The contact angle (θ) is determined by the balance between three interfacial tensions:

γ_SA = γ_SL + γ_LAcosθ

Where:

• γ_SA = solid-air interfacial tension
• γ_SL = solid-liquid interfacial tension
• γ_LA = liquid-air interfacial tension (surface tension)

For water-glass: γ_SA > γ_SL, so cosθ is positive → θ is acute (0-30°)

For mercury-glass: γ_SA < γ_SL, so cosθ is negative → θ is obtuse (~140°)

Wetting occurs when the liquid spreads on the solid surface, which happens when:

γ_SA > γ_SL + γ_LA

Water wets glass because water molecules are strongly attracted to the polar glass surface (adhesive forces > cohesive forces).

Mercury doesn't wet glass because mercury atoms have much stronger cohesive forces (between mercury atoms) than adhesive forces (to glass).

Surface tension (γ) is defined as the force per unit length (N/m) acting at the surface, or equivalently the energy per unit area (J/m²).

It depends only on the nature of the liquid and temperature, not on the area because:

• Surface tension arises from intermolecular forces at the surface
• These forces are short-range and depend only on local molecular environment
• Increasing area simply creates more identical surface with the same properties

Detergents reduce surface tension (γ_LA) and also reduce γ_SL by adsorbing at the interfaces:

• Detergent molecules are amphiphilic (have both hydrophilic and hydrophobic parts)
• They accumulate at interfaces, reducing interfacial tensions
• From Young's equation: γ_SA = γ_SL + γ_LAcosθ
• Reduction in γ_LA and γ_SL makes cosθ approach 1 → θ approaches 0°

In the absence of external forces, surface tension minimizes the surface area for a given volume:

• Surface tension acts like an elastic skin trying to minimize surface area
• For a given volume, the shape with smallest surface area is a sphere
• This is why small droplets (where surface forces dominate over gravity) are spherical
• Larger drops may flatten due to gravity overcoming surface tension