Announcements Paper – due this Thursday: electronic copy ed to me by midnight pages double-spaced, NOT including pictures. Imagine you are writing it for one of your classmates-- an intelligent reader who knows some science but knows virtually nothing about the particular subject you are writing about. You must have an introduction which clearly motivates the reader why you’ve chosen this paper, what is so important about the paper, and what this particular paper adds to the understanding of the subject discussed. You must discuss how they did this (a discussion of their methods). You must discuss what they concluded. You must discuss what questions are left or new questions.

Diffusion con’t Biological example Stopping time of Bacteria. Today

How Bacteria move Inertia doesn’t matter for microscopic world Life at low Reynold’s number Why study? 1.Simple Example of F= ma 2.Doesn’t need much biology 3.Results are broadly applicable to microscopic level. Go ~ 25 um/sec: # body lengths/sec? 10 body length/sec Compared to you walking? 4 miles/hr = 6ft/sec = 1bl/sec Compared to you swimming? 50 m/s ~ min ~ m/min ~ ½ bl/s Bacteria are good swimmers!

If turn off “propeller,” how far Bacteria coast? F = ma ma = mdv/dt – F friction (drag) = -  v  drag coefficient v  linear in v (low Reynold’s #) What is drag coefficient? What does it depend on? a)Goopiness of fluid –  = viscosity b) Dimension of object – bigger object, harder to move F drag = c  rv = 6  rv :  6  r r = radius, v = velocity c= constant What forces are left on bacteria? Remember Stokes-Einstein Equation D = k b T/6  r = k b T/f  = viscosity (1 centipoise for water) r = radius of bead f = frictional coefficient F drag = fv

Solve eq’n of motion: m dv/dt = -  v What units of  r R= meters;  =  = 20x10 -9 N-s/m  = 20 nN-s/m What is mass of bacteria (can you estimate?) Units of  ? (m/v) (v/t) = m/t(good) 4/3  r 3  x kg

Plugging in the #’s Once forces are turned off, bacteria forgets about history very quickly! History doesn’t matter to bacteria. So bacteria stops in 200 nsec—very fast! m =  x kg  = 20 nN-s/m  = m/  = 0.2  sec

Once force is over, no forward motion! How far does bacteria coast in 0.2 usec? Inertia is irrelevant to bacteria.

Scaling up: What about a person swimming? A good swimmer coasts about 1 body length Inertia is much more important for bigger organism

Size of drag force on bacteria? (compared to it’s weight? Bacteria swim as if dragging 10x their own weight!

On to Nerves