Does the Movement of Flagella Contradict Bernoulli's Principle?

[Simfish]

http://en.wikipedia.org/wiki/Flagella

So I was reading Purcell's "Life at Low Reynolds Numbers", which I found interesting. So here's a question:

The flagellum help propel the cell forward. The question is - the flagella should increase the velocities of the fluid molecules behind the cell, right? But if it increases the velocities of the fluid molecules behind the cell, shouldn't the pressure gradient be decreasing behind the cell, causing the cell to move backwards? (as we know from http://en.wikipedia.org/wiki/Bernoulli's_principle). Am I missing something?

 

[arildno]

Bernoulli's principle??
You have not an ideal fluid here, i.e, with no friction, nor is the flow stationary.

It is a complete misapplication of Bernoulli's principle.

Furthermore, you have turned this upside down when it comes to the proper use of Bernoulli along a streamline:

The reason why the velocity then is higher at the point of lower pressure is because the fluid element that has traversed the streamline experienced an ACCELERATION due to the existing pressure difference.

If the pressure on the right hand side is greater than on the left-hand side, then the velocity of the element will be the highest on the left-hand side, since it has experienced a pressure force in that direction, causing acceleration.

 

[sir-pinski]

Great question! The physics of flagella is indeed a fascinating topic. You are correct in thinking that the flagellum helps propel the cell forward by increasing the velocities of the fluid molecules behind the cell. This is due to the motion of the flagellum itself, which creates a force that pushes the fluid molecules in its direction of motion. This is known as the "drag force" and it is what ultimately propels the cell forward.

However, you are also correct in thinking that this increase in fluid velocity behind the cell should result in a decrease in pressure gradient, which could potentially cause the cell to move backwards. This is where the concept of "viscous forces" comes into play. Viscous forces are essentially the resistance that a fluid exerts on an object moving through it. In the case of flagella, the viscous forces acting on the cell are greater than the drag force created by the flagellum. This means that the cell is able to maintain its forward motion despite the decrease in pressure gradient behind it.

Additionally, the shape and flexibility of the flagellum also play a role in the physics of flagella. The flagellum is able to change its shape and direction of motion, allowing the cell to adjust its movement and direction. This helps the cell navigate through complex environments and maintain its forward motion.

In summary, the physics of flagella involves a delicate balance between drag forces, viscous forces, and the shape and flexibility of the flagellum. It is a complex and fascinating phenomenon that continues to be studied by scientists. I hope this helps to answer your question and further piques your interest in the physics of flagella.