Contents

Pendant drop method

Pronunciation: /ˈpɛndənt drɒp ˈmɛθəd/

The pendant drop method measures surface or interfacial tension from the shape of a drop hanging from a needle. Gravity stretches the drop while surface tension holds it together, and fitting the outline to the Young-Laplace equation gives the tension.

Also called

Pendant drop tensiometry Hanging drop method Pendant drop shape analysis

Related terms

Tensiometer Young-Laplace equation Drop shape analysis (DSA)

Topics

Surface tension Interfacial tension Drop shape
Book a 15 minute demo Read the surface tension measurement guide

At a glance

What the pendant drop method measures, why it is popular, and where it reaches its limits.

What it is

A drop hangs from the tip of a needle, in air or inside a second liquid. Its outline is imaged from the side, traced, and compared with shapes predicted by the Young-Laplace equation. The best match gives the surface or interfacial tension.

  • Optical and contact free: nothing touches the interface
  • Needs only a few microlitres of liquid
  • Works for liquid air and liquid liquid interfaces

Why it matters

Because the drop is imaged rather than pulled, the same setup can follow how tension changes as surfactant adsorbs, measure oil and water pairs, and run on small or precious samples. Imaging hardware has also become cheap, so the method now fits teaching labs, as our guide to the best tensiometer for teaching labs discusses.

Typical values

A well set up pendant drop measurement returns known reference values closely:

  • Water at 20 °C: 72.8 mN/m (about 72 mN/m at 25 °C)
  • Ethylene glycol: about 48 mN/m
  • Hexadecane: about 27.5 mN/m

Checking water first is the usual sanity test. Our Droplet Lab reference measurement dataset gives further comparison values.

Expert view

“The critical micelle concentration is not a number you look up; it is where the surface-tension curve flattens, and the only honest way to know it is to measure it.”

Dr. Alidad Amirfazli, Co-founder and Scientific Advisor, Droplet Lab

What the terms mean

How drop size changes what the outline can tell you.

Small, nearly spherical drop

Surface tension dominates and gravity barely changes the shape. The fit cannot tell close γ values apart, so results scatter.

Large, pear shaped drop

Gravity visibly stretches the drop and narrows a neck near the needle. The outline depends strongly on γ, so the fit is precise.

Drop about to detach

The drop is at its largest stable size. Precision is usually best just below this point, as long as the drop is not vibrating or pinching off.

The needle diameter is usually the length reference that sets the image scale, so its value must be entered correctly.

γ Surface or interfacial tension, mN/m
Δρ Density difference between drop and surrounding phase, kg/m³
R0 Radius of curvature at the drop apex, m
Bo Bond number, Δρ g R0² / γ, dimensionless
de, ds Largest drop diameter, and diameter at height de above the apex, m

Key equations

The model the method fits, and the classical shortcut it replaced.

Equation: γ (1/R1 + 1/R2) = 2γ/R0 − Δρ g z

Variable legend:

  • R1, R2: principal radii of curvature along the profile (m)
  • R0: apex radius of curvature (m)
  • Δρ: density difference (kg/m³); g = 9.81 m/s²
  • z: height above the apex (m)

Every outline belongs to one Bond number, Bo = Δρ g R0² / γ. The fit finds Bo and R0, then γ = Δρ g R0² / Bo.

Interpretation: Curvature is greatest at the bottom of the drop and falls with height, because the pressure inside drops as you move up the column.

When to use: Use it for any pendant drop in air or in a second, less dense liquid.

Assumptions:

  • Axisymmetric drop at rest
  • Known density difference
  • Clean, sharp outline with a known image scale

Common mistakes:

  • Using the drop density instead of the density difference for liquid liquid work
  • Fitting drops that are too small

Equation: S = ds / de ; γ = Δρ g de² / H

Variable legend:

  • de: largest diameter of the drop (m)
  • ds: diameter at height de above the apex (m)
  • H: correction factor from published tables, read off using S

Interpretation: Two diameters capture how much gravity has stretched the drop. It was the standard approach before full profile fitting.

When to use: Use it to read older papers or as a quick cross check on a fitted result.

Assumptions:

  • Same as the Young-Laplace model

Common mistakes:

  • Treating a two diameter estimate as precise as a full profile fit

How to read it

What pendant drop results tell you, and what to check when they look wrong.

A trustworthy result comes from a large, steady, symmetric drop and a fit that follows the whole edge. If you are new to drop images, our free contact angle tool is a quick way to see how edge detection works on a real photo.

From result to meaning

If you see It usually means Check next
Pure water well below 72 mN/m Contamination on the needle, syringe or water Clean the dosing path and repeat with fresh water
Value falls steadily while the drop hangs Surface active material is adsorbing, or the drop is evaporating Whether you need a time resolved reading, and humidity
Large scatter between drops Drops are too small or not steady Drop volume, vibration and needle alignment
Water reads high, above about 73.5 mN/m at room temperature Image scale or needle diameter is wrong Calibration entries in the software

How it is measured

The method in four short steps. The surface tension measurement guide has the full procedure.

1

Form the drop

Push liquid slowly through a clean, square tipped needle until a large drop hangs steadily.

2

Capture the profile

Record a sharp side view against even backlighting, with the needle in frame as the scale reference.

3

Trace and fit

Software detects the edge and fits the Young-Laplace equation to find the apex radius and Bond number.

4

Read the tension

Combine the fit with the density difference to report γ, with temperature and drop age.

Common misconceptions

Where the pendant drop method is most often misunderstood.

Any drop size will do

Small drops are nearly spherical and carry little information about γ. Results become noisy and can drift with volume. Use the largest steady drop the needle holds.

It works for every interfacial tension

When γ is very low, or the two liquids have almost the same density, the drop barely deforms and the fit loses precision. Ultralow IFT systems are usually measured with a spinning drop instead.

One reading is the surface tension

For pure liquids a single steady reading is fine. For solutions with surfactant, tension falls with drop age, so a single number without its age can mislead. Report time, or wait for a plateau.

Related terms

Where the pendant drop method sits among other surface tension concepts.

Broader term

  • Drop shape analysis (DSA)
  • Tensiometer

Related terms

  • Young-Laplace equation
  • Interfacial tension (IFT)
  • Dynamic surface tension (time-resolved pendant)
  • Static surface tension

Often confused with

  • Sessile drop method
  • Drop volume

FAQ

Short answers to the questions people ask most about the pendant drop method.

How does the pendant drop method measure surface tension?

A drop hangs from a needle, and gravity pulls it into a pear shape while surface tension resists. The side profile is imaged and fitted to the Young-Laplace equation. With the density difference and image scale known, the fit returns the surface tension, or the interfacial tension if the drop hangs in a second liquid.

Can the pendant drop method measure interfacial tension?

Yes. The denser liquid hangs from the needle inside the lighter one, for example water in oil. For a lighter drop in a denser liquid, such as oil in water, the needle points upward and the drop rises. You must enter the density difference between the two liquids, not the density of the drop alone.

What is the difference between pendant drop and sessile drop?

A pendant drop hangs from a needle and is used to measure surface or interfacial tension. A sessile drop rests on a solid and is mainly used to measure contact angle. Both rely on imaging the drop profile, and both can use a Young-Laplace fit, but they answer different questions.

References

Primary sources and further reading.

1. Andreas, J. M., Hauser, E. A., and Tucker, W. B. (1938). Boundary tension by pendant drops. Journal of Physical Chemistry, 42, 1001 to 1019.
2. Rotenberg, Y., Boruvka, L., and Neumann, A. W. (1983). Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces. Journal of Colloid and Interface Science, 93(1), 169 to 183. https://doi.org/10.1016/0021-9797(83)90396-X
3. Berry, J. D., Neeson, M. J., Dagastine, R. R., Chan, D. Y. C., and Tabor, R. F. (2015). Measurement of surface and interfacial tension using pendant drop tensiometry. Journal of Colloid and Interface Science, 454, 226 to 237. https://doi.org/10.1016/j.jcis.2015.05.012
4. Chen, H., Muros-Cobos, J. L., Holgado-Terriza, J. A., and Amirfazli, A. (2017). Surface tension measurement with a smartphone using a pendant drop. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 533, 213 to 217. https://doi.org/10.1016/j.colsurfa.2017.08.019
5. Surface tension measurement guide
6. Tensiometer
7. Young-Laplace equation