Revision

Surface Tension & Capillarity — A/L Physics

Aligned with the NIE syllabus

What must I remember about Surface Tension & Capillarity?

Surface Tension (γ): Property of a liquid surface film to behave like a stretched elastic membrane; defined as force per unit length acting perpendicular to an imaginary line drawn on the liquid surface: γ = F / L (units N/m = J/m²).
Surface Energy: Work done in increasing liquid surface area by unit amount under isothermal conditions: Surface Energy = Work done / ΔA = γ; liquid drops spontaneously assume spherical shape to minimize surface area and surface energy.
Excess Pressure (Laplace Law): Concave side of curved interface has higher pressure than convex side: 1) Spherical liquid drop: ΔP = (2 γ) / r; 2) Spherical soap bubble (TWO surfaces, inner and outer): ΔP = (4 γ) / r; 3) Cylindrical liquid jet: ΔP = γ / r.
Angle of Contact (θ): Angle between tangent to liquid surface and solid surface inside the liquid at line of contact; θ < 90° for wetting liquids (water on clean glass, concave meniscus); θ > 90° for non-wetting liquids (mercury on glass, convex meniscus).

Capillary Rise (Jurin's Law)

In a capillary tube of internal radius r: Height of liquid column h = (2 γ cos θ) / (r ρ g); liquid rises when θ < 90° (concave meniscus) and depresses when θ > 90° (mercury, convex meniscus); h ∝ 1/r (narrower tube gives higher rise).
Insufficient Length Tube

If a capillary tube is shorter than calculated equilibrium height h (tube length L < h), liquid DOES NOT overflow; instead, meniscus flattens, increasing its radius of curvature R such that h * R = Constant.
Temperature and Impurities

Surface tension decreases with increasing temperature (reaching zero at critical temperature); highly soluble inorganic salts (e.g., NaCl) increase surface tension, while surfactants and detergents significantly decrease surface tension.

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 10: Mechanical Properties of Matter