Surface Tension

Definition and Basic Concept

Surface Tension Defined

Surface tension (γ): energy per unit area at a liquid surface. Force per unit length along liquid interface. Arises due to imbalance of molecular forces at interface.

Physical Interpretation

Liquid surface behaves like elastic membrane. Molecules inside liquid experience symmetric forces; molecules at surface experience net inward force. Surface contracts to minimize area.

Relevance and Importance

Determines droplet shape, capillary action, bubble formation, adhesion. Critical in biology, material science, engineering, and chemistry.

Molecular Origin of Surface Tension

Cohesive Forces

Intermolecular forces (van der Waals, hydrogen bonding) bind molecules in liquid bulk. Cohesion leads to surface tension.

Imbalance at Interface

Molecules at surface lack neighboring molecules above; net inward force exists. Creates energy cost to increase surface area.

Energy Perspective

Surface molecules have higher potential energy than bulk. Surface tension = work required to increase surface area by unit amount.

Measurement Techniques

Capillary Rise Method

Measure height liquid climbs in narrow tube. Surface tension related to height, density, gravity, and tube radius.

Drop Weight and Pendant Drop

Analyze drop shape or weight at tip of tube to calculate surface tension via force balance.

Wilhelmy Plate Method

Thin plate partially immersed; force measured related to wetted perimeter and surface tension.

Units and Typical Values

SI Units

Joule per square meter (J/m²) or equivalently Newton per meter (N/m). 1 N/m = 1 J/m².

Typical Surface Tension Values

Temperature Dependence

Surface tension decreases with temperature increase; approaches zero at critical temperature.

Thermodynamics of Surface Tension

Gibbs Free Energy Relation

Surface tension = (∂G/∂A)_T,P: change in Gibbs free energy with surface area at constant temperature and pressure.

Surface Excess and Adsorption

Surface tension linked to surface excess concentration by Gibbs adsorption isotherm.

Temperature Coefficient

dγ/dT is negative; magnitude depends on liquid type and impurities.

Interfacial Tension vs Surface Tension

Definitions

Surface tension: interface between liquid and gas. Interfacial tension: interface between two immiscible liquids or liquid-solid.

Magnitude Comparison

Interfacial tension usually lower than surface tension of pure liquids due to molecular interactions.

Examples

Water-oil interface (~50 mN/m), water-air interface (~72 mN/m).

Capillarity and Related Phenomena

Capillary Action

Liquid rises/falls in narrow tubes due to surface tension and adhesion. Height inversely proportional to tube radius.

Jurin's Law

h = (2γ cos θ) / (ρgr), where h = height, γ = surface tension, θ = contact angle, ρ = density, g = gravity, r = radius.

Meniscus Formation

Concave or convex meniscus shape depends on adhesion vs cohesion dominance.

Contact Angle and Wetting

Contact Angle Definition

Angle formed at liquid-solid-gas interface. Determines wetting behavior.

Young's Equation

γ_SG = γ_SL + γ_LG cos θ, relates solid-gas, solid-liquid, liquid-gas tensions to contact angle θ.

Wetting Types

Complete wetting (θ ~ 0°), partial wetting (0° < θ < 90°), non-wetting (θ > 90°).

Applications in Science and Industry

Biology and Medicine

Surface tension critical in alveoli function, blood flow, drug delivery (liposomes, emulsions).

Industrial Processes

Paints, coatings, detergents, inkjet printing rely on surface tension control.

Material Science

Fabrication of thin films, nano-structures, self-assembly processes.

Factors Affecting Surface Tension

Temperature

Increased temperature lowers surface tension; molecules gain kinetic energy, reduce cohesive forces.

Impurities and Contaminants

Surfactants reduce surface tension by adsorbing at interface. Electrolytes and organic solvents also influence values.

Pressure and Environment

Minor effect on surface tension; mainly temperature and composition dependent.

Surface-Active Agents (Surfactants)

Definition and Structure

Amphiphilic molecules with hydrophobic tail and hydrophilic head. Concentrate at interfaces.

Effect on Surface Tension

Adsorption lowers γ by disrupting cohesive forces. Critical micelle concentration (CMC) marks saturation point.

Applications

Detergents, emulsifiers, dispersants, foaming agents.

Mathematical Models and Equations

Young-Laplace Equation

Pressure difference across curved interface: ΔP = 2γ / R for spherical interfaces.

Gibbs Adsorption Isotherm

dγ = - Σ Γ_i dμ_iwhereγ = surface tension,Γ_i = surface excess concentration of component i,μ_i = chemical potential of component i 

Jurin's Law Revisited

h = (2γ cos θ) / (ρ g r)Variables:h = capillary rise heightγ = surface tensionθ = contact angleρ = liquid densityg = acceleration due to gravityr = tube radius 

References

• Adamson, A. W., & Gast, A. P., Physical Chemistry of Surfaces, 6th ed., Wiley, 1997, pp. 1-450.
• Israelachvili, J. N., Intermolecular and Surface Forces, 3rd ed., Academic Press, 2011, pp. 50-200.
• Bergeron, V., et al., "Surface Tension and Capillarity," Journal of Colloid and Interface Science, vol. 250, 2002, pp. 1-15.
• de Gennes, P. G., Brochard-Wyart, F., & Quéré, D., Capillarity and Wetting Phenomena, Springer, 2004, pp. 30-120.
• Lyklema, J., Fundamentals of Interface and Colloid Science, Vol. II, Academic Press, 1995, pp. 100-300.