Molecular Motion
Transport Processes and Properties
•
Transport Processes
Transport Processes
•
Diffusion
Diffusion

Thermodynamic driving force

Frick
Frick
’
s first law.
s first law.

Frick
’
s second law.

Stokes

Einstein Equation
•
Viscosity
Viscosity
Molecular Physical Chemistry – Lecture 7
Reading:
Chapter 6 and Lecture Notes
• Till recently we focused on
systems at
equilibrium
where there is no net flow of
heat, work, or matter.
At the microscopic
level, what we have been studying is
time
averaged behavior
.
• There are cases where time average of
forces acting on
a system
results in a
flow
of material
–This leads to transport
phenomena
Transport Processes
•
4 such phenomena we encounter are:
– Diffusion
– Electrical conduction
– Fluid flow (convection)
– Heat flow (conduction)
•
Each of these represents net movement in
the direction of the gradient from a higher
to a lower potential
Transport Processes
•
The gradients arise from differences in
– Chemical potential
– Electrical potential
– Temperature
– Pressure
•
The general equation for all forms of transport:
•
The flow (J) of material in the xdirection is
proportional to the
gradient of force of type A in
the xdirection
.
B is a constant.
A
BF
dx
dA
B
J
0
0
Transport Processes
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•
For
diffusion  Fick’s Law
B=D, the diffusion constant
•
For
electrical conduction  Ohm’s Law
B=
ț
, the conductivity
•
For
fluid movement  Poiseuille’s Law
B=C, the hydraulic conductivity
•
For
heat transfer  Fourier’s Law
B=K
T
, the thermal conductivity coefficient
A
BF
dx
dA
B
J
0
0
Transport Processes
•
The flux of material along a direction through a
unit area in a unit time (second).
dx
dC
D
J
0
J
– Flux; mol cm
2
s
1
D – Diffusion coefficient;
cm
2
s
1
Diffusion – The Definition
•
Let us assume that the concentration of
species x in solution is allowed to vary only in
the xdirection. There is a gradient in
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 Spring '08
 gough
 Fluid Dynamics, Statistical Mechanics, Heat, diffusion equation

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