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 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 2 2 z (t ) ( v )t 3 2 Diffusion across a membrane • Mass/time proportional to: – Diffusion Coefficient, D – Area S of the slab – Concentration of the gradient across the slab m m1 V1 m2 V2 DS t x m C DS t x 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 ~ 2.3e35.0e4 for pipe flow to 10^6 for boundary layers Typical 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?o ption=article&acc ess=standard&Ite mid=129&url=/art icles/aa/full/2006/ 19/aa449905/aa449905.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!