Transcript Size of drag force on bacteria?

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Paper – due this Thursday: electronic copy emailed to
me by midnight.
8-10 pages double-spaced, NOT including pictures.
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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.
Today
Diffusion con’t
Biological example
Stopping time of Bacteria.
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
What forces are left on bacteria?
ma = mdv/dt – Ffriction (drag) = -gv
g = drag coefficient
v  linear in v (low Reynold’s #)
What is drag coefficient? What does it depend on?
a) Goopiness of fluid – h = viscosity
b) Dimension of object – bigger object, harder to move
Fdrag = chrv = 6phrv : g = 6phr
r = radius, v = velocity
c= constant
Remember Stokes-Einstein Equation
D = kbT/6phr = kbT/f
h = viscosity (1 centipoise for water)
r = radius of bead
f = frictional coefficient
Fdrag = fv
Solve eq’n of motion:
m dv/dt = -gv
Units of g? (m/v) (v/t) = m/t
(good)
What is mass of bacteria (can you estimate?)
4/3 pr3r = 4 x 10-15kg
What units of g = 6phr
R= 10-6 meters; h = 0.001
g = 20x10-9 N-s/m = 20 nN-s/m
Plugging in the #’s
m = 4 x 10-15kg
g = 20 nN-s/m
t = m/g = 0.2 msec
So bacteria stops in 200 nsec—very fast!
Once forces are turned off, bacteria
forgets about history very quickly!
History doesn’t matter to bacteria.
How far does bacteria coast in 0.2 usec?
Inertia is irrelevant to bacteria.
Once force is over, no forward motion!
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