Surface tension and Wettability: Tell me more! (Part 1)

You may have already noticed your coffee mysteriously rising in-between the sugar grains against the basic law of gravity, or the surprising behavior of water drops on the lotus leaves that remains almost spherical instead of spreading down. Those phenomena, respectively called capillary rise and super-hydrophobicity, are manifestations of the surface tension and, more especially, of the wettability. Let’s briefly reviews explain what it means.

Surface tension

Where there is an interface between immiscible (liquid or gas) fluids, there is surface tension. Surface tension arises from the attractive forces of that exist between molecules at the interface. Liquid molecules attract each other, gas molecules too, but those on the interface are missing half of their neighbors. As a result, they experience an attraction towards their side, and a tension arises across the surface layer. This mechanical effect is called surface tension and often denoted γ.

Under the influence of the surface tension, fluid interfaces tend to contract to the smallest possible area and, conversely, increasing fluid interfaces area requires energy. Schematically, these interfaces can be thought as the elasticity of a toy balloon rubber membrane: the higher the balloon rubber elasticity γ, the higher the force that tends to reduce its area (Force = γ · Length), the higher the energy required to inflate it (Energy = γ · Surface), and the higher the pressure gap between inside and outside of the balloon (Laplace Pressure = 2 · γ · Curvature).

Surface tension explains why small drops of water are spherical and why water drips from a faucet: the spherical shape is the one that minimizes the area, and a cylindrical water stream reduces its area when deforming toward individual droplets (so-called Plateau-Rayleigh instability).

Wettability

Wettability comes into play when multiple surfaces compete against each other, each one pulling in its direction. As a result of this competition, a regular contact angle is observed between those interfaces to optimize the total surface tension energy.

Consider the case of a drop of liquid (L), put on a planar solid substrate (S), and surrounded by gas (G). Three interfaces are competing: G/L, G/S and L/S. Their respective surface tensions affect the optimized contact angle Θ between the solid plane and the drop tangent:

• Θ = 90° contact angle. This occurs when the two solid-related interfaces have the same surface tension (γ[G/S] = γ[L/S]). The 90 degrees contact angle reduces the gas/liquid interface area.

• High wettability (Θ < 90°). When the gas/solid interface is more energy-greedy than the liquid/solid one (γ[G/S] > γ[L/S]), the drop spreads on the substrate so that the solid substrate is more covered by the liquid and less by the gas. When water is involved, the substrate is said hydrophilic.

• Low wettability (Θ > 90°). Conversely, when the liquid/solid surface tension is higher than the gas/solid one (γ[G/S] < γ[L/S]), the drop retracts to limit its interface with the solid substrate. When water is involved, the substrate is said hydrophobic.

• A substrate is said super-hydrophilic when the contact angle almost reaches Θ = 0°. The drop tends to spread into a thin layer to cover most of the solid. This happens when the gas/solid surface tension is high enough (γG/S > γL/S + γG/L) such that the two liquid-related interfaces are less costly than a single gas/solid interface. Similarly, a substrate is super-hydrophobic when the contact angle almost reaches Θ = 180°. The drop tends to remain almost spherical above the solid surface.

Industrial interest

The understanding of the surface tension and wettability effects is essential for many industrial applications. This includes for instance windshield rain-repellent treatment, anti-fogging agents, waterproof concrete, self-cleaning materials, experiments under micro-gravity, microfluidic application and multiple chemical processes... Therefore, its proper modeling within numerical simulation can be of crucial interest.

In the following parts of this article, the subtleties in terms of the surface tension modeling will be addressed, from the assessment of a numerical model to their practical applications...