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.