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2.3 Surface Tension and Capillarity

3 min readLast Updated on July 19, 2024

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 (N/mN/m) or energy per unit area (J/m2J/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 and wettability

  • Contact angle θ\theta 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° liquid spreads over surface (water on glass)
    • Non-wetting occurs when θ>90°\theta > 90° liquid forms droplets on surface (mercury on glass)
    • Perfect wetting when θ=0°\theta = 0° liquid completely spreads (oil on metal)
  • Young's equation relates contact angle to surface tensions: γsv=γsl+γlvcosθ\gamma_{sv} = \gamma_{sl} + \gamma_{lv} \cos \theta
    • γsv\gamma_{sv}, γsl\gamma_{sl}, γlv\gamma_{lv} are solid-vapor, solid-liquid, liquid-vapor surface tensions
    • Superhydrophobic surfaces have θ>150°\theta > 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 hh in capillary depends on surface tension γ\gamma, contact angle θ\theta, tube radius rr, liquid density ρ\rho
    • Capillary rise equation: h=2γcosθρgrh = \frac{2\gamma \cos \theta}{\rho g r}, gg = acceleration due to gravity
    • Water rises in glass tube, mercury depresses due to non-wetting (θ>90°\theta > 90°)
  • Young-Laplace equation gives pressure difference ΔP\Delta P across curved liquid-vapor interface in capillary
    • ΔP=2γcosθr\Delta P = \frac{2\gamma \cos \theta}{r}
    • Smaller radius produces greater pressure difference (bubbles, droplets)

Calculations for surface phenomena

  1. 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 γwater=0.072N/m\gamma_{water} = 0.072 N/m, ρwater=1000kg/m3\rho_{water} = 1000 kg/m^3, θ=0°\theta = 0°
  2. 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°
  3. 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
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© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
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