1. Life at low Reynolds number
-E.M. Purcell
Summary Presented By: Van Wifvat
MAE 212
1/29/2015

2. Life (In Fluid) as we know it
Swimming and moving around are not too difficult
We don’t even think about the fluids around us
How could travel be any other way?
Let’s think about our relationship with the fluids around us
Take Figure 1: The Reynolds number is the ratio of a fluids inertial forces to viscous forces.
Simplified, we get dimension*velocity / kinematic viscosity
So… Okay. What does this mean for us?
Purcell, E.M.

3. Life (In Fluid) for different sizes
The Reynolds number (Inertial Forces / Viscous Forces)
Another way to think of large Reynolds numbers, is to think of the relationship between a massive objects resistance to changing velocity: F=ma. With a large mass, and a desire to move around, can come a relatively large inertial force.
Relative to the viscous forces of the surrounding fluid.
Think about walking around in air, swimming in water
Another thought: Feather in vacuum
Inertia/viscous forces
Let’s think even smaller…
Small fish
Sperm cell
Purcell, E.M.
Purcell, E.M.

4. Life (In Fluid) for Small Animals
Swimming at small Reynolds number
What is swimming?
Deforming one’s body to move in a liquid
That’s it.
“Careful” deformations
Fig. 5: Solid  Dotted  Dashed, using the motions of S1S5
What is this?
Swimming!
Not very effective though
What is the end result?

5. Life (In Fluid) for small sizes
Another way of saying “moving but going nowhere”?
Reciprocal Motion
This doesn’t make the animal move!
Time of movement?
Other fun “Swimmers”?
Purcell, E.M.

6. Life (In Fluid) for small sizes
A major means of transportation has been left out..
The flagella!
How does it move?
Purcell, E.M.

7. Life (In Fluid) for Small sizes – Getting around
Travel “patterns”
Flagella Behavior
Flagella Behavior
Forming an analysis
Flagella Behavior
Forming an analysis
Purcell, E.M.

8. Life (In Fluid) for Small sizes – Sad Realization
Trying to move at a very low Reynolds number can be a futile experience
Less of “moving through” medium, more like “taking medium with you” – and the medium slowly slips off
The time of transporting a particle by stirring can be summarized as distance/stirring-speed or (l/v)
Consider the time for transport by diffusion – (l^2/D)
Where D is diffusion constant
What does this mean for small animals?
Low Reynolds number  local stirring does nothing
The animal may as well wait for food to arrive (Keep “S” in mind..)
Purcell, E.M.
Purcell, E.M.

9. Life (In Fluid) for Small sizes – Sad Realization
So why move at all??
Diffusion is a bigger impact on the mass transport at this scale, and YOU are victim to it (if you’re the animal..)
How fast would you have to go to increase contact with food?
What??
Wait.. Is there another way to increase your contact with food?
If diffusion is the main means of mass transport..
Can we outrun diffusion?
S = D/v
… And yes we can!!
Purcell, E.M.
Purcell, E.M.

10. Overall The Reynolds number (Inertial Forces / Viscous Forces)
Fig. :
Convection
The Reynolds number (Inertial Forces / Viscous Forces)
Thinking of the dynamics of small animals helps us visualize and understand the mass transfer mechanisms which form the basis of electrochemical reactions.
These transfer mechanisms might not seem intuitive!
“There is plenty of room at the bottom”
Fig. :