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Lecture 1

The document discusses the principles of mass transfer, focusing on concentration expressed on mass and mole bases, and molecular diffusion as the movement of molecules through a fluid. It outlines Fick's Law for molecular diffusion, emphasizing the relationship between driving force and resistance, and details factors affecting diffusion coefficients, such as temperature and medium type. An example is provided to illustrate the calculation of flux in a gas mixture under steady-state conditions.

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16 views11 pages

Lecture 1

The document discusses the principles of mass transfer, focusing on concentration expressed on mass and mole bases, and molecular diffusion as the movement of molecules through a fluid. It outlines Fick's Law for molecular diffusion, emphasizing the relationship between driving force and resistance, and details factors affecting diffusion coefficients, such as temperature and medium type. An example is provided to illustrate the calculation of flux in a gas mixture under steady-state conditions.

Uploaded by

tanyesabe8005
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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PRINCIPLES OF MASS

TRANSFER
Concentration

Mass Basis
On a mass basis, concentration is expressed in terms
of density (or mass concentration).

Mole Basis
On a mole basis, concentration is expressed in terms
of molar concentration (or molar density), which is the
amount of matter in kmol per unit volume.
Molecular diffusion

 Molecular diffusion: transfer/movement of individual


molecules through a fluid by means of random, individual
movements of the molecules.
 Molecules travel in straight lines and changing direction by
bouncing off other molecules after collision
A B Whenever there is an imbalance
1 2 of a commodity in a medium,
nature tends to redistribute it
until a ‘balance’ or ‘equality’ is
established. This tendency is
often referred to as the driving
force, which is the mechanism
behind many naturally occurring
transport phenomena.
When will diffusion stop?

What are the resistance to diffusion?

How to increase the rate of diffusion?


General molecular transport equation

Rate of a transfer process = driving force/resistance

The equation for molecular diffusion of mass is Fick’s Law:

dc A
J * AZ = − D AB
dz
J*AZ : molar flux of component A in the z direction due to molecular
diffusion in kg mol A/s.m2
DAB : molecular diffusivity of the molecule A in B in m2/s
cA : concentration of A in kg mol/m3
z : distance of diffusion in m
Fick’s Law equation for binary mixture of A and B

• Diffusion of molecules when the whole bulk fluid is not moving (stationary).
• Diffusion is due to a concentration gradient.

z2 c2

J * AZ  dz = − D  dc AB
z1 c1

c A1 − c A 2
J * AZ = D AB
z 2 − z1
Diffusion coefficient, DAB

1. Diffusion coefficient is a measure of how fast a commodity diffuses in the


medium.
2. The diffusion coefficients, in general, are highest in gases and lowest in solids.
The diffusion coefficients of gases are several orders of magnitude greater
than those of liquids.
3. Diffusion coefficients increase with temperature. The diffusion coefficient (and
thus the mass diffusion rate) of carbon through iron during a hardening
process, for example, increases by 6000 times as the temperature is raised
from 500°C to 1000°C.
• The diffusion coefficients and thus
diffusion rates of gases depend
strongly on temperature. The diffusion
rates are higher at higher
temperatures.
• The larger the molecular spacing, the
higher the diffusion rate.
Diffusion rate: gases > liquids > solids
Example 1

A mixture of He and N2 gas is contained in a pipe at


298K and 1 atm total pressure which is constant
throughout. At the end of the pipe at point 1 the
partial pressure pA1 of He is 0.60 atm and at the
other end 0.2 m (20 cm) pA2 = 0.20 atm. Calculate
the flux of He at steady state if DAB of the He-N2
mixture is 0.687 x 10-4 m2/s.
√ ? ?
c A1 − c A 2
J * AZ = D AB
z 2 − z1
√

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