Surface tension is a force per unit length, γ = F / L, and it decides both how round a drop sits and how far a liquid climbs a narrow tube. Drag the sliders below to change the tension, the contact angle, the drop volume and the tube radius, and watch the bead, the Laplace pressure and the capillary column respond in real time.
Surface Tension, Beads & Capillary Rise
Surface tension is a force per unit length, γ = F / L. Change it and watch a drop bead up, the Laplace pressure ΔP = 2γ/R climb, and water in a narrow tube climb to h = 2γcosθ / (ρgr).
Surface tension γ = F / L
72.8 mN/m
0.0728 N/m · water at 20 °C
Laplace pressure ΔP = 2γ/R
34.36 Pa
R = 4.24 mm · droplet
Bead height
2.12 mm
free cap: γ cannot raise it
Capillary length a = sqrt(γ / ρg)
2.72 mm
taller beads get flattened
Surface tension γ72.8 mN/m
Contact angle θ60°
Drop volume V50 µL
Liquid surfaces
Liquid density ρ = 1000 kg/m³ · g = 9.81 m/s²
Tip: push the contact angle past 90° and switch to the tube — cosθ turns negative and the column is pushed below the reservoir. That is the mercury case, and it is correct.
What Is the Surface Tension Simulator?
The surface tension simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Drag the tension, contact angle and tube radius sliders to watch a drop bead up and water climb a capillary. It reports surface tension γ, laplace pressure ΔP, bead height and capillary length as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Surface tension | 5 – 500 mN/m | 0.1 |
| Contact angle | 0 – 160 ° | 1 |
| Drop volume | 1 – 200 µL | 1 |
| Capillary tube radius | 0.05 – 5 mm | 0.01 |
Four Sliders, and the One Number They All Feed
Every readout on this lab traces back to a single quantity. The Surface tension slider sets γ in millinewtons per metre, from 5 at the bottom of the range to 500 at the top — wide enough to run from liquid nitrogen, through water at 72.8, to mercury. Watch what moves with it. The Laplace pressure readout climbs in direct proportion, because ΔP = 2γ/R puts γ straight in the numerator. The capillary length, a = sqrt(γ/ρg), climbs too, but only as a square root, so it lags behind. And the bead grows taller — up to a point. Keep pushing γ and the height stops moving altogether, because once the drop has reached its free spherical-cap shape, more tension has nothing left to lift. That ceiling is the honest answer, and the readout says so.
The Contact angle slider is the one that corrects a misconception. It is easy to assume a liquid in a thin tube always climbs, and that a narrower tube simply climbs faster. Switch to Capillary tube, then walk θ up past 90°. The cosθ in h = 2γcosθ/(ρgr) turns negative, and the column inverts: it settles below the reservoir line instead of above it. That is not a glitch in the drawing. It is what mercury does in a glass tube, at a contact angle near 140°, and it is why "capillary action" is a direction as well as a size. Sitting exactly at 90° the rise is precisely zero, and the liquid stays level with the dish. If you want that same behaviour as a number to check against, the surface tension calculator solves the same equation and reports the negative value too.
The remaining two sliders each own one scene. Tube radius shows the 1/r law directly: halve the bore and the column doubles, every time, which is why a 0.05 mm capillary lifts water by metres while a drinking straw barely lifts it at all. Drop volume proves the opposite kind of limit. Small drops grow taller as you add liquid; large ones do not. Once the bead passes the dashed line drawn at 2a sin(θ/2), its weight beats the tension holding it up, the top goes flat, and every further microlitre spreads it sideways instead. The Droplet / Bubble buttons change nothing about the liquid — they change how many surfaces are counted, one for a droplet and two for a soap bubble, which doubles the excess pressure exactly.
The full account of where that surface skin comes from, and the everyday effects it explains, is in the guide to surface tension. Since the Laplace reading is a pressure like any other, it adds to whatever the surroundings already supply — the background on that, including how pressure grows with depth, is in pressure in physics, and the matching tool is the Pressure Simulator.
Frequently asked questions
Why does the column go negative above 90 degrees?
Because capillary rise is h = 2 gamma cos(theta) / (rho g r), and the cosine of any angle past 90 degrees is negative. The liquid does not wet the glass, so instead of being pulled up it is pushed down, and the column settles below the surrounding reservoir. That is a capillary depression, and mercury in a glass tube does exactly this. The lab draws it below the reservoir line rather than clamping it to zero, because the minus sign is the physics, not an error.
What does the capillary length readout mean?
The capillary length a = sqrt(gamma / rho g) is the size at which surface tension and gravity are evenly matched. It is about 2.7 mm for water. Below that scale surface tension wins and a drop holds a rounded shape; above it gravity wins and the drop is squashed into a flat puddle. The lab draws the resulting limit on the canvas as a dashed line at 2a sin(theta/2), so you can see the moment the bead stops growing upward and starts spreading sideways instead.
Why is the bubble pressure double the droplet pressure?
A liquid droplet has a single curved surface, so the excess pressure inside it is 2 gamma / R. A soap bubble is a thin shell with two surfaces, an inner one and an outer one, and each contributes its own 2 gamma / R. Switching the lab from Droplet to Bubble at the same radius therefore doubles the reading exactly, from 2 gamma / R to 4 gamma / R. It is a change in how many surfaces are counted, not a change in the liquid.
What units are the sliders in?
Surface tension is in millinewtons per metre, running from 5 to 500 mN/m, which spans liquid nitrogen at the bottom to mercury near the top; water sits at 72.8 mN/m. The contact angle is in degrees, 0 to 160. Drop volume is in microlitres, 1 to 200. Tube radius is in millimetres, 0.05 to 5. Internally the tension is divided by 1000 to give N/m and the angle is converted to radians, so every readout is in SI.
Why does the bead flatten when I increase the volume?
A small drop is held in a rounded spherical cap by its own surface tension. As you add volume the cap grows taller, but only until it reaches the gravity-flattened limit 2a sin(theta/2), where the weight of the extra liquid overcomes the surface pulling it up. Past that point the height stops rising entirely and every further microlitre spreads the drop sideways instead. The lab pins the top flat at that limit and widens the base, keeping the volume and the contact angle correct.
References & formula source
- de Gennes, Brochard-Wyart & Quéré — Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, Chapter 2 (capillary length and puddle thickness).
- Young & Freedman — University Physics with Modern Physics, §14.3 (Surface Tension) and the discussion of capillarity.
- Bush, J. W. M. — MIT 1.63J/2.21J, Surface Tension Module, Lecture 1: definition, units and scaling.
- Further reading: Surface tension — Wikipedia