Capillary Action Homework: ΔP, γ, R1, R2

In summary, the conversation discusses the topic of fluid mechanics, specifically capillary pressure and surface tension. The question at hand involves the formation of a meniscus in a liquid between two plates, with different behaviors observed for water and mercury due to their varying cohesive forces and adhesion to the plate walls. The young-laplace equation is mentioned, but there is uncertainty about how to proceed with calculating the pressures above and below the meniscus.
  • #1
MFAHH
32
1

Homework Statement



Kindly view the attached.

Homework Equations



ΔP = γ(1/R1 + 1/R2)

The Attempt at a Solution


[/B]
I've began the topic of fluid mechanics, capillary pressure, surface tension and such and was given this question to try. Now from my limited knowledge it seems to me that in the case of the liquid being water, a concave meniscus will be formed due to the water's adhesion to the inner plate walls (due to the water's polarity) and this will result in upwards capillary action. As for the case in which the liquid is mercury, the greater cohesive force between the mercury and the walls will cause the height of the mercury between the plates to drop lower than the surface of the mercury outside, and the mercury will form a convex meniscus. Is this correct?

For the second part of the question, the young-laplace equation as given is in terms of two radii of curvature, but since we are dealing with plates, would I be right in thinking that it only has a single radius of curvature (the distance between the plates) and the other would be undefined (due to their being no definite end to plates in the direction parallel to them)? How this comes into play, and how to calculate the pressure above and below the meniscus, I'm not too sure on though. Can anyone please give some help?

Much appreciated.
 

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  • #2
Anyone?
 
  • #3
MFAHH said:

The Attempt at a Solution


[/B]
As for the case in which the liquid is mercury, the greater cohesive force between the mercury and the walls will cause the height of the mercury between the plates to drop lower than the surface of the mercury outside, and the mercury will form a convex meniscus. Is this correct?

http://en.wikipedia.org/wiki/Meniscus
 
  • #4
SteamKing said:
http://en.wikipedia.org/wiki/Meniscus

Awesome, so from what I read there I'm more or less on the right track. As for the next part of the question, how is it that I am meant to proceed? Is it just that I rearrange the young Laplace equation for the pressures above and below? But then that answer won't be in terms of what I know from the question.
 
  • #5
:oldconfused:
 
  • #6
Anybody? :)
 

1. What is capillary action and why is it important?

Capillary action is the ability of a liquid to flow against gravity in a narrow space, such as a tube or narrow space between two surfaces. It is important because it plays a crucial role in many natural and industrial processes, such as plant water uptake, blood circulation in our bodies, and ink spreading on paper.

2. How is capillary action related to the variables ΔP, γ, R1, and R2?

ΔP represents the pressure difference across the liquid interface, γ is the surface tension of the liquid, and R1 and R2 are the radii of the two surfaces in contact. These variables are related through the Young-Laplace equation, which describes the balance between the pressure difference and surface tension in determining the capillary rise or fall of a liquid.

3. How does the shape of the capillary tube affect capillary action?

The shape of the capillary tube, specifically the radius, plays a crucial role in capillary action. A smaller radius results in a higher capillary rise, as the surface tension forces are stronger in a smaller area. Additionally, the shape of the tube can also affect the contact angle of the liquid, which can impact the capillary action as well.

4. What factors can affect the surface tension of a liquid?

The surface tension of a liquid can be affected by temperature, pressure, and the presence of impurities or surfactants. Higher temperatures tend to decrease surface tension, while higher pressures can increase it. Impurities or surfactants can also disrupt the cohesive forces between liquid molecules, resulting in a decrease in surface tension.

5. Can capillary action occur in non-liquid materials?

Yes, capillary action can occur in non-liquid materials such as porous solids or powders. This is known as capillary rise in porous media and is governed by similar principles as capillary action in liquids. However, the equations and variables used to describe capillary action in liquids may be different for capillary rise in porous media.

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