Diffusion

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Diffusion
What is Engineering
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What do these processes have in common? 1)
Hydrogen embrittlement of pressure vessels in
nuclear power plants 2) Flow of electrons
through conductors 3) Dispersion of pollutants
from smoke stacks 4) Transdermal drug
delivery 5) Influenza epidemics 6) Chemical
reactions 7) Absorption of oxygen into the
bloodstream
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They all depend on Diffusion (conduction)
What is diffusion? The transport of
material--atoms or molecules--by random
motion What is conduction? The transport of
heat or electrons by random motion.
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Brownian motion causes the ink
particles to move erratically in all directions.
A concentration of ink particles will disperse.
DIFUS.HTM
Place a drop of ink into a glass of water. What
happens?
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Why does random motion cause spreading of a
concentration of particles?
Because there are more ways for the particles to
drift apart than there are for the particles to
drift closer together.
We can also explain the spreading of a
concentration by entropy.
The second law of thermodynamics says that
systems tend towards maximum entropy or maximum
disorder.
Area of high concentration and low/zero
concentration is an ordered state and the mixed
state is the disordered state!
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Other examples?
Why do metal cooking spoons have plastic handles?
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Other examples?
What happens if someone across the room sprays
perfume?
Perfume diffusion simulation
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After adding milk and sugar, why do we stir our
coffee?
Diffusion is slow!
Agitation (or stirring) can move fluids much
larger distances in the same amount of time,
which can accelerate the diffusion process.
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Values for Diffusivity D
Greater the diffusivity, greater the flux!
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In each of these examples, molecules (or heat)
are moving down a gradient!
(From an area of high concentration to an area of
low concentration)
Ficks Law
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Do our definitions of flux make sense?

• If double area of capillary, expect the amount
  of gas transported to double.

• Want flux independent of apparatus normalize
  by area.

• Flux is proportional to the concentration
  gradient steeper the gradient, more material
  transported.

• Flux is inversely proportional to capillary
  length increasing the distance to travel will
  decrease the flux.

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Steady diffusion across a thin film
Now lets use our diffusion equation to predict
the concentration profile of a material diffusing
across a thin film!
If we are at steady-state (the concentration
profile has no time dependence, or in other
words, there is no accumulation of i in the
film), we have a linear concentration profile.
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Concentration-dependent diffusion
Consider two neighboring thin films with a
separation at ci,c
Which diffusivity is greater? How do you know?
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Unsteady state diffusion
Back to a drop of ink in a glass of water
If consider diffusion in the z-direction only
How does the concentration profile change with
time?
(add ink drop all ink located at z 0)
A measure of the spread due to diffusion is the
diffusion length Ld (4Dt)0.5, where D is the
diffusivity coefficient and t is time. Note
for small time, spreading is quick, but for long
times it slows down. Thats why you stir your
coffee after adding cream. Diffusion doesnt
work fast enough over long distances.
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Heat Transfer
Occurs by three means

• Conduction
• Occurs between two static objects
• Heat flows from the hotter to the cooler object
• For example, holding a cup of hot coffee
• Convection
• Transport of heat via a fluid medium
• Currents caused by hot air rising, fan
  circulating air
• Radiation
• Transport of energy as electromagnetic waves
  the receiving body absorbs the waves and is
  warmed
• For example, warmth of a fire

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Heat moves down a temperature gradient!
(From an area of high temperature to an area of
low temperature)
Fouriers Law
qz is called the heat flux. It has units of
k is called the thermal conductivity. It has
units of
a is called the thermal diffusivity. It is
defined as
and has units of
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Thermal Conductivity Values
Greater the thermal conductivity, greater the
heat flux!
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Heat Conduction
Consider a two-paneled door
TH
Tc
z
metal
wood
What will the steady-state temperature profile
look like? Why?
kmetal gt kwood
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?1
Heres a heat-conducting bar with a fixed
temperature T at each end T(t,0)0
T(t,100)100. 2k1 k2 .
?2
z0
z100
T(t,0)0
T(t,100)100
At steady-state
(Constant flux)
Therefore, the ratios of the temperature
gradients in each section must equal the inverse
ratios of the ks.
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Gradient transport summary
1. Momentum transferNewtons Law
vx is velocity
,
flux of x-momentum in z direction
is density,
is viscosity.
in x-direction,
r
m
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Diffusion processes
Heat conduction
Diffusion-limited aggregation