Contents

Three-phase contact line

Pronunciation: /θriː feɪz ˈkɒntækt laɪn/

The three-phase contact line is the line where a solid, a liquid and a gas (or a second liquid) meet, such as the edge of a drop on a surface. The contact angle is defined at this line, and its pinning and motion control how drops spread, stick and slide.

Also called

Contact line Triple line Wetting line Three phase boundary

Related terms

Dewetting

Topics

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

At a glance

What the contact line is, and why so much of wetting happens there.

What it is

Every sessile drop has a closed contact line around its footprint. It is the only place where all three interfaces, solid liquid, liquid vapor and solid vapor, meet.

  • The contact angle is measured at this line, through the liquid
  • The Young equation is a force balance on this line
  • For a round drop, the line is a circle around the drop footprint

Why it matters

Roughness and chemical patches matter mainly where the contact line sits, not deep under the drop. A pinned line keeps a drop in place; a mobile line lets it spread, recede or slide. Coating defects such as crawling and fisheyes start when the line retreats from a low energy spot, the subject of our use case on stopping fisheyes, craters and crawling.

Worked example

Does line tension change a measured angle? Take κ = 1 × 10⁻¹¹ N, a value in the range predicted by theory, and water (γLV = 0.0728 N/m).

  • Drop footprint radius 1 mm: κ / (γLV R) = 1 × 10⁻¹¹ / (0.0728 × 10⁻³) ≈ 1.4 × 10⁻⁷
  • Footprint radius 100 nm: κ / (γLV R) ≈ 1.4 × 10⁻³

For millimetre drops the shift in cos θ is negligible. Line tension only matters for nanoscale drops or bubbles.

How it is measured

The contact line is located in a side view image as the point where the drop profile meets the baseline. Accurate baseline and edge detection decide the angle you report. The contact angle measurement guide covers the method, and our free contact angle tool shows how the line is picked from an image.

Expert view

“Wettability is set by the top five to ten ångström of a surface: what the liquid actually sees. It doesn't matter what lies beneath; that outermost layer is what you are really measuring.”

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

What the terms mean

What the contact line can do on a real surface.

Pinned line

The line stays fixed while the angle changes, held by roughness or chemical patches. The angle can take any value between the receding and advancing limits.

Advancing line

The line moves outward over dry solid once the angle reaches θA. Spreading, drop impact and coating flow all advance the line.

Receding line

The line moves inward over wetted solid once the angle falls to θR. Evaporation, drainage and dewetting recede the line.

Seen from the side, the contact line is a point at each edge of the drop. Seen from above, it is the outline of the footprint.

θ Contact angle at the line, measured through the liquid, degrees
γSV, γSL, γLV The three interfacial tensions that meet at the line, mN/m
κ Line tension, the excess energy per unit length of contact line, N
R Radius of curvature of the contact line (footprint radius), m

Key equations

The force balance at the line and its correction for very small drops.

Equation: γSV = γSL + γLV cos θY

Variable legend:

  • θY: equilibrium contact angle on an ideal surface (°)
  • γSV, γSL, γLV: interfacial tensions (mN/m)

Interpretation: Horizontal pulls on a unit length of contact line balance at the Young angle.

When to use: Use it to connect the angle at the line to the energies of the three interfaces.

Assumptions:

  • Smooth, rigid, chemically uniform solid
  • Equilibrium; line tension neglected

Common mistakes:

  • Forgetting the vertical component, which a soft solid can feel as a small ridge at the line

Equation: cos θ = cos θY − κ / (γLV R)

Variable legend:

  • κ: line tension (N), which may be positive or negative
  • R: radius of the circular contact line (m)

Interpretation: Line tension adds a curvature term. It shifts the angle only when R is very small.

When to use: Use it for nanoscale drops, bubbles and particles at interfaces.

Assumptions:

  • Circular contact line on a uniform solid

Common mistakes:

  • Explaining millimetre scale drop size effects with line tension when evaporation, gravity or heterogeneity are more likely

How to read it

What the behavior of the contact line tells you.

Watching the line is often more informative than reading a single angle. Typical water angles for common surfaces are in our contact angle reference values for water.

From line behavior to meaning

If you see It usually means Check next
Line stays put while the drop shrinks Pinning by roughness or heterogeneity Receding angle and hysteresis
Footprint is not round Uneven chemistry or anisotropic texture Angles on both sides of the drop and along different directions
Line jumps in steps Stick slip motion over discrete defects Surface cleanliness and defect spacing
Line keeps advancing without stopping Complete wetting; no equilibrium angle A higher surface tension liquid or a cleaner reference surface

Common misconceptions

Where the contact line is most often misunderstood.

The whole area under the drop sets the contact angle

The contact line sets it. A patch or defect in the middle of the footprint has little effect; the same feature at the line can change the angle. This is why surface preparation at the measurement spot matters.

Line tension explains drop size effects

Theory predicts line tension of order 10⁻¹¹ to 10⁻¹⁰ N, too small to matter for millimetre drops. Experimental reports span many orders of magnitude, as reviewed by Amirfazli and Neumann. Size dependent angles in normal practice usually come from gravity, evaporation or heterogeneity.

The contact line needs a liquid touching a solid

A vapor film can lift the liquid entirely off a hot solid, so no contact line forms. That is the Leidenfrost effect, and it is why drops skate on a very hot pan.

Related terms

Where the contact line sits among other wetting concepts.

Defined at the line

  • Contact angle
  • Young equation
  • Dynamic contact angles

Line behavior

  • Contact angle hysteresis
  • Dewetting
  • Roll-off / sliding angle

What affects it

  • Surface roughness and heterogeneity
  • Wenzel model
  • Cassie-Baxter model

FAQ

Short answers to the questions people ask most about the contact line.

Why is it called the three-phase contact line?

Because three phases meet there: the solid, the liquid and the surrounding gas or second liquid. Each pair forms an interface, and all three interfaces end on the same line. The contact angle is the angle between the liquid surface and the solid surface at that line.

What is contact line pinning?

Pinning is when the contact line stays fixed even though the drop volume or shape changes. Roughness, chemical patches and edges create energy barriers the line must cross. Pinning is the reason for contact angle hysteresis and why coffee drops leave a ring as they dry.

What is line tension?

Line tension is the excess energy per unit length of the contact line, analogous to surface tension for an interface. It adds a term to the Young equation that scales with one over the line radius. Theory predicts very small values, so it matters only for nanoscale drops, bubbles and particles.

References

Primary sources and further reading.

1. de Gennes, P. G. (1985). Wetting: statics and dynamics. Reviews of Modern Physics, 57(3), 827 to 863. https://doi.org/10.1103/RevModPhys.57.827
2. Amirfazli, A., and Neumann, A. W. (2004). Status of the three-phase line tension: a review. Advances in Colloid and Interface Science, 110(3), 121 to 141. https://doi.org/10.1016/j.cis.2004.05.001
3. Bonn, D., Eggers, J., Indekeu, J., Meunier, J., and Rolley, E. (2009). Wetting and spreading. Reviews of Modern Physics, 81(2), 739 to 805. https://doi.org/10.1103/RevModPhys.81.739
4. Contact angle measurement guide
5. Dewetting
6. Contact angle hysteresis
7. Dynamic contact angles