Glossary

2.3 Surface Tension and Capillarity

3 min read•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 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 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+γlvcos⁡θ\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=2γcos⁡θρgrh = \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=2γcos⁡θr\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
    • measures surface tension by force on partially submerged plate

Key Terms to Review (8)

Capillary Action: Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces, primarily due to the interplay of cohesive and adhesive forces. This phenomenon is crucial in various natural and artificial systems, as it allows liquids to move through small channels or porous materials, influencing processes like water transport in plants and ink movement in writing instruments.
Capillary Tube Method: The capillary tube method is a technique used to measure the surface tension of liquids by observing the height to which a liquid rises in a thin tube due to capillarity. This phenomenon occurs because of the balance between adhesive forces between the liquid and the tube and the cohesive forces within the liquid. Understanding this method is essential for analyzing how liquids behave in small spaces and is closely tied to concepts of surface tension and capillarity.
Cohesive Forces: Cohesive forces are the intermolecular forces that hold like molecules together in a substance. These forces are responsible for various phenomena, such as surface tension and capillary action, which occur when liquid molecules stick to each other more than they stick to other materials. Understanding cohesive forces helps explain how liquids behave, especially in interactions with solids and other fluids.
Detergent action: Detergent action refers to the ability of surfactants, commonly found in cleaning products, to reduce surface tension and enhance the wetting of surfaces. This process allows water to spread more easily and penetrate into soils and stains, effectively lifting and removing them. The unique structure of surfactants, with a hydrophilic (water-attracting) head and a hydrophobic (water-repelling) tail, plays a crucial role in this mechanism, enabling them to interact with both water and oily substances.
Inkjet Printing: Inkjet printing is a digital printing technology that works by propelling tiny droplets of ink onto paper or other substrates to create images or text. This method is widely used in both home and commercial printing due to its ability to produce high-quality prints with detailed color reproduction, while also being relatively cost-effective for small to medium-sized print runs.
Meniscus Formation: Meniscus formation refers to the curvature of a liquid's surface in response to the adhesive forces between the liquid and the container's surface. This phenomenon is primarily observed in liquids such as water, where the interaction between the liquid molecules and the surface can lead to either a concave or convex shape, depending on the relative strength of adhesive and cohesive forces. Understanding meniscus formation is crucial in explaining how liquids behave in narrow spaces, which ties closely to concepts of surface tension and capillarity.
Viscosity: Viscosity is a measure of a fluid's resistance to deformation and flow, essentially describing how thick or sticky a fluid is. This property plays a crucial role in understanding fluid behavior under different conditions and directly affects various phenomena, such as flow rates, pressure distribution, and energy loss in fluid systems.
Wilhelmy Plate Method: The Wilhelmy Plate Method is a technique used to measure the surface tension of liquids by utilizing a thin, vertically oriented plate partially immersed in the liquid. This method provides a straightforward approach to quantify surface tension based on the balance of forces acting on the plate, which is affected by the liquid’s wetting properties. It connects to concepts of surface tension and capillarity, revealing how forces at the interface influence liquid behavior and interactions with solid surfaces.
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