2.1 Surface tension and interfacial energy

Surface tension and interfacial energy are the concepts that explain why liquids form droplets, how insects walk on water, and what makes surfactants work. These phenomena all arise from molecular interactions at the boundary between different phases.

These ideas show up constantly in colloid science, from capillary action in plants to emulsion stability in foods to mineral flotation in mining. This guide covers the molecular origins of surface tension, how to measure it, the thermodynamics of interfaces, and the role of surfactants.

Definition of surface tension

Surface tension is the tendency of liquid surfaces to shrink to the minimum possible area. It results from cohesive forces between liquid molecules pulling surface molecules inward.

Technically, surface tension is a property of the interface between two phases (liquid-gas or liquid-liquid), not just the liquid itself. It's what gives liquid droplets their shape, allows bubbles to form, and lets certain insects stand on water without breaking through.

Surface tension has units of force per length (N/m) or, equivalently, energy per area (J/m²). Both descriptions are physically valid: you can think of it as a force acting along the surface or as the energy cost of creating new surface area.

Molecular origin of surface tension

The root cause is an imbalance of intermolecular forces at the surface compared to the bulk.

• Bulk molecules are surrounded on all sides by neighboring molecules. Attractive forces pull equally in every direction, so the net force on a bulk molecule is zero.
• Surface molecules have fewer neighbors above them (only gas molecules, which are sparse). The result is a net inward pull toward the bulk liquid.

This inward pull means surface molecules sit at a higher energy state than bulk molecules. The system naturally tries to minimize the number of molecules in this unfavorable position, which is why liquids minimize their surface area. A sphere has the lowest surface-area-to-volume ratio, and that's exactly why free droplets are spherical.

Factors affecting surface tension

Effect of temperature on surface tension

Surface tension generally decreases as temperature rises. Higher temperature means greater molecular kinetic energy, which weakens the cohesive intermolecular forces holding the surface together.

The Eötvös rule captures this relationship, predicting that surface tension decreases roughly linearly with temperature. For water, surface tension drops from about 72.8 mN/m at 20°C to around 58.9 mN/m at 100°C.

Effect of solutes on surface tension

Dissolved solutes can raise or lower surface tension depending on how they interact with the surface.

• Surface-active solutes (surfactants) preferentially accumulate at the interface and decrease surface tension. Soaps and detergents are classic examples.
• Surface-inactive solutes are depleted from the interface and increase surface tension slightly. Inorganic salts like NaCl raise the surface tension of water by a small amount.

Note: the original classification of "positive" and "negative" surface-active agents can be confusing. The key distinction is whether the solute adsorbs at the surface (lowering tension) or is excluded from it (raising tension). The Gibbs adsorption isotherm formalizes this relationship between surface excess concentration and the change in surface tension with solute concentration.

Measurement techniques for surface tension

Du Noüy ring method

A platinum-iridium ring is submerged in the liquid and slowly pulled upward. The maximum force needed to detach the ring from the surface is recorded.

1. Clean the ring thoroughly (platinum-iridium resists contamination).
2. Submerge the ring below the liquid surface.
3. Raise the ring slowly while measuring the force with a sensitive balance.
4. Record the maximum pull force just before the ring detaches.
5. Calculate surface tension from the force, correcting for the ring's geometry (circumference and a correction factor for the meniscus shape).

This method works for both liquid-gas and liquid-liquid interfaces and suits liquids with low to medium viscosity.

Wilhelmy plate method

A thin plate (typically platinum or glass) is partially immersed in the liquid. Rather than detaching it, you measure the steady-state force the liquid exerts on the plate due to wetting.

The surface tension is calculated from:

$\gamma = \frac{F}{L \cos \theta}$

where $F$ is the measured force, $L$ is the wetted perimeter of the plate, and $\theta$ is the contact angle (zero for a fully wetting platinum plate). This method handles a wide range of viscosities and works for both liquid-gas and liquid-liquid interfaces. Because the plate stays in contact with the liquid, it's also well suited for monitoring surface tension changes over time.

Pendant drop method

A drop of liquid is formed at the tip of a capillary tube and allowed to hang. Its shape reflects the competition between surface tension (which tries to make the drop spherical) and gravity (which elongates it).

1. Form a pendant drop at the end of a capillary.
2. Capture an image of the drop profile.
3. Fit the drop shape to the Young-Laplace equation to extract the surface tension.

This is an optical method, so it requires no mechanical contact with the surface. It works well for liquid-gas interfaces and for small sample volumes.

Spinning drop method

This technique measures very low interfacial tensions between two immiscible liquids, which is especially useful in colloid science.

1. Fill a horizontal capillary tube with the denser liquid.
2. Inject a small drop of the lighter liquid into the tube.
3. Spin the tube at a known angular velocity.
4. The drop elongates along the rotation axis as centrifugal force competes with interfacial tension.
5. Measure the drop's length and diameter, then calculate interfacial tension from the drop geometry and rotation speed.

The spinning drop method can measure interfacial tensions as low as $10^{-6}$ mN/m, making it valuable for studying ultralow-tension systems like microemulsions.

Surface tension vs interfacial tension

These two terms describe the same physical phenomenon at different types of boundaries:

• Surface tension refers specifically to a liquid-gas (usually liquid-air) interface.
• Interfacial tension refers to the boundary between two immiscible liquids (e.g., oil-water).

Both arise from the imbalance of intermolecular forces at the interface. Interfacial tension between two liquids is typically lower than the surface tension of either liquid alone, because each liquid provides some attractive interactions to molecules at the boundary. For example, the surface tension of water against air is about 72.8 mN/m, but the interfacial tension of water against n-octane is only about 50.8 mN/m.

Thermodynamics of interfaces

Gibbs free energy of interfaces

Creating new interface costs energy. The Gibbs interfacial energy quantifies this: it's the reversible work needed to create a unit area of interface at constant temperature and pressure.

$dG = \gamma \, dA$

Here, $G$ is the Gibbs free energy, $\gamma$ is the surface or interfacial tension, and $A$ is the interfacial area. This equation tells you that surface tension is literally the free energy per unit area of the interface. Systems spontaneously minimize $G$, which is why they tend to minimize interfacial area.

Young's equation and contact angle

When a liquid drop sits on a solid surface in the presence of a gas, three interfaces meet at a contact line. Young's equation describes the force balance at that line:

$\gamma_{SG} = \gamma_{SL} + \gamma_{LG} \cos \theta$

where:

• $\gamma_{SG}$ = solid-gas surface tension
• $\gamma_{SL}$ = solid-liquid interfacial tension
• $\gamma_{LG}$ = liquid-gas surface tension
• $\theta$ = contact angle measured through the liquid

The contact angle tells you about wettability:

• $\theta < 90°$: the liquid wets the solid (hydrophilic surface for water)
• $\theta > 90°$: the liquid does not wet the solid (hydrophobic surface for water)
• $\theta \approx 0°$: complete wetting (the liquid spreads into a thin film)
• $\theta \approx 180°$: complete non-wetting (superhydrophobic surfaces)

Laplace pressure and curved interfaces

Any curved interface between two fluids has a pressure difference across it. The higher pressure is always on the concave side (inside a bubble or droplet). The Young-Laplace equation gives this pressure difference:

$\Delta P = \gamma \left(\frac{1}{R_1} + \frac{1}{R_2}\right)$

where $R_1$ and $R_2$ are the two principal radii of curvature. For a spherical droplet or bubble with radius $R$, this simplifies to:

$\Delta P = \frac{2\gamma}{R}$

Smaller droplets have higher internal pressure. This has major consequences in colloid science:

• It explains why small bubbles shrink and large ones grow (coarsening).
• It drives capillary rise: liquid climbs in a narrow tube because the curved meniscus creates a pressure difference that pulls liquid upward.
• For a soap bubble (which has two surfaces, inner and outer), the pressure difference is $\Delta P = \frac{4\gamma}{R}$.

Marangoni effect and surface tension gradients

The Marangoni effect is the flow of liquid along an interface driven by a gradient in surface tension. Liquid moves from regions of low surface tension toward regions of high surface tension.

Two common causes of surface tension gradients:

• Thermal Marangoni effect: Temperature differences along the surface create tension gradients (hotter regions have lower tension, so flow moves toward cooler regions).
• Solutal Marangoni effect: Uneven distribution of surfactant along the surface creates tension gradients (regions with more surfactant have lower tension).

The classic example is "tears of wine": alcohol evaporates faster from the thin film of wine on the glass wall, raising the local surface tension. Liquid is then pulled upward along the glass from the lower-tension bulk wine surface, forming droplets that run back down as "tears."

The Marangoni effect also plays roles in welding (affecting weld pool shape), crystal growth, and the self-healing behavior of soap films.

Applications of surface tension

Capillary action in porous media

Capillary action is the movement of liquid through narrow spaces without external pressure, sometimes even against gravity. It results from the combination of surface tension and adhesive forces between the liquid and the channel walls.

The height of capillary rise in a tube of radius $r$ is:

$h = \frac{2\gamma \cos \theta}{\rho g r}$

where $\rho$ is the liquid density, $g$ is gravitational acceleration, and $\theta$ is the contact angle. This is why water rises higher in narrower tubes and why it won't rise at all if the surface is hydrophobic ($\theta > 90°$).

Capillary action is critical in water transport through plant xylem, wicking in textiles, ink movement in paper, and oil recovery from porous rock formations.

Wetting and spreading of liquids

Wetting describes how well a liquid maintains contact with a solid surface. The spreading coefficient $S$ determines whether a liquid will spread into a thin film or bead up:

$S = \gamma_{SG} - \gamma_{SL} - \gamma_{LG}$

• If $S > 0$: the liquid spreads spontaneously.
• If $S < 0$: the liquid forms a droplet with a finite contact angle.

Controlling wetting and spreading matters for coatings, printing, lubrication, and waterproofing.

Emulsion stability and Ostwald ripening

Emulsions are dispersions of one liquid in another immiscible liquid, stabilized by emulsifiers (surfactants) that sit at the droplet interface and lower the interfacial tension.

Ostwald ripening is a key destabilization mechanism. Because of the Laplace pressure, smaller droplets have higher internal pressure and therefore slightly higher solubility (described by the Kelvin equation). Molecules diffuse from small droplets to large ones through the continuous phase, so small droplets shrink and large droplets grow. Over time, this coarsens the emulsion and can lead to phase separation.

Strategies to slow Ostwald ripening include using surfactants that form rigid interfacial films, adding a small amount of a highly insoluble species to the dispersed phase, or reducing polydispersity.

Foams and foam stability

Foams are dispersions of gas bubbles in a liquid (or solid) medium, stabilized by surface-active agents at the bubble interfaces. Foam stability depends on:

• Drainage: gravity pulls liquid out of the thin films between bubbles.
• Coarsening: gas diffuses from small bubbles (high Laplace pressure) to large ones.
• Film rupture: thin films between bubbles can break, causing coalescence.

Surfactants stabilize foams by lowering surface tension and by creating surface elasticity through the Marangoni effect (if a film thins locally, the surfactant concentration drops, tension rises, and liquid is pulled back in). Foam stability matters in firefighting foams, beer and bread production, shaving cream, and many other products.

Flotation processes in mineral separation

Froth flotation separates minerals from waste rock (gangue) based on differences in surface hydrophobicity.

1. Crush the ore and mix it with water.
2. Add collectors (surfactants that selectively adsorb onto the target mineral, making it hydrophobic).
3. Introduce air bubbles into the slurry.
4. Hydrophobic mineral particles attach to the rising bubbles and are carried to the surface as a froth.
5. Hydrophilic gangue particles stay in the water and are discarded.

Flotation efficiency depends on particle size, bubble size, collector type and concentration, and the surface tension of the solution. This process is the backbone of the mining industry for separating copper, zinc, lead, and many other minerals.

Surfactants and their effect on surface tension

Classification of surfactants

Surfactants (surface-active agents) are amphiphilic molecules with a hydrophilic head group and a hydrophobic tail. They adsorb at interfaces and lower the surface or interfacial tension.

They're classified by the charge on their head group:

The choice of surfactant type depends on the application. Anionic surfactants dominate in cleaning products; cationic surfactants are used as fabric softeners and antimicrobials; nonionics are favored where sensitivity to electrolytes matters.

Micelle formation and critical micelle concentration (CMC)

As you add surfactant to a solution, molecules first adsorb at the surface, lowering surface tension. Once the surface is saturated and the bulk concentration reaches the critical micelle concentration (CMC), surfactant molecules begin assembling into micelles.

In a micelle, the hydrophobic tails cluster together in the interior, shielded from water, while the hydrophilic heads face outward into the aqueous phase. This structure minimizes the thermodynamically unfavorable contact between hydrophobic tails and water.

Above the CMC, adding more surfactant increases the number of micelles but does not significantly lower the surface tension further. This is why a plot of surface tension vs. log(concentration) shows a sharp decrease followed by a plateau; the break point is the CMC.

The CMC depends on the surfactant's molecular structure, temperature, ionic strength, and the presence of co-surfactants. Typical CMC values range from about 0.1 mM for long-chain nonionics to around 8 mM for SDS.

Adsorption of surfactants at interfaces

Surfactants adsorb at interfaces because of their amphiphilic structure: the hydrophobic tail orients toward the non-polar phase (air or oil), while the hydrophilic head stays in the aqueous phase.

This adsorption reduces the interfacial free energy, which is why surface tension drops. The Gibbs adsorption equation quantifies the relationship:

$\Gamma = -\frac{1}{RT} \frac{d\gamma}{d \ln c}$

where $\Gamma$ is the surface excess concentration (mol/m²), $R$ is the gas constant, $T$ is temperature, $\gamma$ is surface tension, and $c$ is the bulk surfactant concentration. A steeper drop in surface tension with concentration means greater surface excess (more surfactant packed at the interface).

Surfactant adsorption at interfaces is the basis for detergency, emulsification, foam stabilization, and wetting control.

Experimental methods for studying interfacial phenomena

Surface pressure-area isotherms

Surface pressure-area ($\pi$-$A$) isotherms characterize insoluble monolayers spread at the air-water interface, typically measured using a Langmuir trough.

Surface pressure $\pi$ is defined as the reduction in surface tension caused by the monolayer:

$\pi = \gamma_0 - \gamma$

where $\gamma_0$ is the surface tension of pure water and $\gamma$ is the tension with the monolayer present.

By compressing movable barriers on the trough, you decrease the area available per molecule and record how $\pi$ changes. The resulting isotherm reveals phase transitions in the monolayer (gas, liquid-expanded, liquid-condensed, solid phases) and the monolayer's compressibility. These isotherms are widely used to study lipids, proteins, polymers, and nanoparticle films at interfaces.

Brewster angle microscopy (BAM)

BAM is an optical imaging technique for visualizing monolayers at the air-water interface in real time, without any fluorescent labels or probes.

It exploits the fact that p-polarized light striking an interface at the Brewster angle is not reflected. For a clean water surface, no light reaches the detector. When a monolayer is present, it changes the local refractive index, causing some reflection. This reflected light forms an image of the monolayer's morphology.

BAM achieves a lateral resolution of a few micrometers, which is enough to observe domain structures, phase coexistence, and defects in monolayers during compression.

Langmuir-Blodgett (LB) films

LB films are created by transferring organized monolayers from the air-water interface onto solid substrates.

1. Spread an insoluble monolayer on the water surface of a Langmuir trough.
2. Compress the monolayer to a target surface pressure.
3. Dip a solid substrate vertically through the monolayer at controlled speed.
4. The monolayer transfers onto the substrate during each dipping pass.
5. Repeat to build up multilayer films with precisely controlled thickness (each layer is typically 1-3 nm thick).

LB films allow you to construct thin films with molecular-level control over composition and architecture. Applications include molecular electronics, chemical and biological sensors, optical coatings, and biophysical studies of membrane proteins.