Capillary Action: Explanation, Derivation, Examples

Capillary action is the movement of liquid in the upward direction with the solid surface. This is caused by the attraction between the molecules of liquid and solid. Molecular attractions arise due to forces, like adhesive, cohesive, and surface tension.

During the process, liquid moves through a narrow glass tube called a capillary. The height (h) of the liquid depends on the diameter (radius r) of the tube. Increasing the diameter of the tube decreases the height of the liquid and vice versa.

To calculate the height of liquid in a capillary tube, this formula is used,

h = 2σcosθ / ρgr

  • h = height
  • σ = surface tension
  • θ = angle of contact (contact angle)
  • ρ = density
  • g = gravity
  • r = radius of tube

capillay action

In the above illustration, water moves upward direction by capillary action. The height of the water is inversely proportional to the radius of the capillary tube. The narrow capillary tube has water at a higher level while the broader capillary tube has water at a lower level.

Angle of contact (contact angle)

The rising of liquid (height h) in a glass tube by capillary action also depends on the angle of contact (θ). The angle of contact (θ) is an angle between the tangents on liquid and solid surfaces. Tangent to the liquid surface is drawn away from the solid. However, the tangent to the solid surface is drawn toward the liquid. This results in the formation of an angle at a point, where tangents are in contact called the angle of contact (θ).

capillay action: contact angle

The contact angle (θ) is directly proportional to the height (h) of the liquid.

h = 2σcosθ / ρgr

  • If the contact angle (θ) is smaller than 90o, the value of Cosθ will be positive in the quadrant. This increases the height (h) of the liquid because its value is also positive.

Contact angle < 90o = +cosθ = +h

  • If the angle of contact (θ) is larger than 90o, this results in a negative value of Cosθ which decreases the height (h).

Contant angle > 90o = -cosθ = -h

Liquids that have a contact angle (θ) of less than 90 degrees are called rising liquids. They can rise in the capillary tube by capillary action. For example, methyl iodide has an angle of contact of 29o. Impure water is also an example of a rising liquid.

θ < 90o = Rising liquids

Those liquids that have an angle of contact (θ) of more than 90 degrees are called depressing liquids. They cannot rise in the tube instead they are depressed. For example, mercury does not rise in the glass tube because its angle of contact is 137o.

θ > 90o = Depressing liquids

 

capillay action

Shapes of meniscus

Depending on the angle of contact (θ) and forces (cohesion, adhesion, surface tension), the meniscus has three types of shapes.

Concave meniscus

When the contact angle of liquid is less than 90o, this creates a concave meniscus. This type of meniscus is like a cave or has depression from the top side. Meniscus side edges are in upward directions.

Concave meniscus = θ < 90o

The cohesive forces are stronger at the center of the meniscus while adhesive forces are stronger at the side edges of the meniscus.

cancave meniscus

Plain meniscus

Different liquids show different types of the meniscus which depend on the contact angle. Those liquids that have a contact angle of 90o have a plain meniscus. The top side of the meniscus is horizontal, that’s why it is called plain meniscus.

Plain meniscus = θ < 90o

plain meniscus

Convex meniscus

This type of meniscus appears, when the contact angle of liquid is greater than 90o. It is like a bubble from the top side. Meniscus side edges are moved downward.

Convex meniscus = θ > 90o

In this case, adhesive and cohesive forces are weak.

convex meniscus

Forces involved in capillary action

When a liquid moves along the solid surface during capillary action. There are some interactions between the molecules of liquid and solid. When liquid molecules come to close solid molecules attract or repel each other.

These are the forces involved in capillary action:

Adhesive forces

Adhesive forces occur between the molecules of different substances. For example, one type of molecule from liquid and other types of molecules from solid. These forces are responsible for the adhesion of liquid molecules on the solid surface.

At the sides edges of the meniscus, these forces are stronger than cohesive forces. This results in the stacking of liquid molecules on each other along the solid surface at the edges of the meniscus.

Cohesive forces

Such kinds of forces exist between the same type of molecules. When liquid moves upward, these forces help in the journey of the molecules because molecules are attracted to each other.

Surface tension

Due to cohesive forces, molecules of liquid come close to each other. This creates a sheet of molecules above the surface of the liquid. This phenomenon is known as surface tension.

Derivation of formula

The formula which is used to calculate the height of any liquid in the capillary tube is given by,

h = 2σcosθ / ρgr

  • h = height of the liquid
  • σ = surface tension of the liquid
  • θ = angle of contact (contact angle)
  • ρ = density of liquid
  • g = gravity
  • r = radius of the capillary tube

Liquids have concave meniscus rise in the capillary tube. On the other hand, liquids have convex meniscus depressed during capillary action. Let a meniscus with the top side be concave and the lower side is convex.

capillay action:derivation of formula

 

Suppose, Po is the atmospheric pressure on the concave side and the pressure on the convex side of the meniscus is less than the atmospheric pressure which is given by 2σ/R (R is the radius of the meniscus).

Pressure on the concave side = Po

Pressure on the convex side = Po – 2σ/R

On the x-point, the pressure is given by,

Px = Po – 2σ/R + ρgh …… eq.1

On y-point and z-point, the atmospheric pressure is applied.

Py = Po

Pz = Po

As we know that when liquid is static then the pressure applied on the horizontal surface is the same, so the pressure on the x-point is Po.

Px = Po …… eq.2

By comparing both equations 1 and 2, we get

Po = Po – 2σ/R + ρgh

Atmospheric pressure (Po) cancel each other, and we get

2σ/R = ρgh

Or

h = 2σ/ρgR …… eq.3

In the above formula, R is the radius of the meniscus. Let’s make a circle (a drop of liquid) on the meniscus. The meniscus radius is represented by (R), while the radius of the capillary tube is (r). The angle formed between this radius is cosθ.

capillay action: why liquid rise

so,

cosθ = r/R

Or

R = cosθ/r

Put the value of R in equation 3, so we get

h = 2σcosθ/ρgr

The above equation is the final formula for calculating the height of liquid in a capillary tube.

Why does liquid rise in the capillary tube?

The liquid rise in the capillary tube by capillary action. Atmospheric pressure is applied to the surface of the liquid around the capillary tube. The pressure in the capillary tube is less than the pressure that is applied to the surrounding areas.

Due to greater pressure, the liquid moves from the surroundings and enters the capillary tube. When the pressure inside and outside of the capillary tube is equal, liquid stops at a specific height. In this way, liquid moves from a higher concentration to a lower concentration.

Capillary action in plants and animals

Plants lose water from leaves by evaporation. This creates small empty spaces in the leaves. To fills these spaces, plants need water which is obtained by capillary action. As we know, capillary action occurs through the capillary tube. Plants use xylem vessels as a capillary tube. Water moves from the soil to the roots and then leaves by using these xylem vessels.

Small animals, such as Ligia exotica and Moloch horridus use water by capillary action. They have open capillaries in the body. By using these capillaries, they transport water in their body by capillary action.

Examples and Applications of capillary action

  • Paper towels use capillary action to absorb water. There are smaller empty spaces in the towel which act as a capillary tube.
  • Textile fabric absorbs sweat (wick) from the skin which gives a cooling effect. These fabrics are called wicking fabrics that use capillary action.
  • Thin layer chromatography uses capillary action to absorb solvent from the medium.
  • During writing, mostly fountain pens are used. These pens draw ink to the nibs from the reservoir of ink inside the pen.
  • Capillary action is used to study hydrology. Dry places obtain water from wet places by capillary action.
  • A capillary action siphon is used to obtain water in dry places. One end of cotton material is dipped in water higher concentration and the second end is dipped in the water lower concentration. Water slowly moves from higher concentration to lower concentration with the help of this fibrous material.
  • Plant uses capillary action to obtain water from the soil.

Concepts Berg

What Is the definition and examples of capillary action?

The movement of water in the upward direction along the solid surface by intermolecular interaction between the molecules of water and solid. For example, the movement of water from the soil to the leaves of the plants.

how to prevent capillary action?

Capillary action occurs due to higher pressure or empty spaces in the object. If these spaces are removed or lower the pressure, this results in stopping the capillary action.

How is capillary action possible?

Capillary action is possible because of intermolecular forces like adhesion and cohesion between the molecules of water and solid. Secondly, surrounding higher pressure help to move water into a capillary tube.

What is the capillary action of water?

Water always moves from higher concentration to lower concentration. By using capillary action, water can move in any direction.

What is the formula of capillary action?

The height of liquid in the capillary tube can be determined by using the formula which is,

h = 2σcosθ / ρgr

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