Different Sizes, Different Forces, Different Problems

1
Different Sizes, Different Forces, Different
Problems
2
Diffusion

• A random walk
• Steps of mean free path length
• Random direction after collision

http//www.geocities.com/piratord/browni/Difus.htm
l
3
Statistics of DiffusionBut its random

• Distance dependent on t(1/2)
• Distances larger than a cell are inefficient to
  diffuse over
• While any one particle is unpredictable, an
  ensemble is
• Diffusion smoothes over concentration gradients

4
Diffusion across a membrane

• Mass/time proportional to
• Diffusion Coefficient, D
• Area S of the slab
• Concentration of the gradient across the slab

5
Diffusion Values
http//www.nanomedicine.com/NMI/Tables/3.3.jpg
6
Convection

• Movement though smooth currents
• Behavior determined through complicated fluid
  dynamics

7
Reynolds Number

• A measure of viscosity versus inertia
• ? is density
• µ is viscosity
• L is a characeristic length
• V is the relative velocity of the fluid relative
  to the object or sides

Spermatozoa 1e-2 Blood flow in brain 1e2
Blood flow in aorta 1e3 Onset of turbulent
flow 2.3e3-5.0e4 for pipe flow to 106 for
boundary layers Typical pitch in Major League
Baseball 2e5 Person swimming 4e6 Blue Whale
3e8 A large ship (RMS Queen Elizabeth 2) 5e9

8
http//www.aanda.org/index.php?optionarticleacce
ssstandardItemid129url/articles/aa/full/2006/
19/aa4499-05/aa4499-05.right.html
9
Low Reynolds Number Regime

• Small organisms with little mass to break surface
  tension
• Cannot stroke and glide

Purcell It helps to imagine under what
conditions a man would be swimming at, say, the
same Reynolds number as his own sperm. Well, you
put him in a swimming pool that is full of
molasses, and then you forbid him to move any
part of his body faster than one centimeter per
minute. Now imagine yourself in that condition
youre in the swimming pool in molasses, and now
you can only move like the hands of a clock. If
under those ground rules you were able to move a
few meters in a couple of weeks, you may qualify
as a low Reynolds number swimmer.
10
High Reynolds Number

• Turbulent, irreversible flow
• Fast forward pushes dominate slow backwards pushes

http//www2.icfd.co.jp/menu1/highreynolds/highre.h
tml
11
Surface Tension

• In water, attractive force between molecules
• On Surface, attractive force in, no force out
• Liquids minimize surfaces
• Order l
• Cross sectional areas go as l2
• But, Distances get further apart as things get
  bigger

12
Gravity

• Order l3
• Cross sectional areas go as l2
• Gravity become increasingly important to big
  things

13
Conclusions

• Size Matters!