The Coquette Bubble: On Interfaces and Measurement Times

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The second law of thermodynamics penalizes an increase in energy while favoring an increase in entropy. The fascinating concept of entropy has been long linked to the disorder, but the two terms don’t necessarily go hand in hand. We will discuss the definition of entropy and how it is maximized (sometimes counterintuitively).

The state of minimum energy determines our environment on many occasions. Water flows from the mountains to the sea, dust settles on our furniture, matter decomposes. In the same way, the geometry that water acquires when in contact with different surfaces responds to the principle of minimum energy.

When it rains, the water droplets acquire their very particular shape on the leaves since they tend to minimize their energy. Plant leaves tend to repel water- we say they are “hydrophobic”: the roots are responsible for absorbing the water from the soil, and the leaves perform other functions. For this reason, the drops minimize their contact with the leaves, forming quasi-spheres of water. The half-moon shape that we can see in the contact line of the water in the glass also responds to the principle of minimum energy.

Drop of water
Drop of water on leaf, indicating the apparent angle of contact with the surface. Image is taken from the documentary “Microcosmos: la Gente de la Herba” (1996) [https://www.youtube.com/watch?v=myfyrpoiysa]

Similarly, when we create a soap bubble, the spherical shape responds to the principle of minimum energy. Contrary to rainwater, the water, in this case, contains “surfactants”, which comes from “Surface Active Agent”. It is just a pretty word to denote, in this case, the molecules that make up the soap. These molecules give bubbles the pinkish hues that water droplets display. One of these “soap molecules” has a mass 20 times that of a water molecule.

Left: A typical component of soap (sodium stearate) compared to a molecule of water. Right: simplified model of surfactant (i.e., how a physicist sees a molecule), with the hydrophobic part in white and the hydrophilic part in red.

These surfactants contain a part that is attracted to water and another that is repelled by it (called, respectively, the hydrophilic part and the hydrophobic part). For this reason, as soon as we create a soap bubble, the surfactants clump together on the surface of the bubble, so the more the merrier can clump together. In this grouping, the hydrophilic part of the molecules points away from the surface of the bubble. The shape that allows more surfactants on the surface in contact with air is the sphere, therefore it is the shape in which the bubble adopts so that the hydrophobic part of the surfactants minimizes contact with water. Due to a difference in concentration between the molecules on the surface and inside the bubble (both of water and soap), a force is created on the surface of the bubble, which acts against any deformation that tries to model the spherical shape. This force is called surface tension.

Is this all the physico-chemistry behind the soap bubbles? Where is the flirtatious bubble promised in the title?

Despite their relatively large size (compared at least to the constituent molecules of water), surfactants are not completely fixed on the surface of the bubble. Like any molecule, they move simply due to the existence of temperature. This is what is known as thermal agitation: the higher the temperature, the more the molecules move. This is why water evaporates when we heat it: the molecules are agitated enough to escape into the atmosphere. In this way, although closely embedded in the surface that separates the air from the water, the surfactants move.

Screenshot of a simulation of the thermal fluctuations of a water-air interface with surfactants. The red part of the molecules has an affinity for the blue compound, while the white part has an affinity for the red compound. Image edited from the video interfacial thermal fluctuations in the presence of surfactants [https://www.youtube.com/watch?v=nhggpzi6q2u].

On a temporary average, the bubble is relatively stable. On our scale, too. For an observer with a shorter and much smaller lifetime, the stability of the bubble is hard to believe.

The flirtatious bubble transmits in its different time and length scales a terrifying message for the cosmophanatic: equilibrium depends on the temporal and longitudinal measuring rod used. The bubble thus invites us to reflect on the size of the human being in the universe and its stability as we understand it. In cosmological terms, the formation of the Earth happened recently, very recently. A mountain is nothing more than a drop that emerges and disappears from the ground, seen on a geological scale.

We know that the planets revolve around the Sun in a dance of balance and harmony. However, this dance is subject to the much larger dance of the galaxies with each other. An observer with an unimaginable life span for the human being will see how Andromeda and the Milky Way dance with each other, perceiving that the planetary harmony of which we believe we are part of is more than a state of transition, called to disappear just like the soap bubbles disappear (shortly) after they are formed (to get an idea of ​​what this collision between galaxies could look like, see video below).

Taken out of context, the words of the wise Evaristo (Spanish singer) establish the position of the human being in the universe to which the bubble has led us: “No somos nada” [We are nothing].

This blog post is an English translation of the author’s following original post in Spanish.


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