Title: Diffusion
1Diffusion
What is Engineering
2What 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
3They 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.
4 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?
5Why 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!
6Other examples?
Why do metal cooking spoons have plastic handles?
7Other examples?
What happens if someone across the room sprays
perfume?
Perfume diffusion simulation
8After 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.
9Values for Diffusivity D
Greater the diffusivity, greater the flux!
10In 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
11Do 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.
12Steady 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.
13Concentration-dependent diffusion
Consider two neighboring thin films with a
separation at ci,c
Which diffusivity is greater? How do you know?
14Unsteady 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.
15Heat 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
16Heat 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
17Thermal Conductivity Values
Greater the thermal conductivity, greater the
heat flux!
18Heat Conduction
Consider a two-paneled door
TH
Tc
z
metal
wood
What will the steady-state temperature profile
look like? Why?
kmetal gt kwood
19?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.
20Gradient 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
21Diffusion processes
Heat conduction
Diffusion-limited aggregation