- #1
Shreya
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- Homework Statement
- Why does surface tension seems to have direction in these images? Isn't it a scalar?
- Relevant Equations
- S=Fl/Av
What is the Young-Laplace equation and its relationship to surface tension?
- Thread starter Shreya
- Start date
In summary, the Young-Laplace equation is a mathematical equation that explains the relationship between surface tension, pressure, and curvature on a liquid's surface. It states that the pressure difference between two points on a curved liquid surface is directly proportional to the surface tension and the curvature at that point. This equation is important in understanding the behavior of liquids, especially in capillary action and the formation of liquid droplets. It is also used in various applications such as in the study of bubbles, foams, and emulsions.
- #2
ergospherical
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It is correct that surface tension is a scalar ##\gamma(\mathbf{r})##. If you have a surface ##\mathcal{S}## containing a bounding contour ##\mathcal{C}## between two different phases, the surface tension force exerted by one phase on the other is ##\displaystyle{\int}_{\mathcal{C}} \gamma(\mathbf{r}) \mathbf{n} ds## where ##\mathbf{n}## is a unit vector tangent to ##\mathcal{S}## but orthogonal to ##\mathcal{C}##.
In your diagram (Young's law), a force balance is being done on a tiny mass element at the lower left corner. Keep in mind that there are three different interfaces.
In your diagram (Young's law), a force balance is being done on a tiny mass element at the lower left corner. Keep in mind that there are three different interfaces.
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- #3
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The images are not illustrating surface tension; they are illustrating forces arising from surface tension.
In the same way, tension in a string is an intensive state of the string, not a force. It results in forces at the ends.
In the same way, tension in a string is an intensive state of the string, not a force. It results in forces at the ends.
- #4
Shreya
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ergospherical said:
Thank you erogospherical and haruspex! It makes sense now!haruspex said:
- #5
Shreya
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Can you explain what you mean by a contour?ergospherical said:
And what is Young's law ? (I haven't studied it yet)
- #6
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Like pressure and rope tension, surface tension is a 2nd order tensor quantity, with bi-directional character. The scalar we call surface tension is just the magnitude of this tensor. Physically, surface tension acts within a free surface, and acts perpendicular to each arbitrary curve or line within the surface.
- #7
Shreya
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Thank you Chester, I get it now !Chestermiller said:
- #8
ergospherical
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- the word contour, in that context, is just a fancy word for a curve :)Shreya said:
- Young's law gives the relationship between the three surface tensions; can you deduce it?
- #9
Shreya
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S(la)cos (theta) + S(sa) = S(sl), right?ergospherical said:
I actually have studied it, but the name of law was not specified
- #10
Shreya
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Tangent to surface would mean 2 directions. So why do we consider a particular direction here. i e how do i know which one of the two to choose?
- #11
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Posts #2 and #6 both mention that the force is in relation to a given line element within the surface, and acts orthogonally to it within the surface.Shreya said:
- #12
Shreya
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Thank you all 
for helping me understand.
for helping me understand.- #13
hutchphd
Science Advisor
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And it helps me to remember the units [force/length] in this context. The force "supplied" by the tension across that line element is proportional to the tension "times" the length of the small element.haruspex said:
And the other very useful relationship in this context is the Young -Laplace equation for curved surfaces:https://en.wikipedia.org/wiki/Laplace_pressure
- #14
Shreya
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Thank you, hutchphd! I had actually learned this, but the textbook didn't mention the name.hutchphd said:
FAQ: What is the Young-Laplace equation and its relationship to surface tension?
What is surface tension?
Surface tension is the force that causes the surface of a liquid to behave like a stretched elastic membrane. It is caused by the cohesive forces between molecules in the liquid, which create a strong attraction at the surface.
How is surface tension measured?
Surface tension is typically measured in units of force per unit length, such as newtons per meter (N/m) or dynes per centimeter (dynes/cm). It can be measured using a variety of techniques, such as the drop weight method or the capillary rise method.
What factors affect the direction of surface tension?
The direction of surface tension is affected by several factors, including the type of liquid, temperature, and presence of impurities. For example, polar liquids tend to have a higher surface tension than non-polar liquids, and surface tension decreases as temperature increases.
How does surface tension impact the behavior of liquids?
Surface tension plays a crucial role in many natural phenomena, such as the formation of droplets, capillary action, and the behavior of bubbles. It also affects the ability of insects to walk on water and allows some plants to float on the surface of water.
Can surface tension be manipulated for practical purposes?
Yes, surface tension can be manipulated for various practical purposes. For example, surfactants can be added to lower the surface tension of a liquid, making it easier to spread or mix with other substances. Surface tension can also be used to create thin films or coatings, and to control the shape and movement of liquids in microfluidic devices.