The Science Of Bubbles: Laws And Theories Explained

Bubbles are a source of wonder for both children and adults, with their vibrant colours and delicate nature. They are formed when a gas substance is trapped in a liquid, and they can be seen in everyday life in carbonated drinks, boiling water, and agitated water. The physics and chemistry behind bubbles are intriguing, and they provide an excellent opportunity to study scientific concepts such as elasticity, surface tension, and light reflection. For example, the Marangoni effect stabilises bubbles by causing the surface tension to increase in areas where the bubble is stretched, preventing it from popping. Additionally, Henry's Law explains the relationship between gas and liquid, stating that when a gas is in equilibrium with a liquid at a constant temperature, the amount of gas dissolved in the liquid is directly proportional to the gas' partial pressure. Furthermore, Laplace's Law describes the relationship between wall tension, pressure, and radius in bubbles. Understanding the science behind bubbles not only enhances our appreciation of their beauty but also has practical applications in various fields, including medicine and engineering.

Laplace's Law

> {\displaystyle \Delta P\equiv P_{\text{inside}}-P_{\text{outside}}=\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right),}

Where {\displaystyle R_{1}} and {\displaystyle R_{2}} are the principal radii of curvature, and {\displaystyle \gamma} is the surface tension.

The law has medical implications, particularly in understanding the mechanics of the heart and lungs. For example, an enlarged heart will require more tension to create the same pressure differential, and so will have to work harder to pump blood around the body.

Snell's Law

When it comes to bubbles, Snell's Law helps explain why we can see them. A bubble is a globule of gas substance in a liquid, like air bubbles in water. Even though both the air and water may appear transparent, they have different refractive indices. The refractive index of air is approximately 1.0003, while the refractive index of water is about 1.333. This difference in refractive indices means that when light passes from air to water, or vice versa, it changes direction.

> \frac{\sin\theta_\text{w}}{\sin\theta_\text{a}}=\frac{v_\text{w}}{v_\text{a}} \approx \frac{1}{1.33} \tag{1}

Where \theta_\text{w} and \theta_\text{a} are the angles of the light ray relative to a line perpendicular to the surface, on the water side and air side respectively, and v_\text{w} and v_\text{a} are the velocities of light in water and air, respectively.

This equation shows that when light passes from air to water, it is refracted or bent. Additionally, if the angle of incidence is greater than approximately 49 degrees, there is no angle of refraction that satisfies the equation, and light is completely reflected. This is why the rim of a bubble acts like a mirror underwater.

Furthermore, when light passes through multiple bubbles, as is often the case in a glass of beer, it undergoes Mie scattering, where it is reflected and refracted many times. This scattering affects all colours of light almost equally, which is why most bubbles appear lighter in colour than the surrounding liquid.

In summary, Snell's Law helps explain how we can see bubbles, why they appear the way they do, and how light interacts with them, even when the substances involved are transparent.

Surface tension

When a bubble is blown into water, it quickly pops due to the high surface tension of the water. However, adding soap decreases the surface tension, allowing the water to stretch and form a bubble. Soap molecules have two ends: a hydrophobic end that avoids water and attaches to oil, and a hydrophilic end that avoids oil and attaches to water. The soap forms a film around the air, with the soap molecules as the outer and inner surfaces of the bubble, and a thin layer of water in between.

The Marangoni effect stabilises bubbles by preventing them from stretching to the point of popping. When a bubble is stretched, the surface concentration of soap decreases, causing the surface tension to increase in that area. This area of increased surface tension then springs back to its original form, maintaining the bubble's shape. As a result, bubbles take on spherical shapes with uniform surface tension.

The tension in the bubble's skin also contributes to its spherical shape. When a bubble is sealed, the tension in the skin shrinks it to the smallest possible shape for the volume of air it contains, which is a sphere. A sphere has the least surface area for a given volume compared to other shapes.

Furthermore, surface tension plays a role in how bubbles interact with each other. Bubbles tend to minimise their surface area, and when they are of similar size, they join together to share a common wall, forming perfect hexagons. This behaviour is similar to bees building a beehive, as they also aim to use the minimum amount of wax to create their spaces.

Elasticity

Surface tension is the force between liquid molecules at the surface of a liquid. For example, water molecules cling to each other, causing the surface of the water to behave like an elastic sheet. This elastic property of water molecules is what allows bubbles to form and maintain their spherical shape.

The elasticity of a bubble is influenced by the presence of soap or other surfactants. Soap molecules have two ends: a hydrophobic end that avoids water and attaches to oil, and a hydrophilic end that avoids oil and attaches to water. When soap is added to water, it decreases the surface tension, allowing the water to stretch more easily and facilitating the formation of bubbles.

The Marangoni effect, caused by the presence of soap, also contributes to the elasticity of bubbles. In areas where the bubble is stretched, the surface concentration of soap decreases, leading to an increase in surface tension. This increase in surface tension acts like a spring, pulling the bubble back towards its original shape and preventing it from stretching to the point of popping. As a result, the bubble maintains its spherical shape with uniform surface tension.

Additionally, the elasticity of a bubble is related to its ability to minimise its surface area. When a bubble is sealed, the tension in the bubble's skin causes it to shrink to the smallest possible shape for the volume of air it contains. This is why a sealed bubble takes on a spherical shape, as a sphere has the smallest surface area for a given volume.

Henry's Law

The law can be expressed as:

> The ratio of P1, the partial pressure of gas overlying a solution initially, to A1, the corresponding amount of gas dissolved in the solution at that pressure, is equal to the ratio of the same gas at a different pressure, P2, and its corresponding amount of dissolved gas, A2, at this new pressure.

It's important to note that Henry's Law has limitations and is inaccurate at high gas concentrations in the liquid phase. It is only applicable when the molecules are at equilibrium and does not account for chemical reactions between the solute and solvent.

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