Different Sizes, Different Forces, Different Problems

Diffusion A random walk Steps of “mean free path” length Random direction after collision

Statistics of Diffusion But 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

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

Diffusion Values

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 SpermatozoaSpermatozoa ~ 1e−2 Blood flowBlood flow in brain ~ 1e2brain Blood flow in aorta ~ 1e3aorta Onset of turbulent flow ~ 2.3e3- 5.0e4 for pipe flow to 10^6 for boundary layers Typical pitch in Major League Baseball ~ 2e5Major League Baseball Person swimming ~ 4e6swimming Blue WhaleBlue Whale ~ 3e8 A large ship (RMS Queen Elizabeth 2) ~ 5e9RMS Queen Elizabeth 2

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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

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 l 2 –But, Distances get further apart as things get bigger

Gravity Order l 3 Cross sectional areas go as l 2 Gravity become increasingly important to big things

Conclusions Size Matters!