Peer reviewed method
How Droplet Lab Measures Surface Tension with a Smartphone
Droplet Lab measures surface tension by photographing a hanging drop with a smartphone and fitting its outline with the Young-Laplace equation on the phone itself. The method was published in Colloids and Surfaces A and closely matched a KRÜSS DSA100E for water, ethylene glycol and dodecane (Chen et al., 2017).
How does a smartphone measure surface tension?
Short answer: the phone photographs a drop hanging from a needle, traces its outline, and fits that outline with the Young-Laplace equation. The surface tension that gives the best fit is the result.
Gravity stretches a hanging drop downwards, while surface tension pulls it back towards a sphere. The balance between the two sets the drop's shape, so the shape tells you the surface tension. This approach is called Axisymmetric Drop Shape Analysis (ADSA).
Droplet Lab's version runs the whole analysis on the phone. It was published in Colloids and Surfaces A (Chen et al., 2017). The surface tension measurement guide compares it with other methods.
How does the smartphone setup differ from a traditional tensiometer?
A traditional optical tensiometer uses a scientific camera, precision optics, a light source and a connected computer. The smartphone version keeps the backlight, needle and syringe, and the phone does both the image capture and the calculation.
That makes the setup smaller and removes the camera, optics and computer from the parts list.
What do you need to run a measurement?
- A smartphone that can capture RAW images, so compression does not blur the drop edge.
- Camera focus and digital zoom.
- An accelerometer, used to correct for tilt.
- A needle or capillary of known diameter, used to calibrate the image scale.
- A syringe to form the drop slowly, at about 0.1 mL/min.
- A diffused backlight placed opposite the camera.
- The Droplet Lab app, which analyses the drop shape and solves the Young-Laplace equation.
- Optional: a phone holder to stop hand movement.
How does the measurement work, step by step?
- Capture. Form a pendant drop at the needle tip with the backlight behind it, and record a RAW image. The accelerometer corrects the image if the phone is not level.
- Trace the outline. The app uses Otsu's thresholding method to find the drop edge. This is the measured profile.
- Calculate a theoretical profile. A numerical solver integrates the Young-Laplace equation from the density difference, gravity and starting guesses for surface tension and drop size.
- Fit. The algorithm changes surface tension, drop size and pressure difference until the distance between measured and theoretical profiles is smallest. That surface tension is the result.
- Scale. The known needle diameter converts pixels to real lengths, so the result comes out in mN/m.
What problems does a phone camera create, and how are they solved?
Phones are not scientific cameras, so the method had to handle three problems:
- Different phones. Processors, memory and camera sensors vary between models.
- Digital zoom. It interpolates pixels and can soften the drop edge.
- Tilt. A hand held or poorly levelled phone adds an angle to the image.
The answers are accelerometer based tilt correction, Otsu thresholding for edge detection, calibration against the needle diameter and a phone holder. Together they keep the result independent of the phone model used in the tests (Chen et al., 2017).
How fast is the calculation on a phone?
Fast enough for routine use. In the published tests, one measurement took 353 ms on an LG G4 and 705 ms on a Nexus 5 (Chen et al., 2017). These are 2015 and 2013 models.
How do the results compare with a benchtop tensiometer?
The team measured water, ethylene glycol and dodecane with the phones and with a KRÜSS DSA100E. They also ran the phone software on images taken by the DSA100E. The results closely matched in each case (Chen et al., 2017).
The same method is built into the Dropometer pendant drop tensiometer. Both validation papers are listed in the validation library.
How sensitive is the method to tilt and pixel errors?
Error on synthetic drop profiles under each disturbance (Chen et al., 2017). With ideal images the error was 0.001%; a 0.5° tilt gave an average of 0.357%; random shifts up to ±50 µm averaged −0.168 ± 0.826%.
| Type of Perturbation | Average e (%) | Median e (%) | Maximum e (%) |
|---|---|---|---|
| Ideal image | 0.001 ± 0.006 | 0.000 | 0.141 |
| 0.5° rotation | 0.357 ± 0.231 | 0.377 | 1.388 |
| −5 μm shift | −0.003 ± 0.102 | 0.002 | 0.285 |
| +5 μm shift | 0.266 ± 0.105 | 0.258 | 0.646 |
| −10 μm shift | 0.822 ± 0.188 | 0.832 | 1.342 |
| +10 μm shift | 1.654 ± 0.346 | 1.709 | 2.450 |
| −15 μm shift | 0.111 ± 1.327 | −0.412 | 4.841 |
| +15 μm shift | 0.273 ± 0.182 | 0.233 | 0.979 |
| −20 μm shift | 0.940 ± 0.310 | 0.855 | 2.213 |
| +20 μm shift | 2.057 ± 0.545 | 1.928 | 3.971 |
| −50 μm shift | 2.965 ± 0.899 | 3.043 | 5.692 |
| +50 μm shift | 4.663 ± 2.258 | 4.082 | 15.204 |
| ±5 μm shift | −0.124 ± 0.139 | −0.120 | 0.540 |
| ±10 μm shift | −0.135 ± 0.200 | −0.138 | 1.661 |
| ±15 μm shift | −0.124 ± 0.265 | −0.113 | 1.010 |
| ±20 μm shift | −0.142 ± 0.342 | −0.129 | 4.370 |
| ±50 μm shift | −0.168 ± 0.826 | −0.200 | 4.370 |
Expert Quote
A pendant drop gives you surface tension only when the Young-Laplace fit follows the whole outline of the drop and you control how old the surface is. Read a fresh drop of a surfactant solution too early and you are measuring the clock, not the liquid.
Where can you go deeper?
These pages cover the methods, standards and data behind this post.
- Buying guide: Optical vs force tensiometers
- Glossary: Young-Laplace equation
- Classroom experiment: Exp 3: Surface tension of water and temperature effect
- Open dataset: Surface Tension of Common Liquids
- Tool: Free Contact Angle Tool
- Related post: Measuring Contact Angles with a Smartphone: A Peer-Reviewed Method
Measure surface tension with a pendant drop
See the smartphone pendant drop method run on a real sample, in a short call.
Frequently Asked Questions
Can a smartphone measure surface tension accurately?
In the published method, errors on synthetic drop images were 0.001%, and results closely matched a KRÜSS DSA100E for water, ethylene glycol and dodecane (Chen et al., 2017).
Does the phone model matter?
Results were independent of phone model in the tests. Older or slower phones only take longer: 705 ms on a Nexus 5 against 353 ms on an LG G4 (Chen et al., 2017).
Why does the needle diameter need to be known?
It is the scale bar. The app uses it to convert pixels in the image into real lengths, so the surface tension comes out in mN/m.
What does the Young-Laplace equation do here?
It links the pressure difference across a curved liquid surface to surface tension and curvature. Solving it gives the theoretical drop shape the measured outline is compared with.