Capillary Action

Capillary Action in Physics is the action of the liquid in the capillary tubes. Capillary tubes, which are narrow cylindrical tubes, have very small diameters. It is observed that the liquid in the capillary either rises (or) decreases in relation to the level of the surrounding liquid when these tiny tubes are submerged in a liquid. The action of these liquids is called the capillary action and it is an important phenomenon in physics.

Capillary action is caused by the intermolecular attraction of the water molecules and the adhesive force between the capillary walls and the liquid. In this article, we will learn about Capillary Action, the Capillary Action Formula, Its derivation, examples, and others in detail.

What Is Capillary Action?

The ascent or rise of liquids through a tube or cylinder with a small diameter is caused by the phenomenon called the Capillary Action. Adhesive and cohesive forces are responsible for capillary action. The liquid will ascend higher if the tube is narrower. If the surface tension, ratio between the cohesion to adhesion force increases the capillary action of the liquid also increases.

The amount of the liquid that surrounds the capillary tube is also responsible for how much the water will rise in the capillary. Groundwater moves through the various zones of soils as a result of capillary action. Capillary action also plays a role in the movement of fluids within a plant’s xylem vessels. Water from the roots and lower levels of the plant is drawn up as the water on the surface of the leaves evaporates.

Fundamentally, liquids have the ability to be pulled into tiny opening, as those between sand grain, and the rise of liquid in the thin tubes. Capillarity or capillary action occurs as a result of the intermolecular force of attraction that exists between solids and liquids.

Capillary Action Definition

Capillary Action also called the capillary motion is the rise of the liquid in the narrow spaces or thin tubes without external forces pulling that liquid. This liquid moves the narrow tubes because of the intermolecular forces, i.e. Cohesion and Adhesion forces.

Capillary Action Formula

If a liquid rises to a height “h” in the capillary tube of radius ‘r’ and surface tension on the surface of the liquid is ‘T’ then its rise in height is given by the formula,

h = (2T cosθ)/rρg

where,

• θ is the Angle of Contact of Liquid
• ρ is the Density of Liquid
• g is the Acceleration due to Gravity

Derivation of Capillary Action Formula

Expression for capillary rise or fall of the liquid in the capillary tube is derived by using pressure difference as,

Pressure resulting from the h height liquid column must be equal to the 2T/R concavity-related pressure difference.

hρg = 2T/R…(i)

where,

• ρ is the Density of Liquid
• g is Acceleration due to Gravity

Let r be the radius of the capillary tube and θ be the angle of contact of the liquid. Consequently, the meniscus’s radius of curvature R is determined by

R = r/cos θ

from (i)

2T/hρg = r/cos θ

h = 2Tcos θ/rρg …(ii)

This is the equation that give the height of liquid in the capillary tube. The angle of contact θ is acute if the capillary tube is maintained vertically in a liquid with a convex meniscus. Cos θ is therefore positive, and so is h.

How Capillary Action Occur?

Intermolecular forces such as Cohesive Force and Adhesive Force and Surface tension is the main cause of the capillary action. These forces cause the liquid to be drawn into the tube. The diameter of the tube must be small to cause the liquid to perform the capillary action.

Capillarity Action Important Point

Various properties or characters on which the capillary action in a tube depends are,

• Nature of Liquids and Solids
• Angle of Contact
• Independent of Shape of Capillary, etc

Let’s learn about them in detail.

Nature of Liquids and Solids: The nature of liquid and solid is responsible for the capillary action in a capillary tube.

Angle of Contact

It also depends on the angle of contact.

If θ > 90°

If the meniscus in convex, then h will be negative, i.e. liquid will fall in the capillary. This happens in the case of mercury in a glass tube.

If θ = 90°

If the meniscus is plane, then h is zero and there is no capillary action observed.

If θ < 90°

If the meniscus in concave, then h will be positive, i.e. liquid will rise in the capillary. This happens in the case of water in a glass tube.

The image showing the capillary action is added below,

Independent of Shape of Capillary: The rise in capillary is independent of the shape of the capillary.

Forces in Capillary Action

There are generally two type of Forces that are responsible for surface tension that are,

• Cohesive Force
• Adhesive Force

Cohesive Force

Cohesion is the term used to describe the interaction of molecules in a certain medium. The same force holds together raindrops before they descend to the ground. Most people are aware of the phenomenon of surface tension, but few are aware that it also results from the idea of cohesiveness. Objects that are denser than the liquids can float on top of them without any assistance and cannot sink due to surface tension.

Adhesive Force

Adhesion is a different idea that may be comprehended with the help of this phenomenon. A solid container and a liquid are two examples of two distinct things that are attracted to one another by adhesion. This similar force also causes water to adhere to glass surfaces.
If the phenomena of adhesion outweigh that of cohesion, liquids soak the surface of the solid they come into touch with and may also be seen curling upwards toward the rim of the container. Mercury-containing liquids, which can be referred to as non-wetting liquids, have a higher cohesion force than adhesion force. These liquids have an inward curvature when they are close to the container rim.

Liquid Meniscus in Capillarity

A liquid in capillary tube shows three different types of Meniscus that are,

• Concave Meniscus
• Convex Meniscus
• Plane Meniscus

Concave Meniscus

If the pressure below the meniscus is less than the pressure above the meniscus then we say the concave meniscus occurs. The concave meniscus is observed in water and glass. Suppose the pressure above meniscus is P_A and the pressure below the meniscus is P_B then the excess pressure is,

P_A – P_B = 2T/r

where, r is the radius of the meniscus.

Convex Meniscus

If the pressure below the meniscus is greater than the pressure above the meniscus then we say the convex meniscus occurs. The convex meniscus is observed in mercury and glass. Suppose the pressure above meniscus is P_A and the pressure below the meniscus is P_B then the excess pressure is,

P_B – P_A = 2T/r

where, r is the radius of the meniscus.

Plane Meniscus

The plane meniscus is observed when the difference between the above and the below meniscus is zero, i.e. pressure above meniscus and pressure below meniscus is equal and excess pressure is zero. And thus no capillary action is observed.

The concave, convex, and plane meniscus is shown in the image added below,

Difference between Concave, Convex and Plane Meniscus

The differences between concave, conves and plane meniscus is added in the table below,

Concave Meniscus	Convex Meniscus	Plane Meniscus
In concave meniscus the pressure below the meniscus (P0 – 2T/r) is less than pressure above the meniscus (Po)	In conves meniscus the pressure below the meniscus (P0 + 2T/r) is greater than pressure above the meniscus (Po)	In plane meniscus the pressure below the meniscus is equal to pressure above the meniscus.
Excess Pressure is given as, P = Pabove – Pbelow P = 2T/r	Excess Pressure is given as, P = Pbelow – Pabove P = 2T/r	Excess Pressure is given as, P = 0
Liquid will wet the solid of contact	Liquid will not wet the solid of contact	Critical case
Angle of contact is acute angle, i.e. (θ < 90°)	Angle of contact is obtuse angle, i.e. (θ > 90°)	Angle of contact is right angle, i.e. (θ = 90°)
Liquid level in the capillary ascends	Liquid level in the capillary descends	No capillarity

Relation between Excess Pressure and Surface Tension

Let’s take a liquid drop of radius (r) having internal pressure P_I and external pressure P_o, then the relation between surface tension and excess pressure for a liquid drop is given as,

Excess Pressure(P) = P_I – P_O

To change the radius of the drop of liquid from r to r + dr, external work(W) is required.

W = F.dr

F = P.A

W = P.A.dr…(i)

A = 4πr²

W = P.(4πr²).dr…(ii)

If the radius of droprs changes from r to r + dr then its area is changed as,

dA = 4π(r + dr)² – 4πr²

dA = 8πrdr…(iii)

Now, we know that workdone (W) is also given as,

W = T.dA…(iv)

where T is surface tension

T = W/dA…(v)

From eq (ii), (iii), and (iv)

T = {P.(4πr²).dr}/{8πrdr}

P = P_i – P_o = 2T/r

This is the relation between Excess Pressure(P) and Surface Tension(T)

Applications of Capillarity

Various applications of the capillarity are given below,

• The capillary action of the threads in the wick of a lamp causes the oil to rise.
• A towel’s ability to absorb moisture from the body is a result of the cotton’s capillary action.
• Because of capillarity, water is kept in a sponge piece.
• Plants use capillary action to extract water from the soil through their root hairs.

Capillary Action Example

The example of capillary is explained using the concept added below,

Capillary Action in Plants

Capillary action is used in plants to climb the water up the roots and stems from the soil in plants. Water molecules are attracted to the molecules inside the stems this cause the water molecule to rise in the stem.

Capillary Action in Soil

Roots of Plants absorb water form the soil and the water moves in the soil because of the capillary action. Water molecules moves in the soil and they carry essential nutrients from soil to water.

Capillary Action in Everyday Life

Capillary Action is also seen in our everyday life that are seen in the scenario added below,

• Water will spontaneously climb up a paper towel when dropped into it, seemingly defying gravity. It makes sense that the water molecules would climb up the towel and tug on other water molecules since you can actually witness capillary action.
• The roots of the plant absorb nutrients that are dissolved in the water, which then begin to grow the plant’s top. Water is delivered to the roots by capillary action.

Read More,

• Tension Force
• Gravitational Force
• Buoyant Force

Examples on Capillary Action

Example 1: A 5 × 10^-4 m radius capillary tube is submerged in a mercury-filled beaker. It is discovered that the mercury level inside the tube is 8 × 10^-3 m below reservoir level. Identify the angle at which mercury and glass are in contact. Mercury has a surface tension of 0.465 N/m and a density of 13.6 × 10³ kg/m³. 

Solution:

Given:

• r = 5 × 10^-4 m
• h = -8 × 10^-3 m
• T = 0.465 N/m
• g = 9.8 m/s²
• ρ = 13.6 × 10³ kg/m³

We have,

T = rhρg/2 cos θ

0.465 = (5 × 10^-4 × -8 × 10^-3 × 13.6 × 10³ × 9.8)/(2 cos θ)

cos θ = -40×9.8×13.6×10^-4 / 2×0.465

-cos θ = 0.5732

θ = 124^o58′

Example 2: If water rises to a height of 12.5 cm inside a capillary tube, and assuming that the angle of contact between the water and the glass is 0°, determine the radius of the tube.

Solution:

Given,

• h = 0.125 m
• T = 72.7 × 10^-3 N/m
• θ = 0^°, g = 9.8 m/s²
• ρ = 1000 kg/m³

We have,

r = (2Tcos θ)/hρg

r = (2 × 72.7 × 10^-3 × cos 0) / (0.125 × 1000 × 9.8)

r = 0. 12 mm

Example 3: Calculate the Height of the capillary tube if the Surface Tension is 32 × 10^-3 N/m, the Radius of the capillary tube is 30 m, Density of liquid is 790 kg/m³ at 0^° angle of contact.

Solution:

Given,

• r = 30 m
• T = 32 × 10^-3 N/m
• θ = 0^°
• g = 9.8 m/s²
• ρ = 790 kg/m³

We have,

h = (2Tcos θ)/rρg

h = (2 × 32 × 10^-3 × cos 0°) / ( 30 × 790 × 9.8)

h = (64 × 10^-3) / (232260)

h = 0.00027 × 10^-3 m

Example 4: Calculate the capillary tube’s density if the liquid is at a 45° angle of contact, the surface tension is 2 × 10³ N/m, the height is 25 m and the capillary tube’s radius is 21 m.

Solution:

Given,

• r = 21 m
• T = 2 × 10³ N/m
• θ = 45°
• h = 25 m
• g = 9.8 m/s²

We have,

h = (2Tcos θ)/rρg

ρ = (2Tcos θ)/rhg

ρ = (2 × 2 × 10³ × cos 45°)/(21 × 25 × 9.8)

ρ = 2.8284 × 10³ / 5145

ρ = 0.0005 × 10³

Capillary Action – FAQs

1. Explain Meaning of Capillary Action with Example

Capillary action is the phenomenon that is responsible for the rise and fall of the liquid in the capillary tube. For example the rise in the level of soda when a straw is placed in the soda is an example of capillary action.

2. What Causes of Capillary Action?

Capillary action is caused by the forces of adhesion, cohesion, and surface tension.

3. What are Examples of Capillary Action?

Examples of Capillary action are,

• Tears flowing through tear ducts
• Water rising in a straw or glass tube defying gravity
• Water passing through a cloth towel, etc.

4. What is the Simple Capillary Action?

The rise in the water in the plants is an example of capillary action. The water reaches the height of 100 m in the plant because of the capillary action.

5. What is Capillarity Formula?

The capillary formula that gives the rise and fall in the capillary tube is given as,

h = (2T cosθ)/rρg

6. What is Capillarity?

Capillarity is the ability of the narrow tube that draes liquid upwards against the force of gravity. The capillarity occurs because of the capillary action.

7. What is the Law of Capillarity?

Law of capillarity states that,

“The maximum height of the liquid in a capillary tube is inversely proportional to the diameter of the tube.”

8. What is another name of Capillarity?

The other name of capillarity is capillary action, and capillary attraction.