Transcript You Know my Name

Reynolds Number Insights in
Biology
http://www.flickr.com/photos/nebarnix/878049616/
• What if you could shrink small enough to
live in a drop of water?
Fantastic Voyage!
http://www.microbiologybytes.com
• Scientists aboard a sub are shrunk to micro-scale.
• They ride and swim through the blood.
• Theoretically, could this work?
Just because something works big
doesn’t mean it will work small (or vice
versa)
Two Blue Whales. Credit: A. Lombardi
Copyright © 2008 Field Studies Council
• Are the concerns of a blue whale
swimming the same as those of a
copepod?
Before we can answer that
question, we have to look at
fluid dynamics!
courtesy Cesareo de La Rosa Siqueira.
[http://www.mcef.ep.usp.br/staff/jmeneg/cesareo/Cesareo_HomePage.
html].
Laminar vs. Turbulent Flow
• Move the straw
through the water
very slowly.
• Describe the fluid
movement around the
straw
• Repeat, moving the
straw more quickly.
• How does fluid
movement differ with
the speed?
Which is laminar?
This is laminar
Very smooth!
But very sticky!
What conditions yielded laminar flow?
This is turbulent
Very chaotic!
But not as sticky!
What conditions yielded turbulent flow?
Let’s look at factors of concern
to a swimmer
Inertia
Let’s look at factors of concern
to a swimmer
Inertia
Viscosity
Let’s look at factors of concern
to a swimmer
Inertia
Viscosity
Density
Let’s look at factors of concern
to a swimmer
Inertia
Viscosity
Density
Speed
Which factors can you observe?
• Wind the fish
CAREFULLY!
• Time its swim across
the tank.
• Measure the distance
(cm) it travelled.
• Calculate its speed.
• Complete 3 runs and
fill in the data table.
A swimmer at the nano scale
faces a different set of
problems.
• Water becomes very sticky – meaning
viscosity dominates!
• Does that mean we can’t model a nanoscale swimmer at the macro scale?
No! That’s what Reynolds
number (Re) is for.
• Measure your swimmer.
• Use the information provided to calculate
the Reynolds number.
No! That’s what Reynolds
number (Re) is for.
• Measure your swimmer.
• Use the information provided to calculate
the Reynolds number (Re):
𝜌𝑉𝐿
𝑅𝑒 =

𝜌 = density of fluid (for this experiment = 1)
𝑉 = speed of swimmer
𝐿 = length of swimmer
= dynamic viscosity of fluid (for water = .01)
Calculate the Re for each of
these animals
Swimmer
Swimming
Speed
(cm/s)
Body Length
(cm)
Blue whale
630
2400
Person
100
180
1
15
Minnow
𝑔
Dynamic viscosity of water = .01 𝑐𝑚 𝑠
Density of water = 1.0 𝑔/𝑐𝑚3
Re
For a big animal, Re is high
Swimmer
Reynold’s Number
(Re)
Blue whale swimming 300,000,000
Person swimming
Minnow
4,000,000
1000
Turbulent flow high Re
• A Reynolds number greater than 2000 is
considered to be turbulent flow.
But what about something
small?
Swimmer
Copepod
E. coli
Electron transport
protein
Swimming
Speed
(cm/s)
Length
(cm)
.5
.15
.001
.0002
?
1 X 10-7
𝑔
Dynamic viscosity of water = .01 𝑐𝑚 𝑠
Density of water = 1.0 𝑔/𝑐𝑚3
Re
Object
Reynold’s
Number (Re)
Copepod
10
E. coli
.00004
Electron transport
protein
.0000025
Laminar flow at low Re
We can model a copepod at large
scale if we can match the Re
𝜌𝑉𝐿
𝑅𝑒 =

𝜌 = density of fluid (for this experiment = 1)
𝑉 = speed of swimmer
𝐿 = length of swimmer
= dynamic viscosity of fluid (for water = .01)
• What can we reasonably change in our
model to accomplish a smaller Re?
Can we change the size of our
model?
𝐿 = length of swimmer
• Probably not. Even if possible, small size
would be difficult to manage.
What about the speed of our
swimmer?
𝑉 = speed of swimmer
• Again, possible but not practical. Winding
slightly enough to effectively change the
speed would be difficult at best.
Can we easily change density?
𝜌 = density of fluid (for this experiment = 1)
• Yes! But even the least dense liquid at
room temperature is only 2/3 as dense as
water. And that would only lower Re by
the same amount.
That leaves us with viscosity!
= dynamic viscosity of fluid (for water = .01)
• By replacing water with a shampoo
mixture we can raise the viscosity by a
factor or 3000!
Reynolds number in higher
viscosity
•
•
•
•
•
•
Wind the fish CAREFULLY!
Time its swim across the tank.
Measure the distance (cm) it travelled.
Calculate its speed.
3 times and average
Calculate its Reynolds number (Re)
Cnidarians fire small harpoons
called nematocysts (or
cnidoblasts) at their prey
Courtesy of James Cook Uni
But a nematocyst is only 10mm,
so Re should be low
Photo courtesy of Dr. Zoltan Takacs
• How do they overcome viscosity to fire
these small projectiles so rapidly?
What could compensate for the small
size and make the nematocysts
turbulent?
• Average velocity = 1860
cm/s
• Nearly 70 km/h or 42 mph
• Not impressed?
– Speed is attained within 13
micrometers
– Acceleration required is
about 5,000,000 g’s!
Figure from Nüchter et al. 2006.
Things behave differently
at different size scales!
As things get
smaller, viscosity
becomes more
important.
Re can be used to
model movement
at small scales.