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Tilting plate

Pronunciation: /ˈtɪltɪŋ pleɪt/

The tilting plate method places a drop on a sample and slowly inclines it until the drop starts to slide or roll. It gives the sliding (roll off) angle, and the advancing and receding contact angles at the front and back of the drop just before it moves.

Also called

Tilted plate method Tilting base method Inclined plane method Tilt stage method

Related terms

Roll off / sliding angle Contact angle hysteresis

Topics

Sliding angle Contact angle Method
Book a 15 minute demo Read the sliding angle measurement guide

At a glance

What the tilting plate method measures, and why it answers a different question from a static contact angle.

What it is

A drop rests on a level sample. The stage tilts slowly while a camera watches the drop from the side. As gravity pulls, the front edge steepens and the back edge flattens, until the drop finally moves.

  • Sliding angle α: tilt at which the drop starts to move
  • Advancing angle θA at the downhill edge
  • Receding angle θR at the uphill edge

Worked example

Illustration with the Furmidge balance: a 20 µL water drop (mass 20 mg) with a base width w = 3 mm, θA = 110° and θR = 90°.

  • w γ (cos θR − cos θA) = 0.003 × 0.0728 × 0.342 = 7.47 × 10⁻⁵ N
  • m g = 20 × 10⁻⁶ kg × 9.81 = 1.96 × 10⁻⁴ N
  • sin α = 7.47 / 19.6 = 0.381, so α ≈ 22°

Expert view

“Repellency and mobility are not the same thing: a high contact angle says a drop is repelled, but whether it rolls off is a separate question; the two can even be mutually exclusive.”

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

What the terms mean

What a drop does as the plate tilts, and the symbols used to describe it.

Level plate

The drop is symmetric. The left and right contact angles are equal and the contact line is at rest.

Tilting, drop pinned

The drop deforms but the contact line holds. The downhill angle rises and the uphill angle falls.

Onset of motion

The contact line lets go and the drop slides or rolls. The tilt is the sliding angle, and the edge angles at that moment approximate θA and θR.

Angles are read through the liquid at the front and back of the drop, relative to the tilted surface, not the horizontal.

α Sliding (roll off) angle, tilt of the plate at onset of motion, degrees
θA Advancing contact angle at the downhill edge, degrees
θR Receding contact angle at the uphill edge, degrees
w Width of the drop base perpendicular to the slope, m
m Mass of the drop, kg

Key equations

The force balance behind a sliding drop, and the hysteresis it reveals.

Equation: m g sin α = k w γ (cos θR − cos θA)

Variable legend:

  • m: drop mass (kg); g: 9.81 m/s²
  • α: sliding angle (°)
  • w: base width (m); γ: liquid surface tension (N/m)
  • k: shape factor, taken as 1 in Furmidge's original form

Interpretation: Gravity along the slope must overcome the pinning force set by hysteresis. Small hysteresis or a heavy drop means a low sliding angle.

When to use: Use it to see why sliding angle depends on drop size and on the gap between θA and θR.

Assumptions:

  • Drop just at the onset of motion
  • The shape factor k depends on the drop outline; values below 1 are reported in later work

Common mistakes:

  • Comparing sliding angles from different drop volumes
  • Treating k as a universal constant

Equation: H = θA − θR

Variable legend:

  • H: hysteresis (°)
  • θA, θR: advancing and receding angles (°)

Interpretation: The width of the range in which the contact line stays pinned. It controls how easily drops move.

When to use: Use it alongside the sliding angle to describe mobility on the surface.

Assumptions:

  • Both angles measured on the same drop at onset of motion

Common mistakes:

  • Assuming tilting plate angles always equal those from adding and removing liquid

How to read it

What a tilting plate result usually tells you about a surface.

Sliding angle results are sensitive to drop size and tilt rate, so compare values only under the same conditions. Our note on reproducible sliding angle measurement covers what to keep fixed, and the measurement method selector helps decide whether tilting is the right test.

From tilting plate result to meaning

If you see It usually means Check next
Sliding angle below about 10° with a high contact angle Low hysteresis, water repellent and mobile surface Durability after wear or contamination
High contact angle but the drop sticks at 90° Strong pinning, a sticky surface despite repellency Receding angle, surface texture
The drop moves in jumps Stick and slip on a patchy surface Coating uniformity
Large spread between repeat runs Drop size, tilt rate or position differ Fixed volume and tilt rate, several positions

How it is measured

The method in four short steps. The sliding angle measurement guide has the full procedure.

1

Place the drop

Set a drop of fixed volume on the level sample and let it settle.

2

Tilt the stage

Incline the sample at a steady rate, or in defined steps, while recording side images.

3

Detect the onset

Note the tilt at which the contact line first moves along the slope.

4

Read the edge angles

Read the downhill and uphill angles in the last frame before motion.

Common misconceptions

Where tilting plate results are most often misread.

A high contact angle means a low sliding angle

Repellency and mobility are separate properties. A rough surface in the Wenzel state can show a high static angle while pinning drops firmly. Measure the sliding angle directly when run off matters.

The sliding angle is a material constant

It depends on drop volume, liquid, tilt rate and how long the drop rested. Larger drops slide at lower angles because their weight grows faster than the pinning force. Always report the drop volume with the angle.

Tilting plate angles are the true advancing and receding angles

The edge angles at onset are close to θA and θR but depend on drop shape and volume. Published tilted plate studies report that they can differ from values measured by adding and removing liquid.

Related terms

Where the tilting plate method sits among other wetting concepts.

Broader term

  • Contact angle
  • Drop shape analysis (DSA)

Related terms

  • Roll off / sliding angle
  • Contact angle hysteresis
  • Advancing and receding contact angle
  • Lotus effect

Often confused with

  • Sessile drop method
  • Static contact angle

FAQ

Short answers to the questions people ask most about the tilting plate method.

What is the difference between sliding angle and roll off angle?

Both name the tilt at which a drop starts to move. Roll off is often used for superhydrophobic surfaces, where drops roll, and sliding for surfaces where they slide with more friction. ISO 19403-7 uses the term roll off angle. Report the drop volume either way.

Can the tilting plate method measure contact angle hysteresis?

Yes. The downhill and uphill angles just before the drop moves estimate the advancing and receding angles, and their difference estimates hysteresis. Published work reports that these values can depend on drop size, so compare them with care against angles from the volume change method.

What equipment do I need for a tilting plate measurement?

You need a stage that tilts smoothly, a drop dispenser and a side camera that tilts with the sample. The Dropometer smartphone drop shape analysis kit measures sliding angle as well as contact angle, with automatic edge and baseline detection.

References

Primary sources and further reading.

1. Furmidge, C. G. L. (1962). Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention. Journal of Colloid Science, 17(4), 309 to 324. https://doi.org/10.1016/0095-8522(62)90011-9
2. Pierce, E., Carmona, F. J., and Amirfazli, A. (2008). Understanding of sliding and contact angle results in tilted plate experiments. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 323(1 to 3), 73 to 82. https://doi.org/10.1016/j.colsurfa.2007.09.032
3. Extrand, C. W., and Kumagai, Y. (1995). Liquid drops on an inclined plane: the relation between contact angles, drop shape, and retentive force. Journal of Colloid and Interface Science, 170(2), 515 to 521. https://doi.org/10.1006/jcis.1995.1130
4. ISO 19403-7:2024. Paints and varnishes. Wettability. Part 7: Measurement of the dynamic contact angles and the roll-off angle on a tilt stage. International Organization for Standardization. https://www.iso.org/standard/87267.html
5. Sliding angle measurement guide
6. Roll off / sliding angle
7. Contact angle hysteresis