Relationship Between Surface Tension and Contact Angle (Young’s Equation)
Surface tension and contact angle are fundamental concepts in fluid mechanics that help explain how liquids interact with solid surfaces. At the molecular level, surface tension arises from the cohesive forces between particles at a liquid’s surface. Contact angle measures how a liquid drop sits on a solid, revealing the degree of wettability. These ideas are vital for JEE Main and NEET learners, as they connect real-world phenomena with equations and experiments often asked in exams.
Understanding Surface Tension and Contact Angle
The term surface tension refers to the force per unit length acting along the surface of a liquid, minimizing its area. This property causes phenomena like water droplets forming beads. In contrast, contact angle is defined as the angle created where a liquid interface meets a solid surface. Both are crucial in predicting how liquids behave on different materials and in capillary action.
The higher the surface tension, the more the liquid resists spreading, often resulting in a larger contact angle. A low surface tension means the liquid spreads easily, showing a smaller contact angle. These relationships are governed by intermolecular forces, especially cohesive and adhesive interactions.
Key Relationships: Surface Tension, Contact Angle, and Young’s Equation
A vital link between surface tension and contact angle is given by Young’s equation. This relation allows us to predict how a droplet will behave on varying substrates. It connects the surface tension of the solid-gas (γsg), solid-liquid (γsl), and liquid-gas (γlg) interfaces:
| Parameter | Symbol | SI Unit |
|---|---|---|
| Surface tension (liquid-gas) | γlg | N·m-1 |
| Surface tension (solid-gas) | γsg | N·m-1 |
| Surface tension (solid-liquid) | γsl | N·m-1 |
| Contact angle | θ | Degrees (°) |
Young’s equation for surface tension and contact angle is:
γsg = γsl + γlg cosθ
Here, θ is the contact angle formed at the triple-phase boundary. This relation appears in practical contexts like droplet formation, detergency, and paint adhesion.
In problem-solving, knowing how to use this equation is crucial. It helps relate measured contact angles to interfacial tensions, which frequently features in JEE numericals and competitive physics questions.
- High contact angle (> 90°) — surface is non-wettable (hydrophobic).
- Low contact angle (< 90°) — surface is wettable (hydrophilic).
- If θ = 0°, the liquid spreads completely.
- Intermediate values show partial wetting.
Measuring Surface Tension and Contact Angle
Both these quantities are measured with specific experimental setups. Surface tension can be measured using a capillary tube or drop-weight methods. Contact angle is typically measured using a goniometer, which analyzes droplet shape on a flat surface.
- Place a droplet of liquid on a smooth solid surface.
- Observe or image the droplet using a camera or a goniometer.
- Measure the angle at which the liquid interface meets the solid.
- Repeat for accuracy and average the results.
Key errors in measurement include surface contamination and uneven substrate. For capillary action-based methods, keep in mind the tube radius and purity of the liquids used.
- Capillary action and meniscus shape allow indirect determination of surface tension and contact angle.
- Viscosity and viscous force relate experimentally with surface tension in fluid studies.
- Properties of solids and liquids are essential to understand substrate effects on measurement.
Applications, Examples, and Numericals on Surface Tension and Contact Angle
Surface tension and contact angle appear in numerous practical and exam-based contexts. During JEE Main or school examinations, problems may involve predicting droplet spread, designing laboratory setups, or explaining capillarity.
- In capillary tubes: the height of rise or fall depends on the surface tension and the contact angle (h = 2γ cosθ / ρgr).
- Detergents: lower the surface tension, reducing contact angle and increasing cleaning power.
- Waterproof textiles: engineered for high contact angles to repel water.
- Surface coatings: paint and ink adhesion rely on surface energies and interfacial tension.
- Medical devices: surface modification controls wetting and spreading of fluids.
- Rain on leaves: pearling effects are caused by high contact angles.
Consider the classic competitive exam problem: “A capillary tube (r = 0.5 mm) is dipped in water (γ = 0.072 N·m-1, θ ≈ 0°, ρ = 1000 kg·m-3). What is the water rise?” Use the formula h = 2γ cosθ / ρgr. With cos0° = 1 and g ≈ 9.8 m·s-2, h ≈ 2 × 0.072 / (1000 × 9.8 × 0.0005) = 0.029 m or 2.9 cm.
Pay attention to units, choose the right formula variant, and remember material surfaces and temperature affect values. Repeated practice with worked examples and mock tests such as the practice tests on properties of solids and liquids will build strong skills.
- Solids and surface tension connect cohesive and adhesive forces.
- Important questions on solids and liquids help reinforce these topics.
- Surface energy topics enrich your perspective on contact angle phenomena.
- Check the dimensions of surface tension when memorizing SI units.
Vedantu content is written and reviewed by subject experts to align with exam trends. Strengthen your problem-solving by referring to the updated material and connecting formulas to real observations.
Common Pitfalls and Key Revision Points for Surface Tension and Contact Angle
When studying surface tension and contact angle, learners often mix up cohesive and adhesive force roles. Use diagrams to clarify force directions at the triple phase line. Remember, temperature rise generally decreases surface tension and makes liquids more wettable, decreasing contact angle on most surfaces.
- Confusing adhesive and cohesive forces when assigning values.
- Missing the effect of impurities on surface tension.
- Forgetting units: always N·m-1 for surface tension.
- Wrongly assuming all liquids behave like water — they don’t.
- Not considering surface roughness and contamination.
- Forgetting to use cosθ in equations; sign errors are common here.
Quick revision with revision notes for solids and liquids or solving the solids and liquids practice paper can boost confidence.
In summary, mastering surface tension and contact angle demands connecting formulas to real-life events, using carefully designed lists and tables, and repeated exam-style practice. The Vedantu team ensures these exam concepts are always up-to-date, accurate, and explained in the most student-friendly manner.
FAQs on Surface Tension and Contact Angle Explained
1. What is the relationship between surface tension and the angle of contact?
Surface tension and contact angle are related by Young’s Equation, which describes the interaction between a liquid and a solid surface. The relationship can be summarised as:
- Young’s Equation: γSG = γSL + γLG cosθ,
- where γSG, γSL, and γLG are the interfacial tensions for solid-gas, solid-liquid, and liquid-gas respectively, and θ is the contact angle.
- A higher surface tension leads to a larger contact angle on hydrophobic surfaces.
- This relationship is widely used in fluid mechanics, wettability analysis, and JEE/NEET exam problems.
2. What is the equation for surface tension and contact angle?
The equation connecting surface tension and contact angle is known as Young's Equation. It is given by:
- γSG = γSL + γLG cosθ
- Where θ is the contact angle, and γ represents surface or interfacial tensions.
- This formula helps determine how a liquid droplet behaves on different surfaces.
3. How do contact angle and surface tension change with temperature?
Both contact angle and surface tension typically decrease as temperature increases.
- Higher temperatures lower a liquid’s surface tension.
- Lower surface tension causes the contact angle to decrease, making the liquid spread more.
- This trend is important for understanding wettability and practical applications in science and engineering.
4. What is the contact angle of water on different surfaces?
The contact angle of water on a surface depends on the surface's material and properties.
- Hydrophilic surfaces (e.g., clean glass): Angle < 90°, water spreads out.
- Hydrophobic surfaces (e.g., wax, Teflon): Angle > 90°, water forms beads.
- This concept is tested in JEE Main, NEET and board exams.
5. How is contact angle measured in experiments?
The contact angle is measured using standard experimental setups:
- Place a liquid droplet on a clean solid surface.
- Use a goniometer or a microscope with a camera to observe the interface.
- Measure the angle between the tangent at the liquid-solid interface and the solid surface.
- Careful control of impurities and temperature gives more accurate results.
6. What are some real-life applications of surface tension and contact angle?
Surface tension and contact angle influence many daily-life situations and technological solutions:
- Droplet formation and movement (e.g., rain on leaves).
- Design of non-stick cookware and waterproof coatings.
- Cleaning efficiency of detergents and soaps.
- Medical applications (e.g., microfluidic devices, lab-on-chip).
7. Why does a droplet sometimes spread and sometimes bead up on surfaces?
Whether a droplet spreads or beads up depends on the balance between cohesive forces within the liquid and adhesive forces between the liquid and the surface.
- More adhesive attraction: Droplet spreads (small contact angle, hydrophilic).
- More cohesive attraction: Droplet beads (large contact angle, hydrophobic).
- This behaviour is determined by surface tension and wettability.
8. Do all liquids have the same contact angle on the same surface?
No, different liquids have different contact angles on the same surface due to variations in their surface tension and molecular interactions.
- Water, oil, mercury, and alcohol each form different contact angles on glass or Teflon.
- This difference affects wettability and is important for material design and selection.
9. What is Young's Equation and how is it used?
Young's Equation mathematically relates surface tension and contact angle at the interface between three phases (solid, liquid, gas):
- γSG = γSL + γLG cosθ
- Used to predict wettability and analyze phenomena like capillary action.
- Essential for solving numerical and conceptual Physics questions in JEE/NEET.
10. Can the contact angle ever be negative or more than 180°?
The contact angle for a liquid on a solid surface ranges from 0° to 180°.
- Values less than 0° and more than 180° are physically not possible.
- Angles near 0°: Complete wetting (liquid spreads fully).
- Angles near 180°: Complete non-wetting (liquid forms nearly perfect spheres).
