Contents

Drop shape analysis (DSA)

Pronunciation: /drɒp ʃeɪp əˈnæləsɪs/

Drop shape analysis (DSA) finds interfacial properties by fitting the imaged outline of a drop or bubble to a theoretical shape, usually the Young-Laplace equation. It gives surface and interfacial tension from pendant drops and contact angle from sessile drops.

Also called

Axisymmetric drop shape analysis (ADSA) Optical tensiometry Drop profile analysis

Related terms

Polynomial fitting method Drop volume Young-Laplace equation

Topics

Surface tension Contact angle Method
Book a 15 minute demo Read the surface tension measurement guide

At a glance

What drop shape analysis does, and why one image can give you a surface tension or a contact angle.

What it is

Gravity pulls a drop out of a perfect sphere, and surface tension resists. The balance sets a precise outline. DSA detects that outline in an image and finds the surface tension, or the contact angle, that best reproduces it.

  • Pendant drop: surface or interfacial tension
  • Sessile drop: contact angle
  • Captive bubble: contact angle under liquid

Why it matters

DSA needs only a few microlitres of liquid and no ring or plate in contact with the surface. One optical setup covers wetting and surface tension, which suits research labs and production lines alike. Teams choosing a surface tension method for quality control can compare options in our guide to the best tensiometer for production QC.

Worked example

A pendant water drop at 20 °C has an apex radius R0 = 1.5 mm. The fit returns a shape factor β = 0.302, with Δρ = 997 kg/m³.

  • γ = Δρ g R0² / β
  • γ = 997 × 9.81 × (1.5 × 10⁻³)² / 0.302
  • γ = 0.0220 / 0.302 ≈ 0.0729 N/m ≈ 72.9 mN/m

That sits close to the textbook 72.8 mN/m. Experiment 3 on the surface tension of water and the temperature effect repeats this in a teaching lab.

Expert view

“A contact angle is a thermodynamic property: fix the liquid and the solid and the same angle appears whether the drop sits on a plate or climbs a capillary.”

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

What the terms mean

The three drop geometries DSA works with, and the symbols in the fit.

Pendant drop

A drop hangs from a needle tip. Its elongated, pear like outline gives the surface tension of a liquid, or the interfacial tension between two liquids.

Sessile drop

A drop rests on a solid. The fitted profile gives the contact angle where the outline meets the baseline.

Captive bubble

An air bubble or oil drop is held under a solid immersed in liquid. The profile gives the contact angle of a wet or swollen surface.

The fit compares the detected edge points with a family of computed Young-Laplace profiles and keeps the one with the smallest error.

γ Surface or interfacial tension, mN/m
Δρ Density difference between drop and surrounding phase, kg/m³
g Gravitational acceleration, 9.81 m/s²
R0 Radius of curvature at the drop apex, m
β Shape factor (Bond number at the apex), dimensionless

Key equations

The physics every drop shape fit rests on.

Equation: Δp = γ (1/R₁ + 1/R₂)

Variable legend:

  • Δp: pressure difference across the interface (Pa)
  • R₁, R₂: principal radii of curvature (m)
  • γ: surface or interfacial tension (N/m)

Interpretation: Curvature and pressure are tied together by surface tension. Because pressure changes with height in a drop, so does curvature, which is what shapes the outline.

When to use: Use it as the model the profile is fitted to, for pendant, sessile and captive geometries.

Assumptions:

  • Axisymmetric drop
  • Uniform γ over the surface, at equilibrium

Common mistakes:

  • Fitting a drop that is still growing, vibrating or evaporating quickly

Equation: Δp(z) = 2γ / R0 + Δρ g z

Variable legend:

  • z: vertical distance from the drop apex (m)
  • R0: apex radius of curvature (m)
  • Δρ: density difference (kg/m³)

Interpretation: At the apex the drop is locally spherical. Moving away from it, gravity adds pressure and the curvature changes accordingly.

When to use: Use it to see why a drop needs enough gravity distortion for surface tension to be found reliably.

Assumptions:

  • Sign of z set so the drop is under gravity in the direction measured

Common mistakes:

  • Using the liquid density alone when the outer phase is another liquid

Equation: γ = Δρ g R0² / β

Variable legend:

  • β: dimensionless shape factor returned by the fit
  • Other symbols as above, in SI units, so γ comes out in N/m

Interpretation: The fit returns the shape (β) and the size (R0). Surface tension follows, scaled by the density difference.

When to use: Use it for pendant drop tensiometry of liquids and liquid liquid interfaces.

Assumptions:

  • Accurate image scale and known Δρ at the test temperature

Common mistakes:

  • Forgetting that a 1% error in Δρ gives a 1% error in γ
  • A wrong pixel to millimetre scale, which enters squared through R0

How to read it

What a DSA result tells you, and what to check before you trust it.

A good fit follows the detected edge closely along the whole outline. Check residuals and repeatability before reading meaning into small differences. Our repeatability and reproducibility calculator helps separate instrument spread from real sample differences, and the dataset of client collected wetting measurements shows typical spread in practice.

From DSA result to meaning

If you see It usually means Check next
Surface tension drifts down over minutes Surfactant or contaminant adsorbing at the drop surface Record dynamic surface tension against drop age
Water reads well below 72 mN/m Contamination, or a wrong density or scale value Needle and syringe cleanliness, calibration
Fit error is large along one side Tilted image, uneven lighting or a drop that is not axisymmetric Camera alignment, backlight, needle centring
Results scatter on nearly spherical drops Too little gravity distortion to pin down γ Use a larger drop, close to detaching

How it is measured

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

1

Form the drop

Hang a drop from a clean needle, or place one on the solid, and let it settle.

2

Capture the silhouette

Take a sharp, backlit side image with a known scale.

3

Detect the edge

Software traces the drop outline, and the baseline for sessile drops, to sub pixel precision.

4

Fit and report

The Young-Laplace model is fitted to the edge, giving γ or the contact angle with its fit error.

Common misconceptions

Where drop shape analysis results are most often misread.

DSA is only for contact angles

The same idea measures surface and interfacial tension from a pendant drop. Contact angle is one output, not the whole method. For contact angles, a polymer tubing extrusion case study shows sessile drop DSA replacing by eye readings in quality control.

Any drop size gives the same accuracy

A small, nearly spherical pendant drop carries little gravity information, so the fitted γ becomes uncertain. Drop size and dosing matter as much as the software. Our note on droplet dosing and volume control explains why.

A smooth looking fit means the answer is right

The fit can only be as good as its inputs. A wrong density, a miscalibrated scale or a tilted camera gives a confident but biased result. Check the inputs against a reference liquid such as pure water.

Related terms

Where drop shape analysis sits among other interfacial methods.

Broader term

  • Tensiometer
  • Goniometer

Related terms

  • Young-Laplace equation
  • Polynomial fitting method
  • Drop volume
  • Sessile drop method
  • Pendant drop method
  • Captive bubble method

Often confused with

  • Du Noüy ring method
  • Wilhelmy plate method

FAQ

Short answers to the questions people ask most about drop shape analysis.

What is the difference between DSA and ADSA?

DSA is the general term for extracting properties from a drop outline. ADSA, axisymmetric drop shape analysis, is the formal approach from the Neumann group that fits the full Young-Laplace equation to an axisymmetric drop. Most modern drop shape software uses an ADSA style Young-Laplace fit for surface tension.

Can drop shape analysis measure interfacial tension between two liquids?

Yes. Hang a drop of one liquid inside the other and fit its outline. You need the density difference between the two phases at the test temperature. The method fails when the densities are nearly equal, because the drop then has almost no gravity distortion.

Does drop shape analysis need an expensive instrument?

It needs a sharp, backlit image, a known scale and good fitting software. The Dropometer smartphone drop shape analysis kit does this with a phone camera and automatic edge and baseline detection. Its drop shape method is validated in peer review against a KRUSS DSA100E.

References

Primary sources and further reading.

1. 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
2. del Río, O. I., and Neumann, A. W. (1997). Axisymmetric drop shape analysis: computational methods for the measurement of interfacial properties from the shape and dimensions of pendant and sessile drops. Journal of Colloid and Interface Science, 196(2), 136 to 147. https://doi.org/10.1006/jcis.1997.5214
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. Young-Laplace equation
7. Polynomial fitting method
8. Drop volume