Kahibaro Login Register
Previous Next
Experimental Physics » Thermodynamics » Surface Tension »

Surface Tension

Surface tension always occurs in liquids whose molecules strongly interact with each other. Since water consists of dipole molecules, strong hydrogen bonds form between the hydrogen atoms of one molecule and the oxygen atom of another. Inside the liquid, the force acts isotropically in all directions. However, at the water surface, the upper component of the force is missing, resulting in a net force acting perpendicular to the surface on these molecules.

When an object is submerged, the water must flow around it, effectively increasing the water's surface area along the immersed boundary. This requires additional molecules to move from the interior to the surface, thereby performing work $W$ against the attractive forces between the molecules. One therefore defines the ratio of work performed to the increase in surface area as:

$$
\varepsilon = \frac{\Delta W}{\Delta A}
$$

This is known as the specific surface energy and has units of J/m². Since $\varepsilon$ depends on the liquid used, it must be determined experimentally.

To do this, a wire is bent into a rectangular frame with a movable crossbar. When dipped into the liquid being measured, a thin film forms between the frame and the crossbar. If the crossbar is moved by a distance $\Delta s$, the work required is:

$$
\Delta W = F \Delta s = \varepsilon \cdot 2L \Delta s = \varepsilon \Delta A
$$

This allows the specific surface energy to be determined by measuring the force and displacement. The factor of 2 arises because both the upper and lower sides of the liquid film must be considered. The parameter $\varepsilon$ can therefore also be interpreted as tensile stress acting tangentially to the water surface:

$$
\varepsilon = \frac{F}{2L}
$$

This tensile stress is called surface tension $\sigma$, with the unit N/m, which is equivalent to J/m².

In everyday life, surface tension plays a key role in the formation of soap bubbles or foam. The surface tension of pure water under normal conditions is about $\sigma = 0.0728\,\mathrm{N/m}$, which would be far too high for the formation of large soap bubbles.

However, added soap consists largely of surfactants, which contain both a water-soluble (hydrophilic or lipophobic) and a fat-soluble (hydrophobic or lipophilic) component. Surfactants reduce the surface tension of water, allowing large soap bubbles to form.

Surface tension also causes the created surface to minimize itself. This continues until the increasing internal air pressure in the bubble compensates the surface tension, forming a stable bubble of constant size.

Experiment: Floating Razor Blade You can demonstrate surface tension with a lightweight razor blade carefully placed on the surface of water. Even though the buoyant force is not sufficient to keep it afloat, the surface tension is strong enough to support it. If you add a drop of dish soap nearby, the surfactants reduce the surface tension, and the blade immediately sinks to the bottom.

Using surface tension, one can easily calculate the maximum volume of a droplet that forms at the bottom of a capillary. A droplet detaches precisely when its gravitational force exceeds the force from surface tension, which tries to minimize its surface area. The condition can be written as:

$$
F_\mathrm{O} = F_\mathrm{G}
$$

The gravitational force can be written as $mg$, and the mass $m$ replaced with $\varrho V$, where $V$ is the volume of the droplet. On the left-hand side, the circumference $\pi d$ of the capillary is crucial and must be multiplied by the surface tension:

$$
\boxed{V = \frac{\pi d \sigma}{\varrho g}}
$$

This gives the maximum volume the droplet can reach before it detaches.

Previous Next