diffusion process and its role .ppt

Diffusion is the movement of molecules from high concentration to low concentration, until equilibrium is reached.

1. DiffusionDiffusion
What is Engineering

2. 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

3. 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.

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?Place a drop of ink into a glass of water. What happens?

5. Because there are more ways for the particles to drift apart
than there are for the particles to drift closer together.
Why does random motion cause spreading of a concentrationWhy does random motion cause spreading of a concentration
of particles?of particles?
We can also explain the spreading of a concentration We can also explain the spreading of a concentration
by entropy.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!

6. Other examples?Other examples?
Why do metal cooking spoons have plastic handles?

7. Other examples?Other examples?
What happens if someone across the room sprays perfume?
Perfume diffusion simulation

8. After adding milk and After adding milk and
sugar, why do we stir our sugar, why do we stir our
coffee?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.

9. TemperatureDiffusivity
(°C) (cm
2
/s)
CO
2-N
20 0 0.096
Ar-O
2 20 0.2
Ethanol(5%)-Water 25 1.13E-05
Water(13%)-Butanol 30 1.24E-05
H
2-Ni 85 1.16E-08
Al-Cu 20 1.30E-30
(gas)
(liquid)
(solid)
Values for Diffusivity DValues for Diffusivity D
Greater the diffusivity, greater the flux!

10. In each of these examples, molecules In each of these examples, molecules
(or heat) are moving down a gradient!(or heat) are moving down a gradient!
(From an area of high concentration to an area of low concentration)
dz
dc
DJ
i
i
Fick’s Law:
J
i is called the flux. It has units of
))((
2
tl
diffused material of amount
D is called the diffusion coefficient. It has units of
t
l
2

11. Do our definitions of flux make sense?
N
2
CO
2
(constant T & P)
C(*)










capillary area time
removed gas of amount
flux) dioxide carbon(
• If double area of capillary, expect the amount of gas
transported to double.
• Want flux independent of apparatus – normalize by area.









lengthcapillary
difference ionconcentrat dioxide carbon
flux) dioxide carbon(
• 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.
2
lengthtime
mass
J


dx
dc
DJ
i
i


12. Steady diffusion across a thin filmSteady diffusion across a thin film
Now let’s 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.
Well-mixed dilute
solution with
concentration c
i,l
Well-mixed dilute
solution with
concentration c
i,0
Thin film
c
i,0
c
i,l
l

13. Concentration-dependent diffusionConcentration-dependent diffusion
z=0 z=z
c
z=l
c
i,0
c
i,c
c
i,l
D
1
D
2
Which diffusivity is greater? How do you know?
Consider two neighboring thin
films with a separation at c
i,c
:

14. Unsteady state diffusionUnsteady 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)
z=0
t = 0
t
z
A measure of the spread due to diffusion is the diffusion length L
d = (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. That’s why you
stir your coffee after adding cream. Diffusion doesn’t work fast enough
over long distances.

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

16. Heat moves down a temperature gradient!Heat moves down a temperature gradient!
(From an area of high temperature to an area of low temperature)
dz
dT
kq
z
Fourier’s Law:
q
z is called the heat flux. It has units of
))((
2
tl
energy
k is called the thermal conductivity. It has units of
))()((Ttl
energy
α is called the thermal diffusivity. It is defined as
)
ˆ
)((
pC
k

and has units of
t
l
2

17. T k
(°C) (cal/cm s C)
H
2 27 4.23E-04
O
2 27 6.35E-05
Benzene 23 3.78E-04
Water 60 1.56E-03
Steel 100 9.08E-01
Wood -- 9.00E-05
(gas)
(liquid)
(solid)
Thermal Conductivity ValuesThermal Conductivity Values
Greater the thermal conductivity, greater the heat flux!

18. Consider a two-paneled door:
metalwood
What will the steady-state temperature profile look like? Why?
T
c
T
H
Heat ConductionHeat Conduction
z
k
metal
> k
wood

19. Here’s a heat-conducting bar with a fixed temperature T at each end:
T(t,0)=0; T(t,100)=100. 2k
1 = k
2 .

z=0
z=100
T(t,0)=0
T(t,100)=100
κ
1 κ
2
At steady-state:
21
21 .
kinkin dz
dC
kconst
dz
dC
k 
Therefore, the ratios of the temperature gradients in each section
must equal the inverse ratios of the k’s.
(Constant flux)

20. Gradient transport summaryGradient transport summary
1. Momentum transfer—Newton’s Law
flux of x-momentum in z direction




zx
xdv
dz

()
, v
x
is velocity
in x-direction,  is density,  is viscosity.
2. Heat transfer—Fourier’s Law
heat flux in z-direction
q
A
dcT
dz
z p

( )
;  is thermal diffusivity,
 is density, cp is heat capacity, T is thermal energy (heat).

3. Mass transfer—Fick’s Law
mass flux of A in z-direction J D
dc
dz
Az AB
A
 ; D is molecular
diffusivity of A in B, CA is the concentration of A.

21. Heat conduction
Diffusion processes
Diffusion-limited aggregation