Surface tension, wetting & capillarity

Picture the molecules in a glass of water all tugging on their neighbours. Deep inside the liquid a molecule is pulled equally in every direction, so the pulls cancel. A molecule sitting at the top surface has water below but only air above, so it feels a net inward tug. The whole surface therefore behaves like a slightly stretched elastic skin that tries to shrink to the smallest possible area — that tendency is surface tension.

This is why a water strider can stand on a pond, why free droplets are round, and why a slightly overfilled glass can bulge above the rim without spilling: the surface resists being stretched.

Now line the inside of a thin straw with a material that water clings to. The water creeps up the walls to touch more of them, dragging the rest of the liquid up behind it — and the narrower the straw, the higher it climbs, with no pump involved. Shrink that straw to the width of a microfluidic channel and the effect becomes strong enough to fill an entire chip on its own.

At a liquid–gas interface, molecules in the bulk are surrounded on all sides by neighbours they attract and are attracted by, so the net force on them averages to zero. Molecules in the surface layer are missing neighbours on the vapour side, leaving a net inward attraction. Enlarging the surface means dragging more molecules out of the comfortable bulk into this higher-energy interfacial layer, and that costs energy. Surface tension, γ, is exactly that cost: the energy needed to create one unit of new interfacial area, set by the strength of the liquid's cohesive interactions (van der Waals forces, plus hydrogen bonding in water).

Because γ is an energy per unit area (J/m²), it is dimensionally identical to a force per unit length (N/m) — the same quantity written two ways. That is why surface tension can be pictured as a tension pulling along the surface, contracting it. For a clean water–air interface at room temperature γ ≈ 0.072 N/m; many organic solvents sit lower, around 0.02–0.03 N/m. (These are standard tabulated values, quoted here only to give a sense of scale.)

Surface energy versus surface tension: for a simple liquid the two are numerically equal, because a liquid can freely bring new molecules to its surface — stretching the area and creating new area are the same physical act. For a solid this is not generally true: a solid surface can be strained elastically without adding atoms, so the energy to create new surface (surface energy) and the mechanical stress in the existing surface (surface stress) differ. Throughout this lesson we stay in the liquid regime, where 'surface tension' and 'surface energy' can be used interchangeably.

Wetting describes how a liquid spreads on a solid. It is a contest between cohesion — the attraction of the liquid's molecules for each other — and adhesion — their attraction to the solid. When adhesion to the solid outweighs cohesion within the liquid, the drop spreads out; when cohesion wins, it beads up. The outcome is summarised by the contact angle θ, measured inside the liquid at the line where liquid, solid and vapour meet.

A low contact angle means the liquid wets the surface; a high angle means it does not. For water, a surface with θ < 90° is called hydrophilic ('water-loving') and one with θ > 90° hydrophobic ('water-fearing'). θ → 0° is complete wetting (the liquid spreads into a film); θ above roughly 150° with low adhesion is superhydrophobic, as on a lotus leaf. The same surface can wet one liquid and repel another, so 'hydrophobic' always refers to water specifically.

At equilibrium the contact angle is fixed by the balance of the three interfacial tensions meeting at the contact line. Balancing the pull along the solid gives Young's equation — the headline equation below — which ties the observable contact angle to the solid–vapour, solid–liquid and liquid–vapour tensions.

Capillarity is the movement of liquid into narrow spaces driven by these interfacial forces rather than by an external pump. Its engine is the pressure jump across a curved interface, the Young–Laplace relation ΔP = γ(1/R₁ + 1/R₂), where R₁ and R₂ are the two principal radii of curvature and ΔP is the pressure difference, higher on the concave side. A flat interface (infinite radii) has no jump; sharper curvature gives a larger one. For a spherical droplet of radius R both radii equal R, so ΔP = 2γ/R; for a long cylindrical meniscus one radius is effectively infinite, so ΔP = γ/R.

At the microscale surface tension is not a minor correction — it is often the dominant force. Understanding it is what lets you make a channel fill itself, form monodisperse droplets on demand, wick a sample through paper, or (just as importantly) diagnose why a channel refuses to fill or keeps trapping bubbles.

Capillary filling. Because ΔP = 2γ·cos θ / r grows as channels shrink, a hydrophilic microchannel fills itself the instant liquid touches its inlet — no pump, tubing or power. Many point-of-care chips load a sample simply by touching a drop to the port.

Paper and thread (paper microfluidics). Paper is a dense mesh of hydrophilic cellulose fibres — effectively millions of tiny capillaries. Patterning hydrophobic barriers into it channels the wicking, so a finger-prick of blood or a drop of urine flows to reaction zones entirely by capillarity. This underpins low-cost diagnostic strips.

Droplet generation. When two immiscible fluids meet at a T-junction or flow-focusing nozzle, surface tension resists stretching the interface and eventually pinches it into uniform droplets. The ratio of viscous shear to interfacial force — the capillary number Ca = μv/γ — selects the regime (dripping versus jetting) and the droplet size.

Open and passive microfluidics. Remove the channel roof and surface tension holds the liquid in an open groove, giving 'open microfluidics' that is easy to access and pipette into. Related passive-pumping schemes use the higher Laplace pressure of a small droplet (ΔP = 2γ/R) to push liquid toward a larger one, driving flow across a chip with nothing but two drops of different size.