Contact Angle Simulator: Wettability & Young's Equation

simulator beginner ~8 min
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θ = 54° — moderately hydrophilic

With γ_SV = 72 mN/m, γ_SL = 30 mN/m, and γ_LV = 72 mN/m, Young's equation gives a contact angle of 54° — a moderately hydrophilic surface typical of common polymers.

Formula

cos θ = (γ_SV - γ_SL) / γ_LV (Young's equation)
S = γ_SV - γ_SL - γ_LV (spreading coefficient)
cos θ_apparent = r × cos θ (Wenzel equation)

Where Three Phases Meet

Place a water droplet on a surface and observe its shape. On clean glass it spreads nearly flat; on a waxed car hood it beads up into a near-sphere. The contact angle — the angle at the liquid-solid-vapor boundary — quantifies this wetting behavior and reveals the balance of intermolecular forces at the interface. Thomas Young first described this equilibrium in 1805, long before the molecular origins were understood.

Young's Equation

Young's equation states that the contact angle results from the mechanical equilibrium of three surface tensions pulling at the contact line. The solid-vapor tension pulls the liquid to spread, the solid-liquid tension resists wetting, and the liquid-vapor tension resists deformation. When the solid-vapor energy is high relative to the other two, the liquid spreads (low contact angle); when it is low, the droplet beads up (high contact angle).

From Hydrophilic to Superhydrophobic

Surfaces with contact angles below 90° are called hydrophilic (water-loving), while those above 90° are hydrophobic (water-fearing). Nature achieves extreme non-wetting on lotus leaves through a combination of waxy chemistry and papillae nanostructures that trap air beneath the droplet. Engineers mimic this 'lotus effect' for self-cleaning windows, anti-icing coatings, and drag-reducing ship hulls using fluoropolymers and laser-textured surfaces.

Beyond the Static Angle

Real surfaces show contact angle hysteresis — the advancing angle (liquid spreading) exceeds the receding angle (liquid retracting). This hysteresis, caused by surface roughness and chemical heterogeneity, determines whether a droplet rolls off a tilted surface or remains pinned. Understanding and minimizing hysteresis is critical for designing effective self-cleaning and anti-fog coatings.

FAQ

What is contact angle?

The contact angle is the angle formed at the three-phase boundary where a liquid, solid, and vapor meet. It quantifies wettability: angles below 90° indicate hydrophilic (wetting) surfaces, while angles above 90° indicate hydrophobic (non-wetting) surfaces. It is measured through the liquid phase.

What is Young's equation?

Young's equation relates the contact angle to three interfacial energies: cos θ = (γ_SV - γ_SL) / γ_LV, where γ_SV, γ_SL, and γ_LV are the solid-vapor, solid-liquid, and liquid-vapor surface tensions respectively. Published by Thomas Young in 1805, it remains the foundation of wetting theory.

What makes a surface superhydrophobic?

Superhydrophobicity (contact angle > 150°) requires both low surface energy chemistry (fluorinated or silicone coatings) AND micro/nanoscale surface roughness. The Cassie-Baxter model explains how air trapped in surface textures supports the droplet, dramatically increasing the apparent contact angle.

How is contact angle measured?

The sessile drop method is most common: a small droplet is placed on the surface and photographed from the side. Software fits the droplet profile to extract the contact angle. Dynamic advancing and receding angles reveal contact angle hysteresis, which indicates surface heterogeneity.

Sources

Embed

<iframe src="https://homo-deus.com/lab/surface-chemistry/contact-angle/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub