Contents

Drop volume

Pronunciation: /drɒp ˈvɒljuːm/

Drop volume is the amount of liquid in the drop used for a contact angle or surface tension measurement, usually given in microlitres (µL). It sets the drop size, which controls how much gravity distorts the shape and how sensitive the result is to evaporation and the needle.

Also called

Droplet volume Drop size Dosing volume

Related terms

Polynomial fitting method Drop shape analysis (DSA)

Topics

Contact angle Surface tension Measurement quality
Book a 15 minute demo Read the contact angle measurement guide

At a glance

What drop volume controls, and why it belongs in every reported result.

What it is

Drop volume is the liquid dispensed for one measurement. One microlitre equals one cubic millimetre, so a 5 µL drop is roughly a sphere about 2 mm across.

  • Set by a syringe, pipette or automatic dispenser
  • Can be fixed (static angle) or changed during recording (advancing and receding)
  • Can be calculated back from the fitted drop profile

Why it matters

Large drops flatten under gravity, small drops evaporate fast and are distorted by the needle. Both shift the measured angle. Keeping the volume consistent is one of the simplest ways to make results comparable between operators, as a polymer tubing extrusion case study shows for production checks.

Typical values

Contact angle drops are usually a few microlitres. The Nature Protocols guide by Huhtamäki and colleagues uses drops between 3 and 10 µL for advancing and receding angles and advises against drops smaller than 3 µL. For water, the capillary length is about 2.7 mm at room temperature, so drops much smaller than that stay close to spherical. Check the volume your own standard or method specifies.

How it is measured

Volume is set when the drop is dispensed and can be checked from the fitted profile. Dosing practice and how volume fits into the full procedure are covered in the contact angle measurement guide.

Expert view

“What a liquid responds to is only the outermost few ångström of a surface: the skin, not the bulk. Change that skin and you change the wetting, even if the material underneath is identical.”

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

What the terms mean

How a sessile drop behaves as its volume grows, and the symbols used.

Small drop (Bo much below 1)

Surface tension dominates and the drop is close to a spherical cap. Evaporation, the needle and edge detection errors weigh more.

Mid size drop (Bo below about 1)

The drop is still nearly spherical near the contact line but slightly flattened on top. A Young-Laplace fit handles the small gravity effect.

Large drop (Bo near or above 1)

Gravity flattens the drop into a puddle. Simple circle fits fail, but the base covers more of the surface and averages out small defects.

For a spherical cap, volume, base radius and contact angle are linked: fix any two and the third follows.

V Drop volume, µL (1 µL = 1 mm³)
a Base (contact) radius, mm
h Drop height, mm
θ Contact angle, degrees
Bo Bond number, gravity relative to surface tension, dimensionless

Key equations

How volume relates to drop geometry, and when gravity starts to matter.

Equation: V = (π h / 6) (3a² + h²)

Variable legend:

  • V: drop volume (mm³ = µL)
  • h: drop height (mm)
  • a: base radius (mm)

Interpretation: Height and base radius from the image give the volume of a small drop directly.

When to use: Use it to check that the dispensed volume matches the drop you actually imaged.

Assumptions:

  • The drop is a spherical cap, so gravity is negligible

Common mistakes:

  • Applying it to large, flattened drops
  • Mixing µL and mL

Equation: V = π a³ (2 − 3 cos θ + cos³ θ) / (3 sin³ θ)

Variable legend:

  • a: base radius (mm)
  • θ: contact angle (°)
  • V: volume (µL)

Interpretation: For the same volume, a higher contact angle gives a smaller footprint. At θ = 90° the drop is a hemisphere and V = 2πa³/3.

When to use: Use it to estimate how large a drop footprint will be on a surface of known angle.

Assumptions:

  • Spherical cap, axisymmetric drop

Common mistakes:

  • Using it near 180°, where sin θ tends to zero and small errors blow up

Equation: Bo = Δρ g a² / γ

Variable legend:

  • Δρ: density difference (kg/m³)
  • g: 9.81 m/s²
  • a: base radius (m)
  • γ: surface tension (N/m)

Interpretation: Below about 1, surface tension shapes the drop. Above it, gravity flattens it.

When to use: Use it to judge whether a chosen volume needs a gravity aware fit.

Assumptions:

  • One length describes the drop size

Common mistakes:

  • Forgetting to convert mm to m before squaring

How to read it

What volume related effects look like in your results.

If results shift when only the drop size changes, volume is part of your measurement and must be reported. Our page on measurement repeatability and reproducibility explains how to separate volume effects from real sample differences, and the repeatability and reproducibility calculator does the arithmetic.

From volume effect to meaning

If you see It usually means Check next
Static angle changes with drop size Hysteresis, gravity or evaporation Advancing and receding angles at fixed volume
Small drops read lower over time Evaporation during the reading Time of reading, humidity, a slightly larger drop
Large spread between operators Volumes dispensed by hand differ Fixed dosing volume and method
Circle fit and Young-Laplace fit disagree Drop large enough for gravity to matter Bond number, use a Young-Laplace fit

Common misconceptions

Where drop volume is most often misjudged.

Contact angle does not depend on drop size

On an ideal surface the Young angle does not. On real surfaces the static angle can, because of hysteresis, gravity and evaporation. Report the volume with every angle so others can compare.

Smaller drops are always more accurate

Very small drops evaporate quickly, are distorted by the needle and have few pixels at the contact line. Very large drops flatten. A consistent, moderate volume is usually the safer choice for comparing samples.

The volume set on the dispenser is the volume on the sample

Some liquid can stay on the needle tip, and drops lose volume to evaporation. Checking volume from the fitted profile catches this. Automated image analysis, discussed in our article on automating contact angle measurement with machine learning, can do this for each image.

Volume only matters for research work

In production quality checks, a changing drop size can look like a changing surface. Fixed volumes keep pass and fail decisions honest. Teams setting up a line can compare options in our guide to the best contact angle goniometer for industrial QA.

Related terms

Where drop volume sits among measurement terms.

Broader term

  • Drop shape analysis (DSA)
  • Contact angle

Related terms

  • Polynomial fitting method
  • Sessile drop method
  • Bond number
  • Capillary length
  • Advancing and receding contact angle

Often confused with

  • Drop weight method (surface tension)

FAQ

Short answers to the questions people ask most about drop volume.

What drop volume should I use for contact angle measurement?

Use the volume your standard or method specifies, and keep it the same for every sample. Without a specified value, drops of a few microlitres are common. The Huhtamäki Nature Protocols guide uses 3 to 10 µL for advancing and receding angles. Always report the volume you used.

Does drop volume affect surface tension measurements?

Yes, for pendant drops. A small drop stays nearly spherical and carries little gravity information, so the fitted surface tension becomes uncertain. Larger drops, closer to detaching from the needle, give more reliable results. Students can explore this in labs from the surface science teaching curriculum hub.

How do I calculate drop volume from an image?

For a small sessile drop, measure the height and base radius and use the spherical cap formula. For larger drops, drop shape software integrates the fitted profile. Comparing your values with a published set, such as the Droplet Lab reference measurement dataset, helps confirm your method.

References

Primary sources and further reading.

1. Huhtamäki, T., Tian, X., Korhonen, J. T., and Ras, R. H. A. (2018). Surface-wetting characterization using contact-angle measurements. Nature Protocols, 13(7), 1521 to 1538. https://doi.org/10.1038/s41596-018-0003-z
2. Drelich, J. (2013). Guidelines to measurements of reproducible contact angles using a sessile-drop technique. Surface Innovations, 1(4), 248 to 254. https://doi.org/10.1680/si.13.00010
3. Drelich, J., Miller, J. D., and Good, R. J. (1996). The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough solid surfaces as observed with sessile-drop and captive-bubble techniques. Journal of Colloid and Interface Science, 179(1), 37 to 50. https://doi.org/10.1006/jcis.1996.0186
4. Contact angle measurement guide
5. Drop shape analysis (DSA)
6. Polynomial fitting method