environmental Applications - page 18

where y = mole fraction in the gas phase

x = mole fraction in the liquid phase

m = Henry's Law constant.

A second example would be the Langmuir isotherm characterizing adsorption
(Chapter 7), which relates the equilibrium amount of a solute sorbed onto a solid to
the concentration in the fluid phase in contact with the solid:

K s bC
1

X =

bC ,

(2.2)

+

=

where X amount of solute sorbed per weight of sorbate

=

C solute concentration in fluid phase

K s , =

b constants.

An important factor in the use of phase partitioning for separations is the degree of
change in composition between the two phases. In the limit where the composition in each
phase is identical, separation by this mechanism is futile. For vapor-liquid equilibrium,
the condition is called an azeotrope. Irrespective of the phases, this condition corresponds
to a partition coefficient of unity.
Some data and model equations will be provided in the appropriate chapters. Appendix E
provides additional information and references for data and calculation methods.

2.5 Rate-based processes

Rate-based processes are those in which one component of a feed stream is transferred
from the feed phase into a second phase due to a gradient in a physical property. Gradients
in pressure or concentration are the most common. Other gradients include temperature,
electric fields, and gravity. The limiting step upon which design is based is the rate of
transfer of the particular component from the feed material to the second phase. For
relative motion (rate) of the various chemical species, the mathematical description relates
the rate of transfer of a particular component across a boundary due to a driving force.
One example is Fick's Law that relates the flux of a component ( N A ) across a layer (fluid
or solid) to the concentration gradient within the layer:

d C A
d x ,

N A =−

D A (2.3)

where D A = diffusion coefficient of A in the medium (physical property found in many

handbooks)

d C A / d x = concentration gradient of A in the direction of interest.

A second example is the use of a mass transfer coefficient to relate the flux across a
fluid boundary layer (fluid region over which the solute concentration changes from the