---
title: "Surface Tension & Capillary Laboratory Interactive Lab | Sandbox Physics"
description: "Can the height a liquid climbs in a thin tube tell surface tension apart from wetting? Not from the height alone."
canonical_url: "https://sandboxphysics.com/labs/capillary-wetting/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/capillary-wetting/"
last_modified: "2026-10-28"
---

M099 · Fluid mechanics

# Surface Tension & Capillary Laboratory

**Can the height a liquid climbs in a thin tube tell surface tension apart from wetting?** Not from the height alone. The rise in a narrow tube depends only on surface tension times the cosine of the contact angle, a combination called the wetting tension. A liquid with weak tension that wets well and one with strong tension that wets poorly can climb to the same height.

Compare capillary tubes of five different bores, look at the actual spherical meniscus in each and switch the imposed contact angle between advancing and receding. Measure the volume-averaged heights to infer the wetting tension.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The model is static: at low Bond number the meniscus is taken as spherical, and the reservoir level is held fixed. Height data determine the surface tension times the cosine of the contact angle; finding the tension alone needs a contact angle known independently. Contact-line dynamics are not solved.

Physics tutorial

## A meniscus as a force balance

**Background** Two separate measurement benches collect data the same way. Each has its own physical law, its own geometry and its own check on when the approximation holds.

**Why it matters** Before you interpret an estimate, connect it to the real geometry, the reference profile and the raw sensor readings.

Start with the essentials

- **Focus question**: Which liquid height belongs in the force balance?
- **One-sentence intuition**: Check first that the approximation applies, then infer parameters from independent raw readings.

### Core mathematical model

#### Force balance on the average column

$$
\rho g\pi r^2\overline h=2\pi r\gamma\cos\theta
$$

The height is the volume-averaged height measured from the fixed reservoir level, and it is negative below that level.

#### Spherical meniscus

$$
\begin{aligned}\overline h&=\frac{2\gamma\cos\theta}{\rho gr}\\\Delta p&=p_l-p_g=-\frac{2\gamma\cos\theta}{r}\end{aligned}
$$

The pressure jump is the reference value for a spherical meniscus at low Bond number. Its sign is opposite for a rising and a depressed column.

#### Gravity compared with capillarity

$$
\mathrm{Bo}=\rho gr^2/\gamma
$$

A spherical shape ignores how gravity varies across the meniscus. Tubes are measured only when this number is at most 0.1; that cutoff is not a universal error tolerance.

#### What the heights can determine

$$
\begin{aligned}\overline h_i&=b+S/r_i\\\widehat{\gamma\cos\theta}&=\rho gS/2\end{aligned}
$$

Fit the heights with a free intercept to infer the wetting tension. Dividing by a separately known cosine of the contact angle gives the tension, except near neutral wetting.

#### The imposed contact angle

$$
\theta=\operatorname{clip}\!\left(\theta_0+b\Delta\theta/2,0^\circ,180^\circ\right)
$$

The angle takes its receding, central or advancing value. These are static cases set by hand; pinning and wetting dynamics are not simulated.

### Common difficulties

#### A reference curve is not an estimate

**Typical misconception** You can read off the estimate without recording any data.

**Better mental model** Clear the recorded data and the estimate disappears. Sensor perturbations can produce unphysical fits; the estimates are neither clipped nor independently calibrated.

### Run the experiment

1. 01

   #### Compare tube radii

   Select Wetting rise, then look at the five menisci and the measurement-station view.

   **What to observe:** Liquid rises higher in narrower tubes. The height at the centre differs from the volume-averaged height.

2. 02

   #### Reverse wetting

   Compare Neutral wetting and Nonwetting depression.

   **What to observe:** The curvature, the signed height and the pressure jump all change together.

3. 03

   #### Compare advancing and receding angles

   Select Angle hysteresis and switch advancing to receding.

   **What to observe:** With the same liquid and the same radius, each imposed angle holds the column at a different static height.

4. 04

   #### Measure the tube array

   Acquire eligible tubes, add height perturbations and export CSV.

   **What to observe:** A straight-line fit of height against inverse radius estimates the wetting tension. At neutral wetting the height cannot determine the tension by itself.

Physical conclusion

A reference curve is not a measurement, and which parameters the data can determine depends on the experiment.

## Related experiments and articles

Dynamic interfaces · Reading path

### Curvature, films, thermal flow and liquid threads

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why surface tension pulls water into beads**](https://sandboxphysics.com/stories/dynamic-interfaces/surface-energy/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)