Title: Diffusion: Lecture 1
1Diffusion Lecture 1
2From EM fields to diffusion
- Fields will be now be of temperature or
concentration (not EM). - Fields will be typically be out of equilibrium.
- We will study the evolution of the fields toward
steady state. - Equations and vector calculus are our main
connections to the past. - Diffusion will provide a first order system to
put us on track to study waves which are second
order (First semester op-amps, hot-wire,
oscillator)
3The diffusion equation
- Mass (Mass diffusivity - Length2/time)
- How should we mix fuel and air in an engine to
reduce pollution? - How can gases change the properties of materials
(semiconductors or carburizing steel) ? - How long does it take to smell your feet?
- Heat (thermal diffusivity - Length2/time)
- How long do we cook a steak to get medium rare?
- How much heat is wasted out the window?
- How do we keep the Pentium cool?
- Momentum (viscosity - Length2/time)
- How do we predict the drag on an airplane?
- Why do golf balls have dimples?
- How do sperm swim?
4Questions
- What is diffusion?
- the process whereby particles of liquids, gases,
or solids intermingle as the result of their
spontaneous movement caused by thermal agitation
(from Webster) - If there were only molecular diffusion, how long
would it take to smell your feet after removing
your sock? - 1 year!
5So why do we smell our feet?
6Mass diffusion in gases
- Easy to understand gas molecules move and
collide with neighbors resulting in randomness. - Mean free path is 0.1 microns in standard air.
- In air molecules undergoes about 1010 collisions
per second. - Kinetic theory can predict everything quite well.
- However, convection dominates most of our
everyday experience in gases.
7Particle view of diffusion
8Assume some fluid flow
9No molecular diffusion
10Diffusion is 1/100 of convection
11Diffusion is 1/20 of convection
12Without convection, mixing in liquids is slow
13Convective diffusive behavior
14Mass Diffusion Coefficients
- Time to move distance L t L2/D
- O2 in N2 D 0.18 cm2/s (0.42 cm/sec)
- Caffeine in H2O D 630 µm2/s (25 micron/sec)
- H2 in Fe D 0.25 µm2/s (0.5 micron/sec)
- Al in Cu D 0.5 angstroms2/million years
15Return of the glob of particles
How fast does it spread? How do we measure?
16Mean distance traveled
17Histogram of x location
numbers
-3 -2 -1 0 1
2 3
location
How does the std. vary with time ?
18Particle location histogram on semi-log plot
Probability
location
19Diffusion of momentum in a fluid
How does the boundary layer thickness change with
time?
20Heat conduction in solids
- Lattice vibrations in non-metals.
- Electrons participate in metals similar
mechanism as electrical conductivity. - No convection pure diffusion problem.
- Can be understood from continuum formulation.
21Thermal diffusivity
- Aluminum a 0.9 cm2/s
- Iron a 0.12 cm2/s
- Air a 0.18 cm2/s
- Water a 0.0017 cm2/s
- Brick a 0.005 cm2/s
- Glass a 0.005 cm2/s
22Cooking a steak - medium
Constant temperature heat source
HOT!
Constant temperature heat source
HOT!
23How long do we cook in order to achieve the same
center temperature when the steak is two times
thicker?
Constant temperature heat source
Meat thermometer
Constant temperature heat source
24Experimental data
25Hot/Cold in contact
----------- Insulated------------------
----------- Insulated------------------
26Fouriers Law
- Empirical Law
- Derivable for gases
K thermal conductivity W/mK
27Heat flow
dT/dx
Distance
Temp. or temp. gradient
28Hot/cold (new condition)
29Heat flow
dT/dx
Distance
Temp. or temp. gradient
30Conservation of energy
31Heat equation