Reproduce capillary action — the way a liquid climbs up a narrow tube all on its own, driven only by surface tension. Change the tube diameter, surface tension, contact angle and liquid density to see the capillary pressure, rise height and meniscus shape update in real time.
Parameters
Tube inner diameter d
mm
Inside diameter of the capillary tube
Surface tension σ
mN/m
About 72.8 for water at 20°C, ~22 for ethanol
Contact angle θ
°
Angle between liquid and wall. Below 90° wets and rises, above 90° depresses
Liquid density ρ
kg/m³
Water 998, ethanol 789, mercury 13546
Results
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Tube radius r (mm)
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Capillary (Laplace) pressure (Pa)
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Capillary rise height h (mm)
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Meniscus radius of curvature (mm)
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Liquid column mass (mg)
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Rise / depression verdict
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Capillary tube and reservoir — rise animation
Inside the narrow tube dipped into a wide reservoir, the liquid level settles to its equilibrium height (or depression). The meniscus is drawn concave for a wetting liquid and convex for a non-wetting one.
Rise height vs tube diameter
Rise height vs contact angle
Theory & Key Formulas
$$h=\frac{2\sigma\cos\theta}{\rho\,g\,r}$$
Capillary rise height h from Jurin's law. σ: surface tension, θ: contact angle, ρ: liquid density, g: gravity, r: inner tube radius. The rise is inversely proportional to the tube radius, and a contact angle above 90° gives a depression (negative value) instead of a rise.
Capillary (Laplace) pressure Δp across the curved meniscus, and the meniscus radius of curvature r_m. When cosθ = 0 (θ = 90°) the radius of curvature is infinite and the meniscus is flat.
$$m=\rho\,\pi r^{2}\,|h|$$
Mass m of the raised (or depressed) liquid column, from the tube cross-section πr² and the absolute rise height |h|.
What is the Capillary Rise Simulator?
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In a science class I saw water creep up a thin glass tube standing in a dish of water. There is no pump or anything — how does the water climb up by itself?
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Great question. That is "capillary action". The key is a contest between two forces. One is adhesion — the attraction between the liquid and the tube wall. The other is cohesion — the attraction of the liquid molecules for one another. Water adheres to glass more strongly than it coheres to itself, so it "wets" the glass, climbs the wall, and the curved meniscus that forms uses its surface tension to pull the whole column upward.
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So does mercury climb up the same way?
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It does the opposite. Mercury has very strong cohesion, far stronger than its adhesion to glass. So it does not wet the glass, its meniscus curves the other way (convex), and the liquid inside the tube actually sits lower than outside. That is "capillary depression". What decides up or down is the contact angle θ: below 90° it wets and rises, above 90° it does not wet and is depressed. Push the contact angle up to 150° on the left and you will see the rise height go negative.
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I see! So what sets how high it rises? What happens if I make the tube finer?
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The height comes from Jurin's law, h = 2σcosθ/(ρgr). The key point is that the rise height h is inversely proportional to the tube radius r. So the finer the tube, the dramatically higher the rise. The default 0.5 mm tube of water rises about 60 mm, but at 0.05 mm it climbs close to 600 mm. Look at the "rise height vs tube diameter" chart below and you will see that steep falling curve clearly.
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Does that mean the way plants pull water up from their roots is capillary action too?
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It is an important part of it. The xylem vessels of a plant are very fine tubes, and capillary force helps lift water and nutrients. But carrying water all the way to the top of a tall tree by capillary force alone is impossible — suction from transpiration at the leaves does most of that work. The same physics appears in ink soaking into paper, a lamp wick drawing fuel, and moisture climbing through soil and brick — the cause of "rising damp" in buildings. It is a very familiar and deep phenomenon.
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Can capillary action ever be a nuisance?
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Yes. When you measure a liquid level with a fine glass tube, the capillary rise makes the level look higher (or lower) than it really is. So precise manometers and burettes need a capillary correction. Rising damp in brick and concrete is also a headache in construction, and the fix is a damp-proof course that physically cuts the capillary path. Know the physics and you can both exploit it and defend against it.
Frequently Asked Questions
The capillary rise height h is found from Jurin's law, h = 2σcosθ / (ρgr), where σ is the surface tension, θ is the contact angle, ρ is the liquid density, g is gravity and r is the inner tube radius. The height is set by the balance between the upward pull of surface tension on the curved meniscus and the weight of the raised column. Because h is proportional to surface tension and inversely proportional to the tube radius, the rise grows dramatically as the tube gets finer.
When the contact angle θ exceeds 90°, cosθ becomes negative and the rise height h becomes negative. This means the liquid is depressed below the surrounding level — a capillary depression. Mercury in a glass tube is the classic example: it does not wet the glass, forms a convex meniscus and sits lower inside the tube than outside. At exactly θ = 90°, cosθ = 0, so there is neither rise nor depression.
The capillary pressure is the pressure difference across the curved meniscus, Δp = 2σcosθ / r. For a wetting liquid (θ < 90°) the meniscus is concave and the liquid just beneath it is at a pressure below atmospheric. That pressure difference is what draws the column up. The smaller the radius, the higher the curvature and the larger the capillary pressure — this is the in-tube application of the Young-Laplace equation.
Capillary action is everywhere: water and nutrients climbing from plant roots to leaves, ink soaking into paper and a wick drawing fuel into a flame, moisture rising through the pores of soil, brick and concrete (the cause of rising damp in buildings), and towels and sponges absorbing water. Conversely, capillary rise is an error source in liquid-level measurement with fine tubes and must be corrected for. It also underlies porous-material design and drying processes.
Real-World Applications
Plant water transport and agriculture: As water and dissolved nutrients move from a plant's roots up the stem to the leaves, capillary force in the fine xylem vessels plays an important role. Soil moisture also moves through the countless tiny pores between soil grains by capillary action. In irrigation design and dry-land farming, understanding the capillary rise height of the soil is key to balancing water supply to the roots against evaporative loss.
Rising-damp control in buildings: Brick, mortar and concrete contain countless fine pores, and ground moisture climbs the wall through them by capillary action. This is "rising damp", a cause of paint peeling, mould and salt efflorescence. Remedies include a damp-proof course (DPC) in the foundation that physically cuts the capillary path, and water-repellent treatment that pushes the contact angle above 90° so a rise turns into a depression.
Wicks, absorbents and microfluidics: A lamp or candle wick lifts fuel to the flame by capillary force, and towels, diapers and sponges absorb moisture through capillary action between fine fibres. More recently, microfluidic devices and paper analytical chips (μPADs) widely use designs that move tiny amounts of liquid to a target spot using capillary force alone, with no pump.
Capillary correction in metrology and porous materials: In manometers, burettes and thermometers that use fine glass tubes, capillary rise is a reading error that must be corrected. Conversely, the capillary-rise method uses this same effect to measure the surface tension of a liquid or the contact angle of a material. Evaluating water uptake of porous ceramics, soil and fibre materials, and designing heat-pipe wicks, all rest on an understanding of capillary force.
Common Misconceptions and Pitfalls
A common misconception is that Jurin's law holds for any tube. The formula h = 2σcosθ/(ρgr) is an approximation for a "narrow tube" — one whose radius r is much smaller than the capillary length of the liquid (about 2.7 mm for water), so that the meniscus can be treated as nearly spherical. As the tube widens, the meniscus departs from a sphere and the calculated value comes out higher than reality. This tool handles diameters up to 10 mm, but for tubes larger than a few mm treat the value as a rough guide; wide tubes and containers need a different treatment.
Next, the assumption that the contact angle is an intrinsic property of the liquid. The contact angle is set by the combination of liquid, solid and gas. The same water gives nearly 0° on clean glass but more than 90° on a surface coated with an oil film or silicone. Furthermore, the advancing and receding angles differ ("contact-angle hysteresis"), and surface roughness and contamination matter a lot, so measured contact angles scatter. This tool calculates exactly with the angle you enter, but predicting the real rise height needs a contact angle that matches the actual surface state.
Finally, the idea that capillary action alone can carry water to the top of a tree. Delivering water to the top of a 100 m tree by capillary force alone would require an extremely small xylem radius and cannot be explained that way. In reality the strong negative pressure (tension) created by transpiration at the leaves is the main agent that pulls the water column up; capillary force only contributes part of it. Capillary action is powerful but not all-powerful — it works within a balance of transpiration, osmotic pressure and gravity.