Peer reviewed method
Measuring Contact Angles with a Smartphone: A Peer-Reviewed Method
A smartphone can measure contact angle by photographing a drop on a surface, finding where the drop meets the surface and fitting its outline. In the peer reviewed method published in Review of Scientific Instruments, the average error on 2,049 synthetic drops was 0.01%, and results on five real surfaces closely matched a KRÜSS DSA100E (Chen et al., 2018).
How can a smartphone measure contact angle?
Short answer: a phone photographs a drop sitting on a surface against a backlight, finds the drop outline and the two points where it meets the surface, and fits the outline to calculate the angle. In the peer reviewed version of this method, the error on 2,049 synthetic drops was 0.01% on average, and results on five real surfaces closely matched a KRÜSS DSA100E (Chen et al., 2018).
Contact angle is the angle a liquid makes where it meets a solid. It shows how well a liquid wets a surface, which is why it is used to check cleaning, surface treatment, coatings and adhesion. The contact angle measurement guide covers the basics.
Why measure advancing and receding angles, not just one angle?
A perfectly smooth, uniform surface would show a single angle, Young's contact angle. Real surfaces are rough or chemically patchy, so a drop can sit at any angle between two limits:
- Advancing angle (θa): measured while the drop grows and its edge moves forward.
- Receding angle (θr): measured while liquid is withdrawn and the edge pulls back.
A drop that is simply placed and read gives an angle somewhere in between, which is hard to compare from one test to the next. That is why the smartphone method was built to measure advancing and receding angles as well as static ones.
How does the smartphone setup compare with a benchtop goniometer?
A benchtop goniometer combines a camera with optical zoom, a backlight, a sample stage, a syringe and a computer. The smartphone instrument keeps the stage, syringe and backlight and lets the phone handle imaging and calculation. It has four modules (Chen et al., 2018):
- Smartphone. The tests used an LG G5 capturing RAW images, with digital zoom and no external lens.
- Drop dispensing. A 500 µL syringe with a threaded plunger for fine manual control.
- Stage. Holds and levels the sample.
- LED backlight. Diffused light for a sharp, high contrast drop silhouette.
How does the software find the drop outline?
- Capture. A sessile drop, for example water, is placed on the sample and the phone records its silhouette against the backlight.
- Trace the outline. Otsu's thresholding separates the drop from the background. It copes well with the slightly soft edges that digital zoom produces.
- Find the contact points. The software locates the two points where the drop meets the surface. This is the hardest step and the one that decides the accuracy of the angle.
How are the contact points detected automatically?
The method handles three cases (Chen et al., 2018):
- Drops with a reflection. On a shiny surface the drop and its mirror image are both visible. At the contact point the slope of the outline changes sign, so the software tracks neighbouring slopes until that change appears.
- Drops without a reflection. The slope of the outline flattens to zero beyond the contact point, and the software detects that plateau.
- Drops near 90°. The edge is almost vertical, so the slope may never change sign. The software looks for at least 8 vertical outline points in a row and places the contact point one third of the way up that stack, a rule set from about 100 test images.
The user taps the screen to mark a rough contact line first. That guides the search to the right area and prevents false detections.
Which fitting methods calculate the angle?
- Young-Laplace fitting. Fits the whole drop outline to the Young-Laplace equation. It works best for symmetric drops with no needle in them and is less affected by small local defects on the surface.
- Polynomial fitting. Fits a second order polynomial to the part of the outline near the contact point. It is faster and still works when a needle in the drop breaks the symmetry.
How accurate is the method on synthetic drops?
The team tested both fitting methods on 2,049 computer generated drop profiles with angles from 10° to 162°. Average and median errors were 0.01% for both methods; the maximum was 0.09% for Young-Laplace and 0.06% for polynomial fitting (Chen et al., 2018).
Synthetic drops have perfect edges, so these numbers show the accuracy of the calculation itself. Real samples add lighting, focus and surface effects, which is why the next step was a side by side test on real surfaces.
How do static angles compare with a KRÜSS DSA100E?
Both instruments imaged the same drops at the same time from perpendicular directions, on five surfaces from hydrophilic glass to a superhydrophobic coating. With Young-Laplace fitting the two instruments agreed within about 1.5° on glass, PMMA, polystyrene and Teflon AF, and within about 3° on the superhydrophobic surface (Chen et al., 2018). Water on glass read about 37° rather than near zero because of imperfections on the glass, but both instruments read the same value.
| Surface and drop | Young-Laplace, smartphone (°) | Young-Laplace, commercial (°) | Polynomial, smartphone (°) | Polynomial, commercial (°) |
|---|---|---|---|---|
| Glass 1 | 39.3 | 39.5 | 41.7 | 37.4 |
| Glass 2 | 37.1 | 37.8 | 40.3 | 36.6 |
| Glass 3 | 36.9 | 37.7 | 37.2 | 36.8 |
| PMMA 1 | 74.3 | 73.8 | 75.9 | 73.1 |
| PMMA 2 | 72.3 | 73.7 | 75.1 | 72.7 |
| PMMA 3 | 72.7 | 73.1 | 73.0 | 72.3 |
| PS 1 | 95.5 | 95.6 | 92.1 | 92.5 |
| PS 2 | 90.3 | 90.9 | 89.6 | 89.7 |
| PS 3 | 90.0 | 90.8 | 88.1 | 89.7 |
| Teflon AF 1 | 122.0 | 123.3 | 119.5 | 123.2 |
| Teflon AF 2 | 119.7 | 119.9 | 119.4 | 118.8 |
| Teflon AF 3 | 121.8 | 123.5 | 119.3 | 121.7 |
| Superhydrophobic 1 | 149.3 | 152.4 | 148.2 | 149.8 |
| Superhydrophobic 2 | 156.5 | 158.8 | 149.3 | 154.3 |
| Superhydrophobic 3 | 156.4 | 154.4 | 145.5 | 150.5 |
How are advancing and receding angles measured with the phone?
- A 50 µL drop is placed on the surface.
- For the advancing angle, liquid is added through the needle at 3 µL/s using the threaded syringe.
- For the receding angle, liquid is withdrawn at the same rate.
The needle stays in the drop, so the outline is no longer symmetric. Only polynomial fitting is used here, applied to the edge near the contact point where the needle does not distort the shape (Chen et al., 2018).
How do advancing and receding angles compare with a KRÜSS DSA100E?
Average of three drops per surface. Advancing angles agreed within about 2° on four of the five surfaces and receding angles fell within the measurement scatter of both instruments (Chen et al., 2018).
| Surface | Advancing, smartphone (°) | Advancing, commercial (°) | Receding, smartphone (°) | Receding, commercial (°) |
|---|---|---|---|---|
| Glass | 46.1 ± 1.5 | 45.1 ± 2.3 | 19.05 ± 1.4 | 19.3 ± 3.0 |
| PMMA | 76.3 ± 1.5 | 76.5 ± 0.7 | 57.6 ± 1.9 | 55.7 ± 1.4 |
| PS | 108.3 ± 1.8 | 107.6 ± 1.1 | 69.0 ± 2.8 | 67.5 ± 1.0 |
| Teflon AF | 124.8 ± 1.2 | 123.1 ± 2.9 | 110.3 ± 2.8 | 110.2 ± 1.5 |
| Superhydrophobic | 150.12 ± 2.8 | 152.92 ± 1.7 | 148.3 ± 3.1 | 150.1 ± 2.7 |
Expert Quote
Place a drop and just read it and you get an apparent angle — a value somewhere between advancing and receding that isn't much use. Zisman settled that in the fifties.
What does this mean for contact angle testing in a lab or on a line?
The study shows that drop shape analysis does not depend on an expensive camera. The accuracy comes from the image processing and fitting: a clean outline, reliable contact points and the right fitting method for the drop.
The Dropometer is built on the same approach, with automatic edge and baseline detection, static, advancing and receding angles, and setup in about 2 minutes. Zeus ran its own Gage R&R on it in production and it passed. If you are comparing instruments, the Dropometer and KRÜSS DSA100 comparison sets the two side by side.
Where can you go deeper?
These pages cover the methods, standards and data behind this post.
- Measurement quality: Droplet dosing & volume control
- Open dataset: Data in Brief dataset 2: Droplet Lab reference measurements
- Tool: Free Contact Angle Tool
- Related post: Developing Automatic Edge and Baseline Detection for Contact Angle Measurement
- Related post: How Droplet Lab Measures Surface Tension with a Smartphone
Measure contact angle on your own samples
See static, advancing and receding angles measured with automatic edge and baseline detection, in a short call.
Frequently Asked Questions
Is a smartphone accurate enough to measure contact angle?
In the peer reviewed method, the average error on 2,049 synthetic drops was 0.01%, and static angles agreed with a KRÜSS DSA100E within about 1.5° on four of five real surfaces and within about 3° on a superhydrophobic one (Chen et al., 2018).
Which phone was used in the study?
An LG G5 capturing RAW images, with digital zoom and no external lens. RAW capture matters because compression blurs the drop edge.
When should I use Young-Laplace fitting rather than polynomial fitting?
Use Young-Laplace fitting for symmetric drops with no needle in them. Use polynomial fitting when a needle stays in the drop, as in advancing and receding measurements, because it only needs the edge near the contact point.
Why did water on glass read about 37° instead of close to zero?
Clean, smooth glass should be almost fully wetted, so the higher angle points to contamination or imperfections on the glass used. Both instruments measured the same value, which is what the comparison tested.
Can the method measure advancing and receding angles?
Yes. Liquid is added and withdrawn at 3 µL/s through a needle in a 50 µL drop, and polynomial fitting is applied near the contact point. Results matched the commercial instrument within the scatter of both (Chen et al., 2018).