Surface tension shapes how liquids behave at interfaces. It's why water beads up on a leaf and insects can walk on ponds. This force arises from molecules at the surface being pulled inward, creating a "skin" effect.
Contact angles and capillary action are key surface tension phenomena. They determine how liquids spread on surfaces and rise in narrow tubes. Understanding these concepts is crucial for many engineering applications, from designing water-repellent coatings to microfluidic devices.
Surface Tension and Capillarity
Causes of surface tension
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Surface tension arises from cohesive forces between liquid molecules attract each other and minimize surface area
Molecules at the surface experience unbalanced forces pulling them inward creating a net inward force (water, mercury)
Liquids with stronger intermolecular forces exhibit higher surface tension
Water has high surface tension due to hydrogen bonding between molecules
Mercury has even higher surface tension from strong metallic bonds
Surface tension quantified as force per unit length γ \gamma γ (N / m N/m N / m ) or energy per unit area (J / m 2 J/m^2 J / m 2 )
Soap reduces water's surface tension by disrupting hydrogen bonds
Insects like water striders can walk on water due to high surface tension
Contact angle θ \theta θ formed between liquid-vapor interface and solid surface determines wettability
Measured where liquid, vapor, and solid phases meet (drop on a surface)
Wetting occurs when θ < 90 ° \theta < 90° θ < 90° liquid spreads over surface (water on glass)
Non-wetting occurs when θ > 90 ° \theta > 90° θ > 90° liquid forms droplets on surface (mercury on glass)
Perfect wetting when θ = 0 ° \theta = 0° θ = 0° liquid completely spreads (oil on metal)
Young's equation relates contact angle to surface tensions: γ s v = γ s l + γ l v cos θ \gamma_{sv} = \gamma_{sl} + \gamma_{lv} \cos \theta γ s v = γ s l + γ l v cos θ
γ s v \gamma_{sv} γ s v , γ s l \gamma_{sl} γ s l , γ l v \gamma_{lv} γ l v are solid-vapor, solid-liquid, liquid-vapor surface tensions
Superhydrophobic surfaces have θ > 150 ° \theta > 150° θ > 150° (lotus leaf effect)
Surface tension in capillary action
Capillary action lifts or depresses liquid in narrow tube due to surface tension
Occurs when adhesive forces between liquid and tube exceed cohesive forces in liquid (water in glass tube)
Liquid column height h h h in capillary depends on surface tension γ \gamma γ , contact angle θ \theta θ , tube radius r r r , liquid density ρ \rho ρ
Capillary rise equation: h = 2 γ cos θ ρ g r h = \frac{2\gamma \cos \theta}{\rho g r} h = ρ g r 2 γ c o s θ , g g g = acceleration due to gravity
Water rises in glass tube, mercury depresses due to non-wetting (θ > 90 ° \theta > 90° θ > 90° )
Young-Laplace equation gives pressure difference Δ P \Delta P Δ P across curved liquid-vapor interface in capillary
Δ P = 2 γ cos θ r \Delta P = \frac{2\gamma \cos \theta}{r} Δ P = r 2 γ c o s θ
Smaller radius produces greater pressure difference (bubbles, droplets)
Calculations for surface phenomena
Apply capillary rise equation to calculate liquid column height in narrow tube
Example: Capillary rise of water in 0.5 mm radius glass tube, given γ w a t e r = 0.072 N / m \gamma_{water} = 0.072 N/m γ w a t er = 0.072 N / m , ρ w a t e r = 1000 k g / m 3 \rho_{water} = 1000 kg/m^3 ρ w a t er = 1000 k g / m 3 , θ = 0 ° \theta = 0° θ = 0°
Use Young-Laplace equation to find pressure difference across curved liquid-vapor interface
Example: Pressure difference across water-air interface in 0.1 mm radius capillary, assuming θ = 30 ° \theta = 30° θ = 30°
Combine surface tension with other fluid mechanics principles for complex problems
Example: Force required to pull thin wire loop out of liquid, considering surface tension and wire dimensions
Wilhelmy plate method measures surface tension by force on partially submerged plate