Angle of Contact — Revision Notes

⚡ 30-Second Revision

Definition: — Angle between tangent to liquid surface and solid surface, measured inside liquid ($\theta$).
Wetting: — $\theta < 90^\circ$ (Adhesive > Cohesive), concave meniscus, liquid rises.
Non-wetting: — $\theta > 90^\circ$ (Cohesive > Adhesive), convex meniscus, liquid falls.
Perfect wetting: — $\theta = 0^\circ$.
Young's Equation: — $\gamma_{SG} = \gamma_{SL} + \gamma_{LG} \cos\theta$.
Capillary Rise/Fall: — $h = \frac{2\gamma \cos\theta}{\rho g r}$.
Factors: — Nature of liquid/solid, impurities, temperature.

2-Minute Revision

The angle of contact ($\theta$) is a crucial parameter defining how a liquid interacts with a solid surface. It's the angle formed by the tangent to the liquid surface at the point of contact with the solid, measured within the liquid.

This angle is a direct consequence of the balance between cohesive forces (liquid-liquid attraction) and adhesive forces (liquid-solid attraction). If adhesive forces are stronger, the liquid wets the surface, resulting in $\theta < 90^\circ$ (e.

g., water on clean glass, $\theta \approx 0^\circ$). Such liquids form a concave meniscus and rise in capillary tubes. If cohesive forces are stronger, the liquid does not wet the surface, leading to $\theta > 90^\circ$ (e.

g., mercury on glass, $\theta \approx 140^\circ$). These liquids form a convex meniscus and fall in capillary tubes. Young's Equation, $\gamma_{SG} = \gamma_{SL} + \gamma_{LG} \cos\theta$, quantitatively describes this balance using interfacial tensions.

Factors like temperature (generally decreases $\theta$ by reducing surface tension) and impurities (e.g., detergents reduce $\gamma_{LG}$ and thus $\theta$) significantly influence this angle. For NEET, remember the capillary rise formula $h = \frac{2\gamma \cos\theta}{\rho g r}$ and its direct dependence on $\cos\theta$ for predicting liquid behavior.

5-Minute Revision

The angle of contact, $\theta$, is a fundamental concept in fluid mechanics, specifically surface phenomena. It is defined as the angle between the tangent to the liquid surface and the solid surface, measured inside the liquid at the three-phase (solid-liquid-gas) boundary. This angle dictates the wettability of a solid by a liquid.

Wetting vs. Non-Wetting:

Wetting liquids ($\theta < 90^\circ$): — Adhesive forces (liquid-solid) are stronger than cohesive forces (liquid-liquid). The liquid spreads, forming a concave meniscus. Example: Water on clean glass ($\theta \approx 0^\circ$). These liquids rise in capillary tubes.
Non-wetting liquids ($\theta > 90^\circ$): — Cohesive forces are stronger than adhesive forces. The liquid beads up, forming a convex meniscus. Example: Mercury on glass ($\theta \approx 140^\circ$). These liquids fall in capillary tubes.

Young's Equation: The equilibrium at the contact line is described by Young's Equation: $\gamma_{SG} = \gamma_{SL} + \gamma_{LG} \cos\theta$, where $\gamma_{SG}$, $\gamma_{SL}$, and $\gamma_{LG}$ are the interfacial tensions between solid-gas, solid-liquid, and liquid-gas, respectively. This equation shows how the angle of contact is determined by the relative strengths of these interfacial energies.

Capillary Action: The angle of contact is directly linked to capillary rise or fall. The height $h$ to which a liquid rises or falls in a capillary tube of radius $r$ is given by:

$$h = \frac{2\gamma \cos\theta}{\rho g r}$$

where $\gamma$ is the surface tension of the liquid, $\rho$ is its density, and $g$ is the acceleration due to gravity.

If $\theta < 90^\circ$, $\cos\theta$ is positive, and $h$ is positive (rise). If $\theta > 90^\circ$, $\cos\theta$ is negative, and $h$ is negative (fall).

Factors Affecting $\theta$:

1
Nature of Liquid: — Its intrinsic surface tension (cohesive forces).
2
Nature of Solid: — Its surface energy (adhesive forces).
3
Impurities: — Surfactants (like detergents) reduce $\gamma_{LG}$, thereby decreasing $\theta$ and improving wetting.
4
Temperature: — Generally, increasing temperature reduces surface tension, leading to a decrease in $\theta$.

Example: If water ($\gamma = 0.072\,\text{N/m}$, $\rho = 1000\,\text{kg/m}^3$) has an angle of contact of $30^\circ$ with a glass tube of $0.2\,\text{mm}$ radius, the capillary rise would be: $h = \frac{2 \times 0.072 \times \cos(30^\circ)}{1000 \times 9.8 \times (0.2 \times 10^{-3})} = \frac{2 \times 0.072 \times 0.866}{1000 \times 9.8 \times 0.0002} \approx 0.0638\,\text{m} = 6.38\,\text{cm}$.

For NEET, focus on the formula for capillary action, the conceptual understanding of wetting/non-wetting, and the factors influencing $\theta$. Always pay attention to units.

Prelims Revision Notes

The angle of contact ($\theta$) is a critical parameter in surface tension phenomena, defined as the angle measured inside the liquid between the tangent to the liquid surface and the solid surface at their point of contact. This angle quantifies the wettability of a solid by a liquid.

Key Points:

Wetting Liquids: — Have $\theta < 90^\circ$. This occurs when adhesive forces (liquid-solid attraction) are stronger than cohesive forces (liquid-liquid attraction). Examples include water on clean glass ($\theta \approx 0^\circ$). They form a concave meniscus and exhibit capillary rise.
Non-Wetting Liquids: — Have $\theta > 90^\circ$. This occurs when cohesive forces are stronger than adhesive forces. Examples include mercury on glass ($\theta \approx 140^\circ$). They form a convex meniscus and exhibit capillary fall.
Perfect Wetting: — $\theta = 0^\circ$. Liquid spreads completely.
Perfect Non-Wetting: — $\theta = 180^\circ$. Liquid forms a perfect sphere, theoretically.

Young's Equation: The equilibrium at the three-phase contact line is given by $\gamma_{SG} = \gamma_{SL} + \gamma_{LG} \cos\theta$, where $\gamma_{SG}$, $\gamma_{SL}$, and $\gamma_{LG}$ are the surface tensions at the solid-gas, solid-liquid, and liquid-gas interfaces, respectively.

Capillary Action Formula: The height $h$ of liquid rise (or fall) in a capillary tube of radius $r$ is given by:

$$h = \frac{2\gamma \cos\theta}{\rho g r}$$

If $\theta < 90^\circ$, $\cos\theta$ is positive, $h$ is positive (rise).
If $\theta > 90^\circ$, $\cos\theta$ is negative, $h$ is negative (fall).

Factors Affecting Angle of Contact:

1
Nature of Liquid: — Its inherent surface tension (cohesive forces).
2
Nature of Solid: — Its chemical composition and roughness (adhesive forces).
3
Impurities: — Surfactants (detergents) reduce $\gamma_{LG}$, decreasing $\theta$ and enhancing wetting.
4
Temperature: — Generally, increasing temperature reduces surface tension, which typically leads to a decrease in $\theta$.
5
Medium above liquid: — Changes in the gas phase can alter interfacial tensions.

Common Traps:

Confusing the measurement of $\theta$ (always inside the liquid).
Incorrectly relating meniscus shape to $\theta$ or forces.
Errors in unit conversion in capillary rise problems.
Forgetting the '2' in the capillary rise formula or the $\cos\theta$ term.

Vyyuha Quick Recall

To remember the relationship between angle of contact, forces, and capillary action:

Wet Angle Concave Rise (WACR)

Wet: Wetting liquid
Angle: $\theta < 90^\circ$
Concave: Concave meniscus
Rise: Capillary rise

Non-wetting Convex Fall (NCF)

Non-wetting: Non-wetting liquid
Convex: Convex meniscus
Fall: Capillary fall

For forces: Wet = Adhesive > Cohesive; Non-wetting = Cohesive > Adhesive.