Surface tension and capillarity

In fluid mechanics, it is essential to understand the concepts of surface tension and capillarity because they explain many everyday observations and natural phenomena. These concepts not only tell us about how fluids interact with surfaces, but also about the forces acting within the fluid. The following lesson explores these two interesting aspects of fluid mechanics.

What is surface tension?

Surface tension is a property of liquid surfaces that makes them 'feel' like a stretched elastic membrane. This phenomenon is caused by cohesive forces between liquid molecules. Surface tension is responsible for the shape of liquid droplets and for insects being able to walk on water, as well as many other effects.

At the molecular level, each molecule inside a liquid is pulled equally in every direction by neighboring molecules, resulting in a net force of zero. However, a molecule at the surface of a liquid does not have other molecules around it in all directions; it experiences significant forces only from the molecules beneath it. This imbalance shrinks the surface and reduces surface area, which contributes to the phenomenon we observe as surface tension.

In the above illustration, the red lines indicate forces acting on the surface molecule that are directed inwards, causing a 'stretched' surface effect.

Mathematics of surface tension

Surface tension (denoted by σ or T) is usually measured in newtons per meter (N/m). It can be defined as the amount of energy per unit area that is required to increase the surface area of a liquid. An alternative definition is the force applied per unit length along a line perpendicular to the surface.

In mathematical terms, surface tension can be expressed by the formula:

σ = F/L

where F is the force and L is the contact length.

Examples of surface tension

The simplest example of surface tension is water droplets on a waxed car. Wax is hydrophobic (repels water), so when water is placed on its surface, the cohesive forces within the liquid cause it to form droplets, minimizing the contact with the surface and the surface area of the liquid.

Another common example is the ability of a small needle to float on the surface of water, even though it is denser than the water. Surface tension in water efficiently supports the needle by creating a "skin" effect on the surface.

What is capillarity?

Capillarity or capillary action is the ability of a fluid to flow through narrow spaces without the aid of external forces such as gravity or even in opposition to them. This behaviour is observed when a fluid rises through a thin tube, porous material or any other confined space.

Explanation of capillarity

Capillarity is caused by adhesive forces between the fluid and the walls of the tube or porous substance, as well as the surface tension of the fluid. Adhesive forces refer to the attraction between molecules of different substances, such as water molecules and glass molecules in a capillary tube.

When the adhesive forces between the fluid and the tube's material are stronger than the cohesive forces within the fluid, the fluid will rise in the tube. Conversely, if the cohesive forces dominate, the fluid will fall, or the surface will become concave.

Mathematics of capillarity

The height to which a liquid will rise in a capillary tube is given by the formula:

h = (2σcosθ) / (ρgr)

Where:

• h is the height to which the liquid rises.
• σ is the surface tension of the liquid.
• θ is the contact angle between the liquid and the tube surface.
• ρ is the density of the fluid.
• g is the acceleration due to gravity.
• r is the radius of the tube.

Examples of capillarity

A classic example of how capillarity works is a thin glass tube, such as a straw, placed in water. The capillary effect will cause the water inside the straw to rise higher than the water level outside.

Capillarity is also important in the way plants move water from their roots through tiny pores in their leaves. Through tiny tubes called xylem, water is pulled upward against gravity, which helps provide moisture and nutrients to the entire plant.

Comparison of surface tension and capillarity

Surface tension and capillarity both involve interactions at the surface of liquids, but they focus on different aspects:

• Surface tension: It emphasizes the cohesive forces between molecules within a liquid, which causes the surface to act like a stretched membrane.
• Capillarity: This involves both the cohesive forces within a fluid and the adhesive forces between the fluid and an external surface, which are relevant to phenomena occurring in narrow spaces.

Understanding these concepts helps us understand why some objects float, why liquids form droplets, how plants drink water, and many other phenomena in nature and industry.

Conclusion

Surface tension and capillarity demonstrate the power of intermolecular forces and their substantial impact on natural and practical applications. In many situations, these forces challenge the forces expected in large-scale interactions, demonstrating the dynamic and complex behavior of fluids.

By understanding the principles of surface tension and capillarity, we can gain a deeper understanding of the incredible phenomena that occur around us in our daily lives, and lay the foundation for understanding more advanced topics in fluid dynamics and engineering.

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