Notes : Angle of Contact , Definition, Young's Equation, Applications - Class 11 Physics

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Complete notes on Angle of Contact with Young's Equation, wetting, non-wetting, applications, MCQs, FAQs, numericals and exam questions for Class 11 Physics chapter 9 Mechanical Properties of Fluids - Physicskund 

Angle of Contact

The free surface of a liquid near the plane of contact with another medium is generally curved. The angle between the tangent drawn to the liquid surface at the point of contact and the solid surface, measured inside the liquid, is called the Angle of Contact.

Symbol: θ

Definition of Angle of Contact

Angle of contact is the angle between the tangent to the liquid surface at the point of contact and the solid surface, measured inside the liquid.

Interfacial Tensions

At the line of contact between solid, liquid and air, three interfacial tensions act:

  • Sla = Surface tension of liquid-air interface
  • Ssa = Surface tension of solid-air interface
  • Ssl = Surface tension of solid-liquid interface

Young's Equation

For mechanical equilibrium at the contact line,

Equation (1)

Ssa = Ssl + Sla cos θ

Rearranging,

Equation (2)

cos θ = (Ssa − Ssl) / Sla

This relation is known as Young's Equation.

Physical Significance of Angle of Contact

The angle of contact determines whether a liquid spreads over a solid surface or forms droplets on it.

  • Small angle of contact → Better wetting
  • Large angle of contact → Poor wetting

Case 1: Acute Angle of Contact (θ < 90°)

When the angle of contact is less than 90°, the liquid spreads over the surface.

Condition:

Ssl < Ssa

Molecular Explanation:

  • Adhesive forces between liquid and solid are stronger.
  • Liquid molecules are strongly attracted towards the solid surface.
  • The liquid wets the solid surface.

Examples:

  • Water on glass
  • Water on clean plastic
  • Kerosene on most surfaces

Case 2: Obtuse Angle of Contact (θ > 90°)

When the angle of contact is greater than 90°, the liquid forms droplets and does not spread.

Condition:

Ssl > Ssa

Molecular Explanation:

  • Cohesive forces among liquid molecules are stronger.
  • Adhesive forces between liquid and solid are weaker.
  • The liquid does not wet the solid surface.

Examples:

  • Water on lotus leaf
  • Water on waxed surface
  • Water on oily surface
  • Mercury on glass

Special Cases

Complete Wetting: θ = 0°

The liquid spreads completely over the surface.

No Wetting: θ = 180°

The liquid forms nearly spherical droplets.

Wetting and Non-Wetting

Wetting

A liquid is said to wet a solid when it spreads over the solid surface.

Examples:

  • Water on glass
  • Ink on paper
  • Paint on walls

Non-Wetting

A liquid is said not to wet a solid when it forms droplets on the surface.

Examples:

  • Water on wax
  • Water on lotus leaf
  • Mercury on glass

Factors Affecting Angle of Contact

  • Nature of liquid
  • Nature of solid surface
  • Impurities present
  • Temperature
  • Surface cleanliness

Applications of Angle of Contact

1. Wetting Agents

Examples: Soap, detergent and dyeing substances.

These substances decrease the angle of contact and increase wetting.

Uses:

  • Better cleaning action
  • Better penetration of dyes
  • Improved spreading of liquids

2. Waterproofing Agents

These substances increase the angle of contact between water and fibers.

Result:

  • Water cannot penetrate the material.
  • The surface becomes water-resistant.

Examples:

  • Raincoats
  • Umbrellas
  • Waterproof fabrics

Important Points for Exams

  • Angle of contact is measured inside the liquid.
  • It depends upon both the liquid and the solid.
  • θ < 90° indicates wetting.
  • θ > 90° indicates non-wetting.
  • Water wets glass.
  • Mercury does not wet glass.
  • Soaps decrease angle of contact.
  • Waterproofing agents increase angle of contact.

Frequently Asked Questions (FAQ)

Q1. What is angle of contact?

The angle between the tangent to the liquid surface and the solid surface measured inside the liquid.

Q2. Why does water wet glass?

Because adhesive forces between water and glass are stronger than cohesive forces within water.

Q3. Why does mercury not wet glass?

Because cohesive forces in mercury are stronger than adhesive forces between mercury and glass.

Q4. What is Young's Equation?

Ssa = Ssl + Sla cos θ

Q5. What is the significance of angle of contact?

It determines whether a liquid will spread over a surface or form droplets.

MCQs

1. Angle of contact is measured inside the:

A) Solid
B) Liquid ✅
C) Air
D) Vacuum

2. Water on glass has:

A) 0°
B) 90°
C) Less than 90° ✅
D) Greater than 90°

3. Mercury on glass has:

A) Acute angle
B) Obtuse angle ✅
C) Zero angle
D) Right angle

4. Soaps act as:

A) Lubricants
B) Waterproofing agents
C) Wetting agents ✅
D) Adhesives

5. Wetting occurs when:

A) θ > 90°
B) θ = 90°
C) θ < 90° ✅
D) θ = 180°

True / False

1. Angle of contact is measured inside the liquid. True

2. Water wets glass. True

3. Mercury wets glass. False

4. Wetting agents decrease angle of contact. True

5. Waterproofing agents increase angle of contact. True

Fill in the Blanks

1. Angle of contact is represented by ________. θ

2. Water on glass forms an ________ angle. Acute

3. Mercury on glass forms an ________ angle. Obtuse

4. Soap is a ________ agent. Wetting

5. Waterproofing chemicals increase the ________ of contact. Angle

Very Short Answer Questions

Q1. What is the symbol of angle of contact?

Ans: θ

Q2. Which liquid does not wet glass?

Ans: Mercury.

Q3. Give one example of wetting.

Ans: Water on glass.

Q4. Give one example of non-wetting.

Ans: Mercury on glass.

Q5. What is the SI unit of angle of contact?

Ans: Radian (rad).

Q6. Name a wetting agent.

Ans: Soap.

Q7. What type of angle does water make on glass?

Ans: Acute angle.

Q8. What type of angle does mercury make on glass?

Ans: Obtuse angle.

Q9. What happens when θ = 0°?

Ans: Complete wetting occurs.

Q10. What happens when θ = 180°?

Ans: The liquid does not wet the surface and forms droplets.

Short Answer Questions

Q1. Define angle of contact.

Ans: Angle of contact is the angle between the tangent drawn to the liquid surface at the point of contact and the solid surface, measured inside the liquid.

Q2. What is Young's Equation?

Ans:

Ssa = Ssl + Sla cos θ

This equation relates the angle of contact with the three interfacial tensions acting at the contact line.

Q3. Differentiate between wetting and non-wetting.

Ans:

  • Wetting: The liquid spreads over the solid surface.
  • Non-Wetting: The liquid forms droplets and does not spread.

Q4. Why does water wet glass?

Ans: Water wets glass because the adhesive force between water and glass is greater than the cohesive force between water molecules.

Q5. Why does mercury not wet glass?

Ans: Mercury does not wet glass because the cohesive force between mercury molecules is greater than the adhesive force between mercury and glass.

Q6. What are wetting agents?

Ans: Wetting agents are substances such as soaps and detergents that decrease the angle of contact and increase the spreading of liquids over surfaces.

Q7. What are waterproofing agents?

Ans: Waterproofing agents increase the angle of contact between water and a surface, preventing water from penetrating the material.

Long Answer Questions

Q1. Explain angle of contact and discuss its significance.

Ans:

The angle of contact is the angle between the tangent to the liquid surface at the point of contact and the solid surface measured inside the liquid. It is represented by θ.

The value of angle of contact determines whether a liquid wets a surface or not.

  • If θ < 90°, the liquid wets the surface and spreads over it.
  • If θ > 90°, the liquid does not wet the surface and forms droplets.

The angle of contact depends on the nature of the liquid, the solid surface, impurities and temperature.

Examples:

  • Water wets glass.
  • Mercury does not wet glass.

Thus, angle of contact plays an important role in capillarity, cleaning action, painting, dyeing and waterproofing processes.

Q2. Derive Young's Equation for angle of contact.

Ans:

At the contact line between solid, liquid and air, three surface tensions act:

  • Sla = Liquid-air surface tension
  • Ssa = Solid-air surface tension
  • Ssl = Solid-liquid surface tension

For equilibrium of forces at the contact line, the horizontal components must balance.

Equation (1)

Ssa = Ssl + Sla cos θ

This equation is known as Young's Equation.

Rearranging,

Equation (2)

cos θ = (Ssa − Ssl) / Sla

This equation explains how the angle of contact depends on the interfacial tensions of the three interfaces.

Q3. Explain the applications of angle of contact.

Ans:

1. Wetting Agents:

Soaps, detergents and dyeing substances decrease the angle of contact. This increases wetting and improves cleaning and dye penetration.

2. Waterproofing Agents:

Waterproofing chemicals increase the angle of contact between water and fibers. As a result, water cannot penetrate the material and the surface remains dry.

Examples include raincoats, umbrellas and waterproof fabrics.

Numerical-Based Questions

Q1. A liquid has an angle of contact of 30°. Will it wet the surface?

Ans:

Since 30° < 90°, the liquid will wet the surface.

Q2. A liquid has an angle of contact of 120°. Will it wet the surface?

Ans:

Since 120° > 90°, the liquid will not wet the surface and will form droplets.

Q3. What is the angle of contact for complete wetting?

Ans: θ = 0°

Q4. What is the angle of contact for complete non-wetting?

Ans: θ = 180°

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