Different Sizes, Different Forces, Different Problems

Different Sizes, Different Forces, Different Problems

Diffusion

• A random walk• Steps of “mean free

path” length• Random direction

after collision

http://www.geocities.com/piratord/browni/Difus.html

Statistics of DiffusionBut it’s 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

tvtz )3

2()( 22

Diffusion across a membrane

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

x

VmVmDS

t

m 2211

x

CDS

t

m

Diffusion Values

http://www.nanomedicine.com/NMI/Tables/3.3.jpg

Convection

• Movement though smooth currents

• Behavior determined through complicated fluid dynamics

Reynolds Number

• A measure of viscosity versus inertia– ρ is density

– μ is viscosity

– L is a characeristic length

– V is the relative velocity of the fluid relative to the object or sides

lv

Re

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 10^6 for boundary layersTypical pitch in Major League Baseball ~ 2e5 Person swimming ~ 4e6 Blue Whale ~ 3e8 A large ship (RMS Queen Elizabeth 2) ~ 5e9

http://www.aanda.org/index.php?option=article&access=standard&Itemid=129&url=/articles/aa/full/2006/19/aa4499-05/aa4499-05.right.html

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: you’re 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.

High Reynolds Number

• Turbulent, irreversible flow

• Fast forward pushes dominate slow backwards pushes

http://www2.icfd.co.jp/menu1/highreynolds/highre.html

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

Gravity

• Order l3

• Cross sectional areas go as l2

• Gravity become increasingly important to big things

Conclusions

Size Matters!