How Do Centrifuges Work From a Newtonian Perspective?

[noodlehed]

Hello! This site has been tremendously helpful over the past few weeks, so first off I wanted to thank the entire community here for the service your provide to others.

I am doing a report on centrifuges, but before I get too far I want to make sure I understand the concept from a Newtonian perspective. I did search the topic here and elsewhere, and just want to make sure I have everything straight. Hopefully this is the right forum for this post :) That being said, here is my take on a centrifuge. Please correct any misinformation I may have gathered on the web.

There are two forces which are both named "centrifugal". One is a reaction force to centripetal force, which acts upon the object causing the rotation. The other is a fictitious force which arises from observing motion from a non-inertial frame of reference, and seems to act upon the object under rotation. In actuality, from a Newtonian perspective, the object is traveling in a straight line and the centripetal force is "pulling in" the object, causing it to follow a circular path. In terms of real forces, the centripetal force acts upon the object under rotation, and the centrifugal force acts upon the object causing rotation.

In terms of a simple human centrifuge (like an amusement ride, rotating upon a vertical axis with the rider strapped into the seat), the centripetal force acts upon the rider, transferred by the seat. If the rider were not strapped in ( ) they would fly off in a straight line at a tangent to their motion. The rider feels a "fictitious" centrifugal force...from their frame of reference it feels as if they are being pulled outwards. The "real" centrifugal force is a reaction force, but what does it act upon? The rotor upon the axle, or the rider upon the strap? Not sure about that one.

Considering a desktop centrifuge...we have an object creating motion (say, an electrostatic motor), an axle out of the motor, a rotor attached to the axle, and tubes in the rotor. They spin up to a constant velocity, but the rotor and tubes are accelerating due to the changing direction vector. Now, the direction of the centripetal force is inward...so why would the heavier particles be at the bottom of the tube? Shouldn't the heavier particles collect on the inner wall, closest to the axis of rotation? (unless, of course, the tubes were placed horizontally; but most centrifuges I've seen have vertical tube slots in the rotors). Furthermore, is the name centrifuge a misnomer? If I am correct, it is centripetal force which causes the precipitate to collect in the tube. The centrifugal force should be acting upon the rotor by the tube, in accordance with Newton's laws. Lastly, am I missing any forces in the description of the machine? I assume I likely am when it comes to the tube and the fluid within it; I can imagine that a highly viscous fluid would be more difficult to separate, for example. I am unfamiliar to forces within fluids, so some assistance in this area would be appreciated as well.


Thank you in advance for any assistance you may be able to give me, and apologies for the long post.

 

[Doc Al]

I would not use the term centrifugal force for anything other than the "fictitious" force as seen from an accelerating frame. Don't use it to refer to the reaction force to the centripetal force.

To find the "reaction" force to any force, start by identifying the two objects that are interacting and apply Newton's 3rd law. (If the seat exerts the centripetal force on the person, the reaction is the person exerting an outward force on the seat.)

The term "centrifuge" seems apt to me. The easiest way to understand its operation is to view things from the accelerating frame: Thing of it as creating an artificial "gravitational" (centrifugal) field pointing outward, so denser things "gravitate" outward. (Viewed from an inertial frame, think of the more dense things as having more inertia to overcome.)

 

[noodlehed]

Thank you for the quick response and the advice. Agreed, using the term centrifugal to describe only the fictitious force will assist in disambiguating the terminology. Is there a less antiquated name for the reaction force? Or would calling it a reaction force suffice?

 

[Doc Al]

Calling it the reaction force (or the 3rd law pair) seems clear enough.

 

[rcgldr]

Personally I have no problem with the term "centrifugal force", as long it's understood to be a reaction force due to inwards circular acceleration. Stating that this force is "ficticious" is misleading. Reaction forces are just a real as the forces that cause the reaction forces.

 

[Doc Al]

Personally I have no problem with the term "centrifugal force", as long it's understood to be a reaction force due to inwards circular acceleration. Stating that this force is "ficticious" is misleading. Reaction forces are just a real as the forces that cause the reaction forces.

That's exactly the reason why I would not use "centrifugal force" to mean the reaction force to a centripetal force. The term "centrifugal force" is generally used to refer to a non-inertial force that appears when viewing things from a rotating reference frame. It's fictitious in the sense that it has no agent, unlike centripetal force, which does.

To use the term centrifugal force to also refer to a reaction force would be confusing. (That usage, as far as I know, went out of favor long ago.)

You are certainly correct that "reaction" forces are just as real as "action" forces.

 

[noodlehed]

In order to ensure my paper is uncluttered, I just used the modern terminology and added footnotes to the two terms and defined them explicitly in the footnotes. Thank you for the assistance in this area...but two questions remain from my rambling post if anyone is able to help.

If the tubes are held in a vertical position, am I correct in thinking the pellet would form on the outside of the tube? Most descriptions state that it forms on the bottom of the tube, but I would assume that is only possible in a swinging bucket rotor...that combined with the fact it is likened to gravity has me a bit confused. The centrifugal force is outward, not downward...unless there are other forces at work which causes the precipitate to form at the bottom of the tube.

Which leads to my other question...which forces are at work inside the tube in a standard centrifuge (no heat applied to the sample) besides the centrifugal force? Thanks again for everything.