Capillary Action

Why capillary action matters

• Plant water transport. Xylem vessels are typically 10–500 μm in radius. Pure capillary rise can lift water several meters, but the cohesion-tension theory (Dixon and Joly 1894) extends this — transpiration at leaves creates negative pressures of −1 to −10 MPa that the cohesive water column supports, lifting sap to the tops of the tallest trees.
• Paper towels and tissue. Cellulose fiber networks have effective pore radii of 5–50 μm and contact angles around 30°, giving capillary pressures of 2–20 kPa. A typical paper towel absorbs 6 to 10 times its dry weight in water, almost entirely by capillary action plus some hydrogen-bonded water in cellulose.
• Soil moisture and groundwater. Capillary fringe above the water table can extend 0.1–2 m into clays (effective r ~10 μm) but only millimeters in coarse sands. This affects irrigation, contaminant transport, and root water uptake.
• Ink wicking on paper. Inkjet droplet penetration follows Lucas-Washburn dynamics L ∝ √t into porous paper. Print quality depends on balancing capillary driving force (γ cos θ) against ink viscosity to avoid feathering or bleed-through.
• Lab thin-layer chromatography. Solvent front migrates up a silica plate by capillarity, separating compounds by their relative affinity for stationary and mobile phases. R_f values are reproducible to within 0.05 because capillary advance is highly regular.
• Capillary blood flow and microfluidics. Blood capillaries are 5–10 μm in diameter; flow is dominated by surface tension, viscosity, and red-cell deformability. Lab-on-chip devices use channel widths of 10–100 μm where capillary forces drive sample loading without pumps.
• Capillary electrophoresis. A 50 μm fused-silica capillary maintains a stable liquid column under high voltage; capillary action helps fill and stabilize the buffer, while electroosmotic flow drives separation. Modern DNA sequencing on capillary arrays processed billions of reads in the early 2000s before next-gen platforms took over.

Common misconceptions

• Capillary rise alone lifts water to the tops of trees. No — bulk lifting is by transpirational tension. Pure capillary rise in 5 μm xylem gets you only ~3 m. The cohesion of water (with breaking strength up to 15 MPa in fine vessels) is what transmits the pull, and capillary forces matter most for re-establishing columns after cavitation.
• Liquid rises in any narrow tube regardless of material. Only when θ < 90°. Mercury in glass has θ ≈ 140° and is depressed below the bulk level. Polytetrafluoroethylene (Teflon) gives water θ ≈ 110° — water also depresses in a Teflon capillary.
• Capillary action contradicts conservation of energy. It does not — the energy comes from reduction of solid–liquid interfacial energy as the wall is wetted. The system reaches a lower total free energy when the column rises and the wetted area expands.
• Higher viscosity gives a higher rise. Viscosity affects how fast the rise happens (Lucas-Washburn √t scaling), but not the equilibrium height. Glycerol has 1000× higher viscosity than water but rises more slowly to a height set by its own γ, ρ, and θ.
• The rise is independent of tube material. Material enters via the contact angle. Clean borosilicate glass gives water θ ≈ 0°; soda-lime glass with adsorbed organics gives θ ≈ 20°; freshly silanized glass gives θ ≈ 90° (no rise at all). The same physics, different θ.
• Jurin's law works in any size tube. Below ~10 nm the continuum description breaks down — molecular layering and disjoining pressure become important. Above ~3 mm radius (the capillary length for water), gravity dominates and the meniscus is essentially flat.

Derivation of Jurin's law

Consider a vertical glass tube of radius r dipped in a wetting liquid (θ < 90°). At the meniscus, surface tension γ pulls along the contact line, which has length 2πr. The vertical component of this force is γ cos θ × 2πr, pulling the liquid column upward. Gravity opposes this with weight ρ g π r² h, where h is the column height. Balance: 2π r γ cos θ = π r² h ρ g. Solving for h gives Jurin's law: h = 2γ cos θ / (ρgr). For water in glass at 20°C with γ = 0.0729 N/m, θ ≈ 0, ρ = 998 kg/m³, g = 9.81 m/s², the constant 2γ/(ρg) = 1.49 × 10⁻⁵ m². So h(in meters) = 1.49 × 10⁻⁵ / r(in meters). At r = 0.1 mm = 10⁻⁴ m, h = 0.149 m = 14.9 cm.

The same balance can be derived from the Young-Laplace pressure jump across the meniscus. A concave meniscus of radius r/cos θ has Laplace underpressure ΔP = 2γ cos θ / r below atmospheric. The atmospheric pressure outside the tube must therefore push the liquid column up by hydrostatic head ρgh = ΔP, giving the same expression. The two viewpoints — force balance at the contact line and pressure balance in the column — are physically equivalent.

Time-dependent capillary filling follows the Lucas-Washburn equation (Lucas 1918, Washburn 1921). For a horizontal capillary or a vertical capillary far from equilibrium, balance of capillary driving pressure against Poiseuille viscous resistance gives dL/dt = γ r cos θ / (4η L), integrating to L(t) = (γ r cos θ t / 2η)^(1/2). Filling distance scales as the square root of time — doubling the fill distance quadruples the time required. In porous media a tortuosity factor reduces the effective r, but the t^(1/2) scaling is observed across paper, wood, soil, and ceramics.

Capillary rise — Jurin's law applied across systems (water at 20°C unless noted)

System	Effective radius	Predicted h or pressure	Notes
Glass capillary, r = 1 mm	1 mm	1.5 cm rise	Lecture-bench demonstration
Glass capillary, r = 0.1 mm	100 μm	14.9 cm rise	Standard reference
Glass capillary, r = 10 μm	10 μm	1.5 m rise	Microfluidic channel scale
Plant xylem (large vessel)	200 μm	~7.5 cm rise (capillary alone)	Insufficient — needs cohesion-tension
Plant xylem (small tracheid)	5 μm	3 m rise (capillary alone)	Still insufficient for tall trees
Tall tree (redwood, total)	—	up to 116 m (Hyperion)	Driven by transpiration tension up to −10 MPa
Paper towel pore	10–50 μm	30 cm to 1.5 m wick	Multiple parallel pores; θ ≈ 30°
Soil — clay (saturated)	1–5 μm	3–15 m capillary fringe	Slow; viscosity-limited
Soil — sand	50–500 μm	3–30 cm capillary fringe	Fast wetting front
Mercury in glass, r = 1 mm	1 mm	−1.1 cm depression	θ ≈ 140°, cos θ < 0

Capillary rise of different liquids in 0.1 mm radius glass

Liquid	γ (mN/m)	ρ (kg/m³)	θ on glass	h (cm)
Water	72.86	998	~0°	14.9
Ethanol	22.0	789	~0°	5.7
Glycerol	64	1260	~0°	10.4
Olive oil	33	910	~25°	6.6
n-Hexane	17.9	655	~0°	5.6
Acetone	23.5	790	~0°	6.1
Mercury	485	13534	~140°	−5.5

Applications

• Plant transpiration and forestry. Trees lift up to 200 L of water per day per tree from roots to leaves. Capillary forces in fine xylem (radii 5–20 μm) plus the cohesion-tension mechanism (Dixon-Joly 1894) overcome 100+ m of hydrostatic head. Drought stress is fundamentally a capillary-pressure failure when xylem cavitates.
• Paper, textile, and inkjet manufacturing. Wicking specifications for paper towels, diapers, and surgical fabrics are tuned via fiber size, surface chemistry, and pore structure. Inkjet print head designs balance droplet size, capillary uptake into paper, and Marangoni flow during drying to control print quality.
• Soil hydrology and irrigation engineering. Drip-irrigation design and flood-recharge models use Lucas-Washburn-style infiltration laws (the Green-Ampt model). Capillary rise from a water table determines whether crop roots access groundwater between rainfall events.
• Building materials and weathering. Mortar, brick, and limestone have pore networks that wick groundwater upward into walls — the rising-damp phenomenon in old buildings. Damp-proof courses (DPCs) interrupt the capillary path with a non-porous layer.
• Microfluidics and lateral flow assays. Home pregnancy tests, COVID rapid antigen tests, and many point-of-care diagnostics use capillary action through nitrocellulose strips to deliver sample to test lines without pumps. Channel geometry and fiber chemistry are tuned for predictable arrival times of 5–15 minutes.