Forces

[mundane]

So the other day I had a circular tub filled with water. I added a few grams of detergent to it and started stirring with my hands. As expected, detergent tended to settle right at the center of the tub. Was this because of centripetal force? In washing machines, the clothes are spinning but are pushed away from the centre due to centrifugal force. I am not sure. Can someone help me understand the forces acting in both the scenarios?

[Genady]

It is effect of buoyancy. If it floats, it will move to the center. If it sinks, it will move outside.

[sethoflagos]

18 hours ago, mundane said:

So the other day I had a circular tub filled with water. I added a few grams of detergent to it and started stirring with my hands. As expected, detergent tended to settle right at the center of the tub. Was this because of centripetal force? In washing machines, the clothes are spinning but are pushed away from the centre due to centrifugal force. I am not sure. Can someone help me understand the forces acting in both the scenarios?

Best to consider this in terms of pressure gradients as concepts such as centrifugal force are artefacts of circular frames of reference and lead to misunderstandings. 

Suppose the fluid comprises x parcels all of equal volume. Each parcel is subject to an acceleration towards the centre of the bowl due to the rotational flow regime that you initially imposed on it. Each responds by generating a reactive inertial force (your 'centrifugal' force) in the opposite direction acting on their immediate outward neighbour. These reaction forces stack up to generate a pressure field that is a minimum at the centre of the bowl and a maximum at the outer wall. And it is this pressure field that gives a nett push toward the centre (ie, your 'centripetal' force) on each parcel causing the acceleration that maintains the rotational flow regime.

Now consider a single parcel that is a little denser than its immediate neighbours. Due to its extra mass, the local pressure gradient is insufficient to accelerate it as much and so it tends to better maintain its course and moves outward, using its extra inertia to displace its outward neighbour(s). In turn, lower density (lower mass) parcels subject to the same pressure gradient will tend to accelerate toward the centre more readily, lacking the inertial punch necessary to prevent heavier neighbours from displacing them.

 

[swansont]

20 hours ago, mundane said:

In washing machines, the clothes are spinning but are pushed away from the centre due to centrifugal force. 

They are not. There is no (real) force away from the center.

Objects move in a straight line unless a force is exerted, which only happens once they reach the edge, where an inward force can be exerted, to cause them to move in a circle.

[exchemist]

1 hour ago, swansont said:

They are not. There is no (real) force away from the center.

Objects move in a straight line unless a force is exerted, which only happens once they reach the edge, where an inward force can be exerted, to cause them to move in a circle.

Strictly speaking, doesn't this depend on what frame of reference you select? In the frame of reference of a rotating object, isn't centrifugal force real?  

[studiot]

I have been trying to find the density of the detergent powder particles themselves, before attempting an explanation.

Unfortunately all I can find is lots of information on the bulk density of the powder, which includes the voids.

Clearly I can't directly measure this by a displacement method, as the particles are soluble!

So if anyone can help with this I would be grateful as it is the density of the particles (relative to the liquid) that determines what they do.

 

22 minutes ago, exchemist said:

Strictly speaking, doesn't this depend on what frame of reference you select? In the frame of reference of a rotating object, isn't centrifugal force real?  

Any object following a curved path (ie non straight) is not in equilibrium  - that is it has a net force acting on it, even if its speed is constant.

This net force is called the centripetal force, which is a real force that must be supplied by some agent, eg the rope tied to block swung around your head.

D'Alambert invented a system of reducing such systems to equilibrium by applying an imaginary force opposing the real net force, thus allowing the equations of equilibrium to be used.

This imaginary force is called the centrifugal force.

It should be noted that the motion is at right angles to the resultant of the real and imaginary force and is the direction the object will travel if either is removed eg by cutting the rope.
That is the object will fly off tangentially, not radially.
So there is nothing forcing partcles radially outwards.

These systems are called 'central forces' and are often analysed by accelerations, rather than forces directly.

[Genady]

1 hour ago, studiot said:

Clearly I can't directly measure this by a displacement method, as the particles are soluble!

Perhaps you could measure this by displacement in a liquid that doesn't dissolve them.

[studiot]

58 minutes ago, Genady said:

Perhaps you could measure this by displacement in a liquid that doesn't dissolve them.

Thanks but I don't have the petrol to spare these days.

Surely someone in the industry might know this. Seth and Exchemist were both in petrochem industries.

[sethoflagos]

56 minutes ago, studiot said:

Surely someone in the industry might know this. Seth and Exchemist were both in petrochem industries.

Just reproduced the experiment with a capful of Ariel Original in a saucepan of freshly swirled water.

The powder takes a significant time to wet thoroughly (about a minute). So while many of the individual components may well have densities equal to or exceeding that of water, under what I understand to be the OP's conditions, it appears that the detergent 'phase' while it exists retains a substantial air content, significantly suppressing its density. Putting numbers to this would be very difficult, but the proof of the pudding is in the eating. Until wetting and dissolution is complete, the detergent sits in the central vortex of the swirling liquid. 

Edited April 27, 2022 by sethoflagos
sp

[swansont]

3 hours ago, exchemist said:

Strictly speaking, doesn't this depend on what frame of reference you select? In the frame of reference of a rotating object, isn't centrifugal force real?  

We’re discussing physics so the implication is we are applying Newton’s laws of motion. You can analyze the problem in an accelerating frame, but to use the laws the centrifugal force is still a pseudoforce.

 

[beecee]

5 hours ago, swansont said:

Objects move in a straight line unless a force is exerted, which only happens once they reach the edge, where an inward force can be exerted, to cause them to move in a circle.

Hence why Centrifigal and centrepedal forces are know as pseudo forces.

2 minutes ago, beecee said:

Hence why Centrifigal and centrepedal forces are know as pseudo forces.

I'm wrong of course! Only centrifigal forces are pseudo....centripedal forces are real. 

Edited April 27, 2022 by beecee

[studiot]

2 hours ago, sethoflagos said:

Just reproduced the experiment with a capful of Ariel Original in a saucepan of freshly swirled water.

The powder takes a significant time to wet thoroughly (about a minute). So while many of the individual components may well have densities equal to or exceeding that of water, under what I understand to be the OP's conditions, it appears that the detergent 'phase' while it exists retains a substantial air content, significantly suppressing its density. Putting numbers to this would be very difficult, but the proof of the pudding is in the eating. Until wetting and dissolution is complete, the detergent sits in the central vortex of the swirling liquid. 

Looking forward to the next installment !  +1

I would observe that density is important because there is an unaccounted for force acting here  -  gravity. We should not losse sight of that in the discussion about central forces. But you are correct that using pressure would be more appropriate since this is a fluids calculation.

 

1 hour ago, beecee said:

I'm wrong of course! Only centrifigal forces are pseudo....centripedal forces are real. 

I hesitate to use the term pseudo-force, since a force is a vector and there is something called a pseudovector which is a horse of a different colour alltogether, which is definitely not  non-real.

Centrifugal force could be called virtual or imaginary, since it is introduced by the analyst to aid calculation (and perhaps visualisation). Virtual may be too general. Imaginary might be confused with complex numbers. The point is that it does not exist.

 

[sethoflagos]

16 minutes ago, studiot said:

I would observe that density is important because there is an unaccounted for force acting here  -  gravity. We should not losse sight of that in the discussion about central forces. But you are correct that using pressure would be more appropriate since this is a fluids calculation.

Of course this is true. 

However centrifuges can work perfectly well in the absence of gravitational forces so for the purposes of the OP ... etc.

Not that it's much of a complication. Gravity simply adds a vertical gradient to the pressure field caused by the fluid rotation, and the particles respond accordingly.  

Btw For some light reading, try 'Spray Drying of Detergents in Counter Current Towers', Victor Francia Garcia, School of Chem. Eng., University of Birmingham (2014).

Link https://etheses.bham.ac.uk/id/eprint/5646/1/Francia-Garcia15EngD.pdf  (if permitted)

Interesting stuff on particle structures, density, porosity etc in Appendix II (page 260 and on)

[Genady]

The so called centrifugal force acts like a gravitational force, or a horizontal component added to the Earth gravitational force. The rest goes according to Archimedes.