TBR Physics Section VII - Fluids and Solids - Ex. 7.5b

[gettheleadout]

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The problem shows a fluid-filler container bisected by a phospholipid membrane. After conduction of some experiment, the membrane is shown to be bowed out toward the left side of the container. The question says "This distortion [of the membrane] may have occurred because the pressure on the right side of the vessel:

A. Increased, and the membrane's surface tension increased.
B. Increased, and the membrane's surface tension decreased.
C. Decreased, and the membrane's surface tension increased.
D. Decreased, and the membrane's surface tension decreased.

I answered A. Only an increase in pressure in the right side of the container would cause the bisecting membrane to bow outward away from that side, so that half of the question was easy. With regard to surface tension, I considered the example given in a previous answer explanation, "...increasing surface tension on a membrane makes it less pliable...Imagine how the pliability of a balloon surface decreases as you inflate it."

The answer explanation gives B as the correct choice, saying, "Because the molecules of the membrane are being stretched apart, they are feeling less of an attractive force towards one another. This means that the membrane's surface tension must have decreases, making B and better explanation than choice A."

If the pressure on one side of the membrane, effectively the force on the membrane times its area, increases, then without an increase in the tension in the membrane (effectively the restoring force opposing the pressure) the membrane molecules would no longer exist in translational equilibrium, and would be forced apart to rupture the membrane, right? The fact that the membrane is in translational equilibrium in this bowed state means that the restoring force of the membrane is equal to the now-greater force of the pressure on the right side of the container. How can the pressure increase without the tension in the membrane increase if the membrane remains steady and taut?

Further, considering the balloon example, how is the membrane different from the balloon? You blow up the balloon (bowing out the "membrane") and in doing so increase the tension on the membrane, making it less pliable.

Am I missing something here?

 

[milski]

I would expect that the pressure is balanced by the fluid/gas on the other side of the membrane. As the membrane bows to the left, pressure on the right goes down, pressure on the left goes up (or stays the same if the left end of the tube is open), eventually you reach new equilibrium.

 

[noobtech]

i would've picked A too..wth

 

[FormerPhysicist]

TBR stated in the section that surface tension refers to the tendency of the surface of a liquid (or membrane) to pull inward and shrink due to proximity of its molecules. As a surface expands then, it follows that the surface tension decreases as the distance between molecules increases. As milski said, the pressure on the other side of the compartment accounts for the pressure difference.

Increasing surface tension (thereby increasing that "inward pull") should make the surface less pliable. I feel like the analogy with the balloon might have been slightly misleading. If it helps, a good example of this sort of thing is surfactant in the alveoli of lungs. Without it, surface tension goes up, causing the alveoli to collapse (rather than explode).

 

[gettheleadout]

I would expect that the pressure is balanced by the fluid/gas on the other side of the membrane. As the membrane bows to the left, pressure on the right goes down, pressure on the left goes up (or stays the same if the left end of the tube is open), eventually you reach new equilibrium.

Couldn't you say the same thing for the air on the outside of a balloon?

TBR stated in the section that surface tension refers to the tendency of the surface of a liquid (or membrane) to pull inward and shrink due to proximity of its molecules. As a surface expands then, it follows that the surface tension decreases as the distance between molecules increases. As milski said, the pressure on the other side of the compartment accounts for the pressure difference.

Increasing surface tension (thereby increasing that "inward pull") should make the surface less pliable. I feel like the analogy with the balloon might have been slightly misleading. If it helps, a good example of this sort of thing is surfactant in the alveoli of lungs. Without it, surface tension goes up, causing the alveoli to collapse (rather than explode).

I'm not really able to imagine the membrane in this case not being less pliable when bowed out...

With regard to the pressure on the other side of the membrane increasing to balance it out (as a result of it bowing and decreasing the left side's volume), is this totally relevant? I mean, if you stretch a flexible membrane/string/whatever, isn't the restoring force it resists with going to increase proportionally (at least until the elastic limit)? Is this tension in the string / membrane that manifests as the restoring force not the same as surface tension? It's pulling the molecules of the membrane "inward" back to the state of lowest tension is it not?

 

[FormerPhysicist]

Couldn't you say the same thing for the air on the outside of a balloon?

I'm not really able to imagine the membrane in this case not being less pliable when bowed out...

With regard to the pressure on the other side of the membrane increasing to balance it out (as a result of it bowing and decreasing the left side's volume), is this totally relevant? I mean, if you stretch a flexible membrane/string/whatever, isn't the restoring force it resists with going to increase proportionally (at least until the elastic limit)? Is this tension in the string / membrane that manifests as the restoring force not the same as surface tension? It's pulling the molecules of the membrane "inward" back to the state of lowest tension is it not?

I feel like you might be overthinking this example a little bit...but I agree, it is counterintuitive. When I was studying this, it helped me to realize that surface tension of a liquid/thin solid was not quite the same as physics I type of tension (as in a rope/string...although again, I'm not sure if that helps you or not).

I'll try explaining it this way: surface tension is defined (by wikipedia) as a contractive force that resists change. If this particular force is due to the proximity of molecules to each other, then that particular resistive force should decrease when the molecules are spread further apart. This is the case with the membrane in the example.

 

[gettheleadout]

I feel like you might be overthinking this example a little bit...but I agree, it is counterintuitive. When I was studying this, it helped me to realize that surface tension of a liquid/thin solid was not quite the same as physics I type of tension (as in a rope/string...although again, I'm not sure if that helps you or not).

I'll try explaining it this way: surface tension is defined (by wikipedia) as a contractive force that resists change. If this particular force is due to the proximity of molecules to each other, then that particular resistive force should decrease when the molecules are spread further apart. This is the case with the membrane in the example.

Okay, that makes sense. I think the issue is that I haven't learned a specific enough (or clear enough?) definition for surface tension for me to recognize that it's different in this case from the restoring force / tension of the membrane. I'm also a little confused as to how we can have surface tension in a membrane (e.g. the phospholipid bilayer or a balloon) if it's a phenomenon of liquids?

By the way thanks for helping me out with this, are you really a former physicist?

 

[milski]

Couldn't you say the same thing for the air on the outside of a balloon?

I'm not really able to imagine the membrane in this case not being less pliable when bowed out...

With regard to the pressure on the other side of the membrane increasing to balance it out (as a result of it bowing and decreasing the left side's volume), is this totally relevant? I mean, if you stretch a flexible membrane/string/whatever, isn't the restoring force it resists with going to increase proportionally (at least until the elastic limit)? Is this tension in the string / membrane that manifests as the restoring force not the same as surface tension? It's pulling the molecules of the membrane "inward" back to the state of lowest tension is it not?

Yes, you could. In the inflated balloon there is an equilibrium between outside pressure and the tension of the balloon against the pressure inside it. For reasonably stretched balloon, the equilibrium pressure inside is proportional to 1/R. In other words, the equilibrium pressure decreases as the balloon inflates. That's easy to demonstrate with the popular trick of having a more inflated and less inflated balloons and connecting their ends. Contrary to popular expectations, the balloon don't equilibrate at some size in the middle but the smaller one inflates the larger one even further.

Anyway, seems that you got things covered with FormerPhysicist while I was on the bus headed home. 👍

 

[FormerPhysicist]

Okay, that makes sense. I think the issue is that I haven't learned a specific enough (or clear enough?) definition for surface tension for me to recognize that it's different in this case from the restoring force / tension of the membrane. I'm also a little confused as to how we can have surface tension in a membrane (e.g. the phospholipid bilayer or a balloon) if it's a phenomenon of liquids?

By the way thanks for helping me out with this, are you really a former physicist?

The quick answer (and I realize this is a cop-out) is that surface tension is complicated and should only be considered for a solid/membrane when it is thin or highly elastic, as is the case with the lipid bilayer.

I did graduate with a physics degree...which it turns out is useless for people that don't want to teach high school/get a PhD. I definitely enjoyed other subjects (nuclear/astrophysics) quite a bit more than the physics tested on the MCAT, unfortunately.

 

[Laureatebarrel]

Baloon tension is like rope tension, surface tension is different though.i think you miss the concept. Great review for me though.

 

[gettheleadout]

Yes, you could. In the inflated balloon there is an equilibrium between outside pressure and the tension of the balloon against the pressure inside it. For reasonably stretched balloon, the equilibrium pressure inside is proportional to 1/R. In other words, the equilibrium pressure decreases as the balloon inflates. That's easy to demonstrate with the popular trick of having a more inflated and less inflated balloons and connecting their ends. Contrary to popular expectations, the balloon don't equilibrate at some size in the middle but the smaller one inflates the larger one even further.

Anyway, seems that you got things covered with FormerPhysicist while I was on the bus headed home. 👍

That is an amazingly counterintuitive example, but from considering that (and looking up a video and explanation) I understand now.

Thanks milski!

The quick answer (and I realize this is a cop-out) is that surface tension is complicated and should only be considered for a solid/membrane when it is thin or highly elastic, as is the case with the lipid bilayer.

I did graduate with a physics degree...which it turns out is useless for people that don't want to teach high school/get a PhD. I definitely enjoyed other subjects (nuclear/astrophysics) quite a bit more than the physics tested on the MCAT, unfortunately.

I can accept that, and I also sympathize, I would love to take Modern Physics, but with no relevance to my studies and no room in my schedule it won't happen.

Baloon tension is like rope tension, surface tension is different though.i think you miss the concept. Great review for me though.

lol thanks 🙄 I blame TBR's balloon example for my confusion.