Download presentation
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 S1S5 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. :
Similar presentations
© 2025 SlidePlayer.com Inc.
All rights reserved.