# Capillary Action and Young-Laplace

• EtherealPanMan
In summary, the slide does not clearly explain why capillary action occurs. It appears that capillary action occurs because of the pressure difference between the air and the liquid.
EtherealPanMan
Hello all. This is my first post and I wasn't exactly sure where to put it, so I apologize if it could be in a better place.

Ok... here is my issue. I am currently enrolled in a Surfaces/Interfaces course. Capillary action eludes me. I do not understand WHY capillary action occurs in relation to interface pressure differences. I have attached the slide in question.

My biggest confusion is the line "because of the pressure difference...". What about the pressure difference causes the liquid to rise up the tube? It seems counter intuitive. If the surface is curved as shown, this implies that the pressure of the air is greater than the pressure of the liquid (ΔP wrt to liquid is negative). It seems like the greater pressure would push DOWN on the water and cause it to go down the tube...

Any explanation of this would be VERY helpful! Cheers!

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If the surface is curved as shown, this implies that the pressure of the air is greater than the pressure of the liquid (ΔP wrt to liquid is negative). It seems like the greater pressure would push DOWN on the water and cause it to go down the tube...
Your idea is understandable, but this is not how surface tension works. Unfortunately the slide does not give very accurate explanation either. Here is one way to understand it:

When the pipe is immersed in water, water comes into contact with glass. In the end, the water will assume such position that the whole system is in equilibrium (does not move).

Now, water "loves" glass if the latter is clean enough (no fat on it). Some water near the wall gets higher to touch the glass and thus increase the total area of contact with it. That is why the boundary water-air is not plane but forms a meniscus. Initially, this meniscus has unknown shape (it is improbable that it is spherical).

But when the meniscus is formed, instantly the pressure in the water just beneath the surface tends to decrease. This is because the force of the atmospheric pressure pushing surface down from above is partly balanced by the capillary forces due to glass, acting on the water on the circumference of the water surface, pulling water up.

As a result, the water in the pipe experiences two pressures from above and from below, and that from below is slightly higher. For this reason, water starts rising up.

Roughly speaking, the water rises as long as the pulling force of the glass is stronger than the force of gravity pulling the water down. The equilibrium height of the water surface is such that the two forces are equal. If ##r## is radius of the sphere which meniscus is a part of, we have equation of equilibrium

magnitude of decrease of pressure force from above = weight of the column of water above the normal water level

$$\frac{2\sigma}{r} \pi a^2 = \rho g h \pi a^2$$

Using ##r = a/ \cos \theta##, you can find the equilibrium height ##h## for given pipe.

This analysis is correct for water; it rises and has convex surface (U).

If the liquid is mercury, the surface tension force will push the mercury down at the contact rim, so the surface will set down and have concave surface ( U upside down).

EtherealPanMan said:
<snip>

My biggest confusion is the line "because of the pressure difference...". <snip>

The Laplace equation (ΔP = 2σκ) relates the interface curvature κ to a pressure jump across the interface, and is derived from conservation of energy. Young's equation represents mechanical equilibrium at a three-phase contact line (where the solid and both fluid phases meet). The slide appears to connect the two in an unclear manner.

Capillary rise (or the converse, depending on the contact angle), meaning the height of a fluid column, is also a force balance- a balance of the weight of fluid and 'surface tension force' from Young's equation.

Does this help?

## 1. What is capillary action?

Capillary action is the movement of a liquid along a narrow space, such as a tube or between two closely spaced surfaces, due to the adhesive and cohesive forces between the liquid and the surface. This phenomenon is also known as capillarity.

## 2. How does capillary action work?

Capillary action is the result of two main forces: adhesive forces, which are the attractive forces between the liquid molecules and the surface, and cohesive forces, which are the attractive forces between the liquid molecules themselves. When these forces are strong enough, they can overcome the force of gravity and cause the liquid to move upwards against it.

## 3. What is the Young-Laplace equation?

The Young-Laplace equation is a mathematical equation that describes the relationship between surface tension, pressure, and curvature of a liquid interface. It is commonly used to explain the shape of liquid droplets and the behavior of capillary action.

## 4. How is capillary action important in nature?

Capillary action is important in nature for many reasons. It is the driving force behind water movement in plants, allowing them to absorb water and nutrients from the soil. It also plays a role in the movement of groundwater and the formation of natural structures such as stalactites and stalagmites. Additionally, capillary action helps to maintain the shape and stability of soap bubbles and is crucial for the functioning of some medical devices.

## 5. What factors affect capillary action?

The strength of capillary action is affected by several factors, including the surface tension of the liquid, the size of the tube or space, and the contact angle between the liquid and the surface. Temperature and the type of liquid also play a role in the strength of capillary action. Additionally, the presence of impurities or contaminants on the surface can disrupt capillary action.

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