Would there be any varying forces acting on individual wells in rotation? (stir/shaker plate)

[HavensXL]

Depicted is a plate of 48 wells on a ridged plane that is rotated or stirred using a hub with an off center pin to mix a fluid in each well. My question is thus: Do all wells experience the same amount of force or does the red well experience more/less than blue? I would assume that the forces acting on all wells are the same but I have had some individuals try and reason that the red well will experience a different force as it is farther from the rotating cam. I just want to learn more about the forces applied in this situation. I'm new and not sure if this is something for this forum so apologies if it's not. Thank you.

 

[A.T.]

Depicted is a plate of 48 wells on a ridged plane that is rotated or stirred using a hub with an off center pin to mix a fluid in each well.

I assume the plate is not rotating (it's orientation doesn't change), but merely translating along a circular (or otherwise curved) path.

My question is thus: Do all wells experience the same amount of force or does the red well experience more/less than blue?

Since each well performs the same motion and acceleration, the forces on their content are the same, if the mass of the content is the same.

I would assume that the forces acting on all wells are the same but I have had some individuals try and reason that the red well will experience a different force as it is farther from the rotating cam.

They probably confuse translation along a curved path (fixed orientation), with rotation (orientation changes).

The animations in this article visualize the difference:
https://www.vialattea.net/content/tides-and-centrifugal-force/

In the animation below, the big blue circle moves like your plate. It translates along a circular path, but doesn't change it's orientation relative to an inertial frame (red axes on the left side).

So it's not rotating, and therefore in the rest frame of the plate, you don't have a position dependent inertial centrifugal (radial) force. Instead you have a time dependent uniform inertial force (yellow arrows on the right). Since the force field is uniform, it affects all wells (distributed across the blue circle) in the same way.

 

[Lnewqban]

Welcome, @HavensXL !

Could you please post a diagram of the machine?
It is not clear to me what kind of movement the gears satellite mechanism in the last posted picture is inducing in your wells plate.

Also, where is the axis of rotation located respect to the red and blue highlighted wells?
Is that axis perpendicular to the plate?

 

[A.T.]

Could you please post a diagram of the machine?

@HavensXL Or a slow-motion video of the machine in action from a camera fixed above it. Or attach your smart phone to the plate at different locations and log the accelerometer output.

Common sense suggests that such stirrers are designed to stir all wells in the same way, and not introduce any bias. Otherwise they would be pretty useless for any study that compares the samples from different wells. They might have different modes tough.

 

[HavensXL]

Welcome, @HavensXL !

Could you please post a diagram of the machine?
It is not clear to me what kind of movement the gears satellite mechanism in the last posted picture is inducing in your wells plate.

Also, where is the axis of rotation located respect to the red and blue highlighted wells?
Is that axis perpendicular to the plate?

Ill see about a diagram, the tho cams that are placed at the top and bottom drive the center of the top and bottom plates(the one depicted with the two colored wells is one plate, another one is placed below.) the center gear spins causing the other two to rotate with a pin that is of center. This creates a translation of sorts.

 

[HavensXL]

@HavensXL Or a slow-motion video of the machine in action from a camera fixed above it. Or attach your smart phone to the plate at different locations and log the accelerometer output.

Common sense suggests that such stirrers are designed to stir all wells in the same way, and not introduce any bias. Otherwise they would be pretty useless for any study that compares the samples from different wells. They might have different modes tough.

I tried to attach a video but it was not supported. I'll try something else.

 

[Andy Resnick]

Depicted is a plate of 48 wells on a ridged plane that is rotated or stirred using a hub with an off center pin to mix a fluid in each well. My question is thus: Do all wells experience the same amount of force or does the red well experience more/less than blue? I would assume that the forces acting on all wells are the same but I have had some individuals try and reason that the red well will experience a different force as it is farther from the rotating cam. I just want to learn more about the forces applied in this situation. I'm new and not sure if this is something for this forum so apologies if it's not. Thank you.

As others have mentioned, please provide information about the shaker.

If you are using an orbital shaker, then yes- all wells move identically, so the acceleration will be identical. However, the origin of fluid flow (for mixing) relies on the interaction of fluid and solid walls of the well, and so there are two effects: the magnitude of induced flow velocity will depend on how much fluid is present in the well, and the velocity field within the fluid will not be uniform- the center of each well will be nearly stagnant, while flow is a maximum at the edge. With a 48-well plate, you may have trouble generating sufficient flow due to the small size of each well.

On the other hand, if you are using a rocking shaker, because the fluid flow is induced by gravity, the fluid velocity will be (AFAIK) very uniform (on average) and you should have no problem with a 48-well plate.

Not sure about reciprocating shakers, I have never used those.

 

[HavensXL]

I assume the plate is not rotating (it's orientation doesn't change), but merely translating along a circular (or otherwise curved) path.

Since each well performs the same motion and acceleration, the forces on their content are the same, if the mass of the content is the same.

They probably confuse translation along a curved path (fixed orientation), with rotation (orientation changes).

The animations in this article visualize the difference:
https://www.vialattea.net/content/tides-and-centrifugal-force/

In the animation below, the big blue circle moves like your plate. It translates along a circular path, but doesn't change it's orientation relative to an inertial frame (red axes on the left side).

So it's not rotating, and therefore in the rest frame of the plate, you don't have a position dependent inertial centrifugal (radial) force. Instead you have a time dependent uniform inertial force (yellow arrows on the right). Since the force field is uniform, it affects all wells (distributed across the blue circle) in the same way.

View attachment 360360

This clears so much up, translation along a curved plane will exert an equal force as long as the plane is ridged. If one well had a larger mass in the corner of the plate would that effect any of the wells around it? Or is it isolated because again the plane is ridged?

 

[HavensXL]

Depicted is a plate of 48 wells on a ridged plane that is rotated or stirred using a hub with an off center pin to mix a fluid in each well. My question is thus: Do all wells experience the same amount of force or does the red well experience more/less than blue? I would assume that the forces acting on all wells are the same but I have had some individuals try and reason that the red well will experience a different force as it is farther from the rotating cam. I just want to learn more about the forces applied in this situation. I'm new and not sure if this is something for this forum so apologies if it's not. Thank you.View attachment 360333

Here are attached links to videos of the mechanism in motion.

 

[A.T.]

This clears so much up, translation along a curved plane will exert an equal force as long as the plane is ridged.

It will create the same accelerations, and thus the same inertial force fields in the rest frame of each well. The external conditions will be the same for each well. The actual force depends on what mass is being accelerated: F = m * a

If one well had a larger mass in the corner of the plate would that effect any of the wells around it? Or is it isolated because again the plane is ridged?

As long as the plate doesn't deform in a relevant matter (is rigid enough) the wells won't affect each other. The plate should also be well attached, so there are no resonant vibrations (standing waves in the plate material), as those might cause different acceleration at different locations across the plate.