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Brownian Motion Diffusion

Reading Chap7

HISTORY In 1827 the English botanist Robert Brown

noticed that pollen grains suspended in water

jiggled about under the lens of the microscope,

following a zigzag path. Even more remarkable was

the fact that pollen grains that had been stored

for a century moved in the same way. Magic?

http//galileo.phys.virginia.edu/classes/109N/more

_stuff/Applets/brownian/brownian.html

http//www.geocities.com/piratord/browni/Difus.htm

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Q Observation?

- Definition
- Brownian motion irregular wiggling motion of a

particle caused by random bombardment of gas

molecules against the particle - Diffusion the net transport of particles from a

region of higher concentration to a region of

lower concentration - The primary transport mechanism for small

particles (lt 0.1 ?m) Important when transport

distance is small e.g. filter, airway in human

lung, loss in sampling path

Ficks First Law of Diffusion

- The net flux of aerosols (the net number of

particle traveling through a unit area per unit

time) is proportional to the concentration

gradientJ flux (/area/time)D diffusion

coefficient (area/time)n particle number

concentration (/cm3)

Ficks Second Law of Diffusion

A

A

B

B

D

D

C

C

Spread of particles over time and space

1/16

Numbers on curves are values of Dt

1/2

1

- Solve 1-D equation

Solution

(normal distribution!)

Mean Square Displacement of particles

Recall Mean Surface Area

Q Why not mean displacement?

Stokes-Einstein Equation for Diffusion

Coefficient

- Assumptions
- the Brownian motion of an aerosol is equivalent

to that of a giant gas molecule the kinetic

energy for aerosol Brownian motion is the same as

the gas molecules (KE3/2KT) - the diffusion force on a particle is equal to the

friction force

HISTORY The first mathematical theory of Brownian

motion was developed by Einstein in 1905. For

this work he received the Nobel prize

for particles greater than the mean free path of

air

Q What are the parameters that affect an

aerosols diffusivity?

Particle Mean Free Path

Mean thermal velocity

(Chap. 2.2.2-2.3)

Particle mean free path

aerosol

Gas molecule

Diffusional Deposition

- Aerosols adhere when they hit a surface.
- Ex. A vertical surface in a infinitely large

volume of aerosol

Solution

Q What if dp is larger?

Deposition Rate

- Concentration gradient at the surface
- Using Ficks First Law
- Integrating over time
- Deposition velocity

General form of the concentration profile near a

wall

Q Which mechanism (diffusion and gravitation

settling) is more important to deposit

particles?

Penetration

- Dimensionless deposition parameter
- Penetration

Q How does P change if the tube diameter doubles

while the volume flow rate remains the same? Why?

Tube

Rectangular channel

tube

rectangular channel

Penetration versus deposition parameter for

circular tubes and rectangular cross-section

channels

- Diffusion Battery tube bundle parallel plate.

Same equation for a single long tube or by

cutting it into n parallel tubes each carrying

1/n of the total flow

Penetration for an aerosol flowing through a

tube (1m length) at 3 laminar flow rates

Screen-type Diffusion Battery/Classifier

Aerosol Measurement, Ed. Willeke, K. Baron, P.

A., 1993.

Aerosol Measurement, Ed. Willeke, K. Baron, P.

A., 1993.

Diffusion Denuder

Aerosol Measurement, Ed. Willeke, K. Baron, P.

A., 1993.

- Diffusion Dryer

Reflection

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