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Capillary Action – Definition, Formula, Causes, Examples

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  • Last Updated : 05 Aug, 2022
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Capillary tubes, also known as 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. Such tubes are referred to as capillary and this phenomenon as capillary action. Such capillary action in a moist fluid is also brought about by the combined forces of surface tension and cohesion. Capillary action is caused by the intermolecular attraction of the water molecules and the adhesive force between the capillary walls and the liquid. Let’s examine the topic of capillary action in more detail.

Capillary Action

The ascent of liquids through a tube or cylinder is a process known as capillary action. Adhesive and cohesive forces are the main causes of this.

This interplay of the phenomena causes the liquid to be dragged higher. The liquid will ascend higher if the tube is narrower. The rise will also grow if one of the two phenomena – surface tension or the cohesion to adhesion ratio increases. Although the liquid’s rise in the capillary will be lessened if its density rises.

The capillary’s ability to hold water affects how much water is kept there as well as how quickly it will rise. The substance that surrounds the pores both fills and creates a film over the pores. The closest solid objects to the water molecules have the strongest adherence. As more water is introduced into the pore, the capillary force’s strength decreases, increasing the film’s thickness.

The film that was created on the soil molecules’ outer surface may also start to flow. Groundwater moves through the various soil zones 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 crevices, as those between sand grain fragments, and to rise into thin tubes. Capillarity or capillary action occurs as a result of the intermolecular force of attraction that exists between solids and liquids. Similar results occur when a piece of paper is placed on a puddle of water; it absorbs the water. This occurs as a result of water absorption into the paper’s microscopic spaces between fibers.

Capillary Action Formula

Surface tension is another factor that causes a liquid column inside a tiny capillary tube to rise. For capillary rise or fall, use the following formula:

Using Pressure Difference,

h=\frac{2Tcos\theta}{r \rho g}

Where,

  • h = Height of liquid column,
  • T = Surface Tension,
  • r = Radius of capillary tube,
  • θ = Angle of contact of the liquid,
  • ρ = Density of liquid,
  • g = Acceleration due to gravity.

Using Force,

T=\frac{rh \rho g}{2cos\theta}

Where,

  • h = Height of liquid column,
  • θ = Angle of contact of the liquid,
  • T = Surface Tension,
  • r = Radius of capillary tube, 
  • ρ = Density of liquid,
  • g = Acceleration due to gravity.

Derivation of Capillary action formula

Expression for capillary rise or fall

Method 1: Using Pressure difference

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

h \rho g=\frac{2T}{R}       …(Equation 1)

Where, ρ is the density of the liquid and 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=\frac{r}{cos\theta}

h \rho g=\frac{2Tcos\theta}{r}

h=\frac{2Tcos\theta}{r \rho g}       …(Equation 2)

The expression for a liquid’s capillary rise or fall is given by the equation above. The higher the liquid rises, the narrower the tube must be (or falls).

The angle of contact θ is acute if the capillary tube is maintained vertically in a liquid with a convex meniscus. Cosθ is therefore negative, and so is h. This implies that the liquid will experience capillary depression or fall.

Method 2: Using Force

Water rising inside a capillary defies gravity. Thus, at the point of contact, the weight of the liquid column must be equal to and in opposition to the appropriate component of the force caused by surface tension.

The circumference 2πr is the length of liquid in contact inside the capillary. Consequently, surface tension’s force is represented by,

fT = Surface Tension × Length in contact

∴ fT = T × 2πr

Direction of this force is along the tangent. Vertical component of this force is,

∴ (fT)v = T × 2πr × cosθ  …(Equation 1)

The amount of liquid in the capillary rise, disregarding the fluid in the concave meniscus, is V = πr2h.

Mass of the liquid in the capillary rise,

∴ m = πr2hρ  …(Equation 2)

Weight of the liquid in the capillary rise or fall,

∴ w = πr2hρg  …(Equation 3)

The vertical component of the surface tension force must be equal to and opposite to this. Thus, equating right side of equation 1 and equation 3, we get

∴ πr2hρg = T × 2πr × cosθ

h=\frac{2Tcos\theta}{r \rho g}

In terms of capillary rise or fall, the expression for surface tension is,

T=\frac{rh \rho g}{2cos\theta}

How does Capillary action occur?

Together, the cohesive forces of the liquid and the adhesive forces between the liquid and the tube material cause capillary action. Two kinds of intermolecular forces are adhesion and cohesion. These forces cause the liquid to be drawn into the tube. A tube’s diameter must be sufficiently tiny for the capillary to form.

Forces in Capillary Action

Cohesion

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.

Adhesion

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.

Applications of Capillary action

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

Real-life uses of capillary action

  • 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.

Solved Examples based on Capillary action

Problem 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=\frac{rh \rho g}{2cos\theta}

0.465=\frac{-8×10^-3 × 5×10^-4 × 13.6×10^3 × 9.8}{2cos\theta}

∴ cosθ = -40×9.8×13.6×10-4 / 2×0.465

∴ -cosθ = 0.5732

∴ θ = 124o58′

Problem 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,

h=\frac{2Tcos\theta}{r \rho g}

r=\frac{2Tcos\theta}{h \rho g}

∴ r = 2 × 72.7 × 10-3 × cos 0° / 0.125 × 1000 × 9.8

∴ r = 0. 12 mm

Problem 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=\frac{2Tcos\theta}{r \rho g}

h=\frac{2×32×10^-3cos0^o}{30×790×9.8}

∴ h = 64 × 10-3 / 232260

∴ h = 0.00027 × 10-3 m

Problem 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=\frac{2Tcos\theta}{r \rho g}

\rho=\frac{2Tcos\theta}{rhg}

\rho=\frac{2× 2×10^3cos45^o}{21×25 ×9.8}

∴ ρ = 2.8284 × 103 / 5145

∴ ρ = 0.0005 × 103

FAQs on Capillary Action

Question 1: How do plants benefit from capillary action?

Answer:

A helpful characteristic in vascular plants is capillary action. Along with root pressure, capillary action plays a role in the plant’s ability to absorb water from the soil through its root system and transport it to other parts of the plant, such the leaves, for photosynthesis, in the xylem vessels. The ability of the plants to absorb water from the soil may be compromised without capillary action. Due to their tiny diameter, the root system’s fine root hairs serve as capillary tubes.

Question 2: Can capillary action continue in an environment without gravity, like as space?

Answer:

The letter “h” stands for the capillary tube’s column rise, which is inversely proportional to the force of gravity given by the letter “g.” For a finite length of capillary tube, the liquid will rise and entirely fill the tube if “g” becomes 0 (as in space).

Question 3: What are the causes of capillary action?

Answer:

Capillary action is caused by the forces of adhesion, cohesion, and surface tension. Surface integrity is maintained by the friction at the surface. When the cohesive forces are outweighed by the liquid molecules’ adherence, capillary action results.

Question 4: List some examples of capillary action.

Answer:

Tears flowing through tear ducts, water rising in a straw or glass tube defying gravity, and water passing through a cloth towel These represent examples of capillary action.


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