# Surface Tension & Capillarity - Capillary Rise, Laplace Pressure, Stokes' Law

> Surface tension calculator: animated Jurin capillary rise, Laplace pressure of drops and soap bubbles, drop shapes, Stokes' law settling and a floating needle.

- URL: https://qilingtools.com/en/physics/capillary
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Choose a liquid and a tube material and watch the columns in four tubes of different radii rise or fall with Lucas–Washburn dynamics, with the height, capillary length and validity range from Jurin's law. The other tabs cover Laplace pressure (including two connected soap bubbles and a numerically integrated sessile drop), Stokes settling (an RK4 fall from rest to terminal velocity with a Reynolds-number check and a falling-ball viscometer), and the largest load a water surface can hold up on a needle or a water strider.

## How to use

1. On the Capillary rise tab pick a liquid (water, ethanol, mercury, glycerol, soapy water or custom γ, ρ, μ) and a tube material, then adjust the contact angle and radius
2. Press Dip the tubes to watch the columns move and read the height, h·r, pressure jump and rise time constant
3. On the Laplace pressure tab choose a drop, bubble or soap bubble and a radius, open the valve between two bubbles, and change the drop volume to see the Bond number and shape
4. On the Stokes' law tab pick a fluid, sphere material and radius, release the sphere to compare pure Stokes drag with corrected drag, or enter a measured time to get the viscosity
5. On the Needle & water strider tab change the needle diameter or the strider's legs to see whether it floats and by what margin

## Features

- Jurin's law with a Lucas–Washburn rise animation and concave or convex menisci drawn from the contact angle
- Laplace pressure for drops, bubbles and two-film soap bubbles, plus the true equilibrium of two connected bubbles
- Sessile drop shapes from the Young–Laplace equation, compared with a spherical cap of equal volume
- Stokes terminal velocity, Reynolds-number validity check and an RK4 fall including added mass
- Falling-ball viscometer with optional Faxén wall correction
- Maximum support for a floating needle or water strider, with the meniscus profile and force arrows

## FAQ

### Why does water climb higher in a thinner tube?

The weight of the column, ρgπr²h, is held up by the vertical pull of surface tension around the rim, 2πrγcosθ. Setting them equal gives h = 2γcosθ/(ρgr), so the height scales as 1/r. Water rises about 3 cm in a clean 0.5 mm glass tube and about 30 cm in a 0.05 mm one. The formula is accurate only when r is much smaller than the capillary length ℓc = √(γ/ρg), about 2.7 mm for water. In wider tubes gravity flattens the meniscus and the real rise falls short of the formula.

### Why does mercury go down in a glass tube?

Mercury does not wet glass. Its contact angle is about 140°, so cosθ is negative and h is negative: the level inside sits below the outside level under a convex meniscus. Water in a paraffin or PTFE tube (contact angle above 90°) is depressed in the same way. Contact angles depend on the liquid–solid pair and on cleanliness, so real values may differ from the presets.

### Why does the small soap bubble empty into the big one?

A soap bubble has two films, so the pressure jump is ΔP = 4γ/R and smaller bubbles have higher pressure. Air flows from the small bubble to the large one, the small one shrinks, its pressure rises further and the process runs away. Once the small bubble shrinks past a hemisphere, though, the cap on the tube flattens and its radius grows again. Flow stops when both curvatures match, leaving a shallow cap attached to a bigger bubble.

### When is Stokes' law valid?

It assumes slow creeping flow where inertia is negligible, which needs a Reynolds number Re = ρv·2r/μ well below 1 (Re < 0.1 keeps the error near 1–2%). Small steel balls in glycerol or honey, fog droplets and fine dust in air qualify. A few-millimetre steel ball in water has Re in the thousands, and Stokes' law overestimates its terminal speed many times over. The tool also uses the Schiller–Naumann drag law and shows both results.

### How can a water strider or a steel needle float?

The object presses a small dimple into the surface. The water on each side pulls up along the surface at angle ψ, giving γ sinψ of vertical force per unit length, and the dimple also displaces some water for extra buoyancy. Support peaks near ψ ≈ 90° at roughly 2γL plus buoyancy. A 1 mm steel needle weighs only about a third of that, so it floats if laid down gently. Counting surface tension alone the limit is about 1.5 mm in diameter, or about 2 mm with the dimple's buoyancy. Adding soap cuts γ to roughly a third, the maximum support drops sharply, and a thicker needle that was floating sinks.

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