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Contact angle hysteresis

Pronunciation: /ˈkɒntækt ˈæŋɡəl ˌhɪstəˈriːsɪs/

Contact angle hysteresis is the difference between the advancing contact angle θA and the receding contact angle θR of a liquid on a solid: H = θA − θR. It measures how strongly the surface pins the contact line, and so how easily a drop moves.

Also called

CAH Wetting hysteresis Advancing minus receding angle

Related terms

Dynamic contact angles Tilting plate Roll-off / sliding angle

Topics

Wetting Contact angle Sliding angle
Book a 15 minute demo Read the contact angle measurement guide

At a glance

What contact angle hysteresis is, why it decides whether drops stick or roll, and what values look like.

What it is

A real surface does not show one contact angle. As liquid is added, the edge of the drop stays put until the angle reaches θA, then advances. As liquid is withdrawn, the edge holds until the angle falls to θR, then recedes. Any angle in between can be stable.

  • Hysteresis H = θA − θR, in degrees
  • On an ideal smooth, uniform solid, H would be zero

Why it matters

Hysteresis, not the static angle, sets how hard it is to move a drop. Low hysteresis lets rain roll off glass, as in windshield rain repellent performance testing. It also matters for glide, as a ski wax contact angle case study shows. Hysteresis also reveals roughness, heterogeneity and contamination that a single angle hides.

Worked example

Water (γLV = 72.8 mN/m) with θA = 112° and θR = 95°.

  • H = 112° − 95° = 17°
  • cos θR − cos θA = −0.087 − (−0.375) = 0.288
  • Retention force per unit width ≈ 72.8 × 0.288 ≈ 21 mN/m
  • For a 3 mm wide drop: 21 mN/m × 0.003 m ≈ 63 µN

A 20 µL water drop weighs about 196 µN, so it would start to slide near sin α ≈ 0.32, about 19°. Treat this as an estimate: real drops add a shape factor of order one.

Expert view

“The gap between the advancing and receding angle, the hysteresis, is where a surface reveals its roughness, its heterogeneity, and whether something is reacting.”

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

What the terms mean

The two limiting angles and the range of stable angles between them.

Advancing (θ = θA)

The largest angle the drop can hold before its edge moves outward over dry solid. Reached by adding liquid or on the downhill side of a tilted drop.

Pinned (θR < θ < θA)

The contact line stays fixed while the angle changes. A static sessile drop sits somewhere in this window, which is why its angle depends on how it was placed.

Receding (θ = θR)

The smallest angle the drop can hold before its edge pulls back over wetted solid. Reached by withdrawing liquid or on the uphill side of a tilted drop.

On a tilted surface the downhill edge of the drop approaches θA and the uphill edge approaches θR. The drop slides once both limits are reached.

θA Advancing contact angle, degrees
θR Receding contact angle, degrees
H Contact angle hysteresis, θA − θR, degrees
α Tilt angle at which a drop starts to slide, degrees
w Width of the drop footprint across the slope, m

Key equations

Hysteresis and the force it produces on a drop.

Equation: H = θA − θR

Variable legend:

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

Interpretation: A small H means the contact line moves easily. A large H means the surface pins the drop.

When to use: Use it to compare how strongly different surfaces hold drops in place.

Assumptions:

  • θA and θR measured with the same liquid, temperature and line speed
  • Slow enough line motion that viscous effects are small

Common mistakes:

  • Comparing H values from different methods without saying which was used
  • Reading θR from an evaporating drop without checking that the line actually receded

Equation: F ≈ k w γLV (cos θR − cos θA)

Variable legend:

  • F: force needed to start the drop moving (N)
  • k: shape factor of order one that depends on the footprint and angle profile
  • w: footprint width perpendicular to the motion (m)
  • γLV: liquid surface tension (N/m)

Interpretation: The force that holds a drop scales with the cosine difference, not the angle difference. The same H costs more force when the angles are near 90°.

When to use: Use it to link hysteresis to sliding angle: at the onset of sliding, F equals m g sin α.

Assumptions:

  • Contact line at the advancing and receding limits at the onset of motion
  • Homogeneous surface along the drop path

Common mistakes:

  • Using H in degrees as if it were proportional to force
  • Dropping k and quoting the result as exact

How to read it

What a hysteresis value usually tells you about a surface.

Hysteresis is a sensitive surface check because roughness, chemical patches and adsorbed films all pin the contact line. Values for common surfaces are in our contact angle reference values for water, and our measurement method selector helps choose between needle and tilting methods.

From hysteresis to meaning

If you see It usually means Check next
H below about 10° on a smooth sample A clean, chemically uniform surface Whether the static angle is close to the middle of the window
H of several tens of degrees Roughness, chemical heterogeneity or a liquid filled texture (Wenzel state) Surface topography and cleanliness
High θA but very low θR Drops pinned despite high repellency Sliding angle; a high static angle alone does not mean easy roll off
θR keeps falling with each cycle Adsorption, swelling, dissolution or reaction at the surface Repeat cycles and a fresh spot on the sample
θA above 150° and H below about 10° A superhydrophobic surface with air trapped under the drop (Cassie-Baxter state) Whether the state survives pressure, drop impact or time

Common misconceptions

Where hysteresis is most often misread.

A high static contact angle means drops roll off

A static angle says nothing about pinning. Some rough surfaces show high static angles with large hysteresis, so drops stick even when vertical. Report θA and θR, or a sliding angle, as described in our note on reproducible sliding angle measurement.

Hysteresis is just measurement error

It is a real surface property, caused mainly by roughness and chemical heterogeneity that pin the contact line. Adsorption, swelling and reaction add to it. Good technique reduces scatter but cannot remove hysteresis, as students see in experiment 7 on advancing and receding angles and hysteresis.

The Young angle is the average of θA and θR

The average is a convenient estimate, not a law. On some surfaces the equilibrium angle sits closer to one limit, and the cosine average gives a different value. Treat any single equilibrium angle from hysteresis data as approximate.

Related terms

Where contact angle hysteresis sits among other wetting concepts.

Broader term

  • Dynamic contact angles
  • Wettability

Ways to measure it

  • Tilting plate
  • Roll-off / sliding angle
  • Sessile drop

Causes and models

  • Surface roughness and heterogeneity
  • Wenzel model
  • Cassie-Baxter model
  • Three-phase contact line

FAQ

Short answers to the questions people ask most about contact angle hysteresis.

What causes contact angle hysteresis?

Mainly surface roughness and chemical heterogeneity, which create energy barriers that pin the contact line. Adsorbed films, swelling of polymers, and reaction or dissolution at the surface add to it. On an ideal smooth, uniform and inert solid, θA and θR would coincide and hysteresis would be zero.

How do Wenzel and Cassie-Baxter states differ in hysteresis?

When liquid fills the texture (Wenzel state), the contact line is pinned on many edges and hysteresis is usually large. When air stays trapped (Cassie-Baxter state), the drop touches only the tops of the texture and hysteresis can be very low. That is why a lotus leaf sheds water while some rough surfaces hold it.

What is a good contact angle hysteresis value?

It depends on the goal. Self cleaning and rain shedding surfaces aim for hysteresis below about 10°. Smooth, clean coatings often fall in the range of a few degrees to about 15°. Surfaces meant to hold drops, such as some printing or sensing surfaces, can benefit from higher hysteresis.

References

Primary sources and further reading.

1. Joanny, J. F., and de Gennes, P. G. (1984). A model for contact angle hysteresis. The Journal of Chemical Physics, 81(1), 552 to 562. https://doi.org/10.1063/1.447337
2. Gao, L., and McCarthy, T. J. (2006). Contact angle hysteresis explained. Langmuir, 22(14), 6234 to 6237. https://doi.org/10.1021/la060254j
3. Eral, H. B., 't Mannetje, D. J. C. M., and Oh, J. M. (2013). Contact angle hysteresis: a review of fundamentals and applications. Colloid and Polymer Science, 291(2), 247 to 260. https://doi.org/10.1007/s00396-012-2796-6
4. Contact angle measurement guide
5. Dynamic contact angles
6. Roll-off / sliding angle
7. Surface roughness and heterogeneity