Chapter 1
Mass Transfer
Organization, Introduction, Brownian Diffusion
Prof. S.E. Pratsinis Lecture 16.09.2015
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Mass Transfer – Introduction, Brownian Diffusion
Literature:
E.L. Cussler, “Diffusion, Mass Transfer in Fluid Systems”
2nd edition, 1997, Cambridge University Press
3rd edition, 2009, Cambridge University Press
2 TESTS of 45 min.
October 20
November 24
(2009)
Mass Transfer – Introduction, Brownian Diffusion
(1997)
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1. Introduction
To travel from high concentration to low concentration:
Tea from a tea bag in hot water
This process is a slow, rate limiting step that:
• Limits efficiency of commercial distillations.
• Limits rate of industrial reactions w. catalysts.
• Influences corrosion of metals and marbles.
• Controls the growth of microorganisms.
Further examples include:
Waste treatment
Combustion
Pollution control (scrubbers)
Flavor retention (spray drying)
Mass Transfer – Introduction, Brownian Diffusion
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Types of Mass Transfer:
1.
Molecular diffusion (or just diffusion).
Mass is transferred by the random motion of molecules across
a concentration gradient. Sometimes, but not always, this is
similar to heat transfer by conduction.
2.
Eddy diffusion (mixing or dispersion or agitation).
Mass is transferred by finite parcels of fluids as in momentum
and heat transfer.
Approximate rates of diffusion in:
Gases: 10 cm/min
(a lady with a nice perfume).
Liquids: 0.05 cm/min
(stir cream into the coffee).
Solids: 0.00001 cm/min (takes long to rust an iron axe)
Mass Transfer – Introduction, Brownian Diffusion
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Relationship with Momentum and Heat Transfer
Mass transfer is similar to momentum and heat transfer but there
is nothing equivalent to radiation heat transfer.
Molecular diffusion easily gives rise to convection something that
was not so with conduction heat transfer. This is distinguished by
talking about diffusion at low and high concentrations.
Mass Transfer – Introduction, Brownian Diffusion
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Description of Mass Transfer
1.
Molecular model (Fick’s laws and diffusivity).
This is an elegant model based on first principles that
everyone dreams of having to work with especially in physics,
physical chemistry and biology.
2.
Mass transfer coefficient model (Mass Transfer correlations)
This is a model typically employed by chemical and process
engineers when the complexity of the process leaves little
space for elegance.
The choice between models is a compromise between ambition and
resources. Put another way, between Greek & Roman styles.
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Example for Models
Imagine two large bulbs with equal volume connected by a long
thin capillary at constant temperature.
2
Measure now the
CO2 concentration
inside the bulb
containing nitrogen.
N2
area
1
CO2
Goal: To determine physical properties that determine the amount
of mass transferred.
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Mass Transfer – Introduction, Brownian Diffusion
Define the flux: CO2 flux 
2
N2
amount of gas from 1 to 2
time  area
This removes the influence of a particular apparatus.
area
Model 2: Recognize that the CO2 flux is proportional to CO2
concentration difference between 1 and 2.
CO2
1
CO2 flux  k  (CO2 concentration difference)
k is a mass transfer coefficient and this is the mass transfer coefficient model.
Model 1: Recognize that increasing the length of the capillary will
decrease the flux.
CO 2 flux  D
concentration difference
capillary length
D is the diffusion coefficient and this is the other model or Fick’s first law.
Mass Transfer – Introduction, Brownian Diffusion
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This is similar to electric circuits, Ohm’s law:
current
voltage




1




or
=
×
or




 area × flux of electrons  resistance  potential difference 




Thus the mass transfer coefficient k is analogous to the reciprocal
of the resistance.
An alternative form to Ohm’s law is:
 current density 
 potential difference 
1


or
=
×


 resistivity 
length


 flux of electrons 


The diffusion coefficient D is analogous to the reciprocal of resistivity.
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In heat transfer k is analogous to the heat transfer coefficient h,
while D is analogous to thermal conductivity .
Neither the k-model nor the D-model are always successful as
they depend heavily on the assumptions made in their
development.
For example:
The flux  CO2 concentration difference if the capillary is too thin
or if the gases react.
Similarly Ohm’s law is not always valid at very high voltages.
However both Fick’s and Ohm’s law work well in most practical
uses.
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The use of the resistance or resistivity gives a clue about the
choice of the two models. Using the resistance is a simple action
for practical applications and rough measurements. In contrast
the resistivity is a more fundamental material property.
We will start with the fundamental description of the diffusion
coefficient, the D-model, and we will follow with the presentation
of the k-model later on.
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