Calculating Surface Tension Force in a Hemispherical Water Bulge

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Discussion Overview

The discussion revolves around calculating the surface tension force in a hemispherical water bulge formed at the top of a glass tube filled with water. Participants explore the implications of surface tension, pressure differences, and the stability of the bulge, while considering the geometry of the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about calculating the surface tension force given limited information, suggesting the use of Bernoulli’s equation.
  • Another participant explains that surface tension can be conceptualized as a stretched membrane at the liquid-gas interface, prompting questions about the downward surface tension force around the tube's circumference.
  • A participant notes that the question is ill-posed due to the pinned contact line at the tube edge, indicating that a range of curvatures and contact angles complicates the application of Young's equation.
  • Concerns are raised about the stability of a hemispherical bulge with a specified diameter, with one participant questioning the feasibility of such a configuration in a tube of the given diameter.
  • Another participant shares experimental observations using different tube sizes, noting that a hemispherical bulge forms but collapses under certain conditions, suggesting that material properties and curvature influence stability.
  • A mathematical expression related to the balance of forces involving surface tension and pressure difference is presented, although its context and implications remain open for discussion.

Areas of Agreement / Disagreement

Participants express differing views on the stability of the hemispherical bulge and the implications of the tube diameter. There is no consensus on the correct approach to calculating the surface tension force or the stability of the bulge.

Contextual Notes

Participants highlight the complexity of the problem due to varying curvatures, contact angles, and the physical properties of materials involved, which may affect the interpretation of the bulge's stability and the calculations required.

Just_enough
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I have a 8mm diameter glass tube willed with water that have a bulge outward above the top.
49ab5f8e805c29ae568a2fd192a755d9.gif
I know that the preasure inside the bulge is higher than the outside (not positive as to why, probably due to it being in a liquid compare to the atmophere)
the question is:
1. how do I calculate the force due surface tension when this is all the info I was given?

I feel like I have to use BERNOULLI’S equation, but I think I am missing too much info to do this.
 
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Are you familiar with the concept of surface tension?
 
Chestermiller said:
Are you familiar with the concept of surface tension?
yes
 
Surface tension works the same as if there is a stretched membrane at the interface between the liquid and the gas. The tension in the membrane per unit length within the surface is equal to the surface tension. What is the downward surface tension force around the circumference of the tube exit.
 
Chestermiller said:
Surface tension works the same as if there is a stretched membrane at the interface between the liquid and the gas. The tension in the membrane per unit length within the surface is equal to the surface tension. What is the downward surface tension force around the circumference of the tube exit.
I tried to go back and read on "fluids" chapter in my boo (Principle of physics by eric mazur) to try to understand what you mean, but I don't get it
 
Just_enough said:
I have a 8mm diameter glass tube willed with water that have a bulge outward above the top.
I know that the preasure inside the bulge is higher than the outside (not positive as to why, probably due to it being in a liquid compare to the atmophere)
the question is:
1. how do I calculate the force due surface tension when this is all the info I was given?

This question is ill-posed, since the contact line is pinned at the tube edge. The pressure jump across the water-air interface is proportional to the curvature of the interface, and a range of curvatures are possible. Similarly, using Young's equation is complicated as a range of contact angles are possible.
 
Hi Andy,
The problem title calls the surface hemispherical, so the contact angle is specified. I have trouble with the specification that the tube diameter is 0.8 cm and the surface could be hemispherical. I don't think this could be stable. I could better believe a 0.8 mm tube diameter.

Chet
 
Chestermiller said:
Hi Andy,
The problem title calls the surface hemispherical, so the contact angle is specified. I have trouble with the specification that the tube diameter is 0.8 cm and the surface could be hemispherical. I don't think this could be stable. I could better believe a 0.8 mm tube diameter.

Chet
In what way would it not be stable. Do you have some mathematical reason? Genuinely interested in your statement
 
lychette said:
In what way would it not be stable. Do you have some mathematical reason? Genuinely interested in your statement
It must seems to me that a hemispherical bulge 1 cm in diameter would not stay stable under the action of surface tension.
 
  • #10
Chestermiller said:
It must seems to me that a hemispherical bulge 1 cm in diameter would not stay stable under the action of surface tension.
I tried it out with a plastic straw - 07mm OD, maybe .065 cm ID, so a very thin wall.
What looks like a hemisphere of water does form above by squeezing the straw.
Any more squeezing and there is a collapse.

Also tried a coke bottle - approx. 2 cm ID. The wall is 1.5 mm, somewhat flat.
The water rises up to what looks to be about 2 to 3 mm, and then collapses.

Now that is with plastic tubing.
Glass and water would ( should ) behave differentially.
And curvature of the rim would have an effect also.

Maximum radius for a hemispherical bubble?
Seems to be just what you had stated.
 
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  • #11
Chestermiller said:
Hi Andy,
The problem title calls the surface hemispherical, so the contact angle is specified. I have trouble with the specification that the tube diameter is 0.8 cm and the surface could be hemispherical. I don't think this could be stable. I could better believe a 0.8 mm tube diameter.

Chet
Yes, that's the title of this thread. But it's not in the stated problem ("a bulge outward").
 
  • #13
I get $$2\pi r \sigma=\pi r^2 \Delta p$$
 

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