The Physics of Bubbles: Why They Form, Float, and Pop — and Why Some Produce Temperatures Hotter Than the Sun

The Simplest Beautiful Thing

A soap bubble is, by almost any measure, the simplest beautiful object in physics. A thin film of soapy water — about a micrometre thick — enclosing a pocket of air, shaped by surface tension into a nearly perfect sphere, reflecting light into iridescent colours.

And yet this simple object touches some deep physics. The shape of a bubble is a solution to a variational problem (minimise surface area for a given volume). The pressure inside obeys a law that connects curvature to force. The colours come from thin-film interference — the same wave optics that produces the colours of oil slicks and anti-reflection coatings. The instability of foams connects to statistical mechanics and coarsening theory. And in the most extreme case — a bubble collapsing under ultrasound — the physics produces temperatures rivalling the surface of a star.

Bubbles are underrated.

Laplace Pressure: Why Small Bubbles Push Harder

The defining equation of bubble physics is the Young-Laplace equation, which relates the pressure difference across a curved liquid surface to the curvature and surface tension:

ΔP = γ(1/R₁ + 1/R₂)

where γ is the surface tension and R₁ and R₂ are the principal radii of curvature. For a sphere, R₁ = R₂ = R, so:

ΔP = 2γ/R (for a gas bubble in liquid — one surface)

ΔP = 4γ/R (for a soap bubble in air — two surfaces, inner and outer)

The pressure inside a bubble is always higher than outside. And the critical feature is the inverse dependence on radius: smaller bubbles have higher pressure.

For a 1 cm soap bubble in air (γ_soap ≈ 0.025 N/m): ΔP = 4 × 0.025 / 0.005 = 20 Pa — barely noticeable.

For a 1 µm bubble in water (γ ≈ 0.072 N/m): ΔP = 2 × 0.072 / 0.5 × 10⁻⁶ = 288,000 Pa — about 2.8 atmospheres.

For a 10 nm bubble: ΔP ≈ 14.4 million Pa — about 142 atmospheres.

This has profound consequences. Very small bubbles are thermodynamically unstable: the gas inside is compressed to such high pressure that it redissolves into the liquid. There is a critical radius below which a bubble cannot survive. This is why spontaneous bubble formation (homogeneous nucleation) in a liquid requires either extreme supersaturation or an external energy source — the Laplace pressure barrier is a formidable obstacle.

The inverse-radius relationship also drives Ostwald ripening in foams: when two bubbles of different sizes are connected (directly or through a shared film), gas flows from the smaller bubble (higher pressure) to the larger one (lower pressure). The small bubble shrinks, the large one grows. Over time, the foam coarsens — the average bubble size increases as small bubbles are consumed by large ones. This is why beer foam collapses and why whipped cream deflates.

Why Bubbles Are Spherical

A bubble adopts the shape that minimises its surface area for the enclosed volume. Since surface tension acts as an energy per unit area (γ has units of J/m²), minimising area minimises the surface energy.

The mathematical answer is the isoperimetric theorem: of all closed surfaces enclosing a given volume, the sphere has the minimum area. This is one of the oldest results in mathematics, known in some form to the ancient Greeks, and rigorously proved in the 19th century.

Real bubbles are nearly perfect spheres — deviations are measurable only when gravity becomes significant (the Bond number Bo = ΔρgR²/γ measures the ratio of gravitational to surface tension forces; when Bo ≪ 1, the bubble is spherical). For a 1 cm soap bubble in air, Bo ≈ 0.03 — surface tension dominates, and the shape is spherical to within fractions of a percent.

When bubbles touch, the geometry becomes more interesting. The interface between two bubbles is a minimal surface — a surface with zero mean curvature. Where three bubble walls meet, they always meet at 120° angles (a consequence of equal surface tension forces at the junction, requiring equilibrium of three equal-magnitude tension vectors). Where four edges meet at a point, they meet at the Plateau angle of about 109.47° (the tetrahedral angle). These rules, established experimentally by Joseph Plateau in the 1870s, constrain the geometry of all foams and bubble clusters.

The Colours: Thin-Film Interference

Soap bubbles shimmer with colour because of thin-film interference. White light reflecting from the outer surface of the film interferes with light reflecting from the inner surface. The path difference between these two reflections depends on the film thickness and the angle of observation.

When the path difference equals a whole number of wavelengths for a particular colour, that colour interferes constructively and appears bright. Other colours interfere destructively and are suppressed. Since the film thickness varies across the bubble (gravity pulls the liquid downward, thinning the top), different colours appear at different positions — the swirling rainbow patterns you see on a soap bubble.

The film thickness for first-order constructive interference of visible light (400–700 nm wavelength) is about 100–350 nm — a few hundred water molecules thick. As the film drains and thins further, it eventually becomes so thin that no visible colour satisfies the constructive interference condition. Just before popping, the thinnest part of the film appears black — all visible wavelengths interfere destructively. This “black film” stage, at about 5–30 nm thickness, represents the bubble’s last moments.

The physics is identical to the interference that produces colours in oil films on water, in the wings of morpho butterflies, and in anti-reflection coatings on camera lenses. The bubble is a textbook demonstration of wave optics.

Nucleation: How Bubbles Are Born

Opening a bottle of champagne drops the pressure from about 6 atmospheres to 1 atmosphere. The liquid is now supersaturated with CO₂ — it contains far more dissolved gas than it can hold at the new, lower pressure. Bubbles should form immediately.

But they don’t — at least not uniformly. Bubbles appear at specific points on the glass surface and rise in steady streams from those points. The liquid between the streams appears calm. Why?

Homogeneous nucleation — forming a bubble from nothing, in the bulk liquid — requires overcoming the Laplace pressure barrier. A tiny embryo bubble, say 1 nm across, would have an internal pressure of hundreds of atmospheres — far exceeding the ~5 atm of CO₂ supersaturation in champagne. The embryo would be crushed by its own surface tension. Spontaneous nucleation in the bulk liquid is effectively impossible at normal supersaturation levels.

Instead, bubbles form by heterogeneous nucleation at pre-existing gas pockets trapped in surface defects — scratches, fibres, pits in the glass. These trapped gas cavities provide a starter bubble with a radius large enough that the Laplace pressure is manageable. Dissolved CO₂ diffuses into the cavity, the gas pocket grows, and when buoyancy exceeds adhesion, a bubble detaches and rises. A new bubble immediately begins growing at the same site.

This is why champagne glasses are sometimes etched at the bottom — to provide controlled nucleation sites and produce a visually appealing stream of bubbles. It’s why dropping a grain of sugar into a glass of cola produces an eruption (the rough, porous surface provides thousands of nucleation sites). And it’s why the famous Mentos-and-Diet-Coke fountain works: the candy’s surface is covered in microscopic pits that act as superb nucleation sites.

The physics of nucleation is the same process that controls crystal growth, cloud droplet formation, and the boiling of water. The Laplace pressure barrier is nature’s kinetic lock against spontaneous phase transitions — and heterogeneous nucleation is the universal key.

Champagne Physics: A Bubble’s Journey

Gérard Liger-Belair, a physicist at the University of Reims, has spent decades studying the physics of champagne bubbles. His work has quantified every stage of a bubble’s life:

Birth: A bubble nucleates at a surface defect, typically from a cellulose fibre (from cloth, paper, or dust) about 100 µm long and 10 µm in diameter trapped on the glass surface. The gas cavity inside the fibre acts as the nucleation site.

Growth while attached: The bubble grows by diffusion of dissolved CO₂ from the surrounding liquid. The growth rate depends on the local CO₂ supersaturation and the bubble’s surface area. A bubble reaches a diameter of about 10–50 µm before detaching.

Rise: The detached bubble rises under buoyancy, accelerating as it grows (more CO₂ diffuses in during the rise, increasing the buoyancy). A bubble that starts at 50 µm diameter at the bottom of a flute reaches about 1–2 mm diameter at the surface, having absorbed CO₂ from the surrounding liquid throughout its 1–2 second journey. The rising speed increases from about 1 mm/s near the bottom to about 30 cm/s near the top.

Surface arrival: The bubble reaches the surface and joins the mousse (foam layer). Bubbles at the surface gradually lose gas, thin, and eventually pop. The bursting of each bubble ejects a tiny jet of liquid (a Worthington jet) upward, producing micro-droplets that carry flavour and aroma compounds into the air above the glass — this is a significant part of the sensory experience of champagne.

A typical glass of champagne releases about 10–20 million bubbles before going flat. Each one follows the same physics. Each one is a miniature lesson in nucleation, diffusion, fluid dynamics, and surface tension.

Soap Films: Minimal Surfaces in Nature

Soap films stretched across wire frames naturally find minimal surfaces — surfaces with zero mean curvature at every point. This happens because the film, pulled by surface tension from all sides, settles into the configuration that minimises its total area.

The study of minimal surfaces goes back to Euler and Lagrange in the 18th century, and the Belgian physicist Joseph Plateau systematically studied soap film shapes in the 1870s, establishing the geometric rules that govern their structure (Plateau’s laws):

Films meeting at an edge always form angles of 120°. Edges meeting at a vertex always form angles of approximately 109.47° (the tetrahedral angle). Only three films can meet at an edge, and only four edges at a vertex.

These rules arise from the equilibrium of surface tension forces at junctions. Any configuration violating these rules is unstable and immediately rearranges.

The mathematics of minimal surfaces — the study of surfaces that locally minimise area — has been extraordinarily productive. It connects to calculus of variations, differential geometry, and computational architecture. The Munich Olympic Stadium (1972) was designed using soap film experiments to determine the optimal shape for its lightweight tensile roof.

Cavitation: The Violent Collapse

When the local pressure in a flowing liquid drops below the vapour pressure, the liquid vaporises — forming a cavity or bubble of vapour. This is cavitation, and it’s the destructive cousin of gentle bubble-blowing.

Cavitation occurs behind rapidly spinning propeller blades, in hydraulic pumps, in constrictions where flow accelerates (by Bernoulli’s principle, faster flow means lower pressure), and even in the joints of your knuckles (the pop when you crack your knuckles is likely a cavitation event).

The bubble formation is quiet. The bubble collapse is catastrophic.

When the cavitation bubble is swept into a region of higher pressure, the vapour recondenses and the bubble collapses. The collapse happens in microseconds, driven by the pressure difference between the surrounding liquid and the vapour inside. The inward-rushing liquid walls accelerate to extraordinary speeds. At the final moment of collapse, the conditions at the bubble’s centre can reach:

Temperatures: 5,000–20,000 K (estimated) Pressures: 10,000–50,000 atmospheres Collapse wall velocity: 1,000–4,000 m/s

If the collapse occurs near a solid surface, the bubble collapses asymmetrically — the side furthest from the surface collapses first, forming a high-speed liquid microjet (100–500 m/s) that strikes the surface. The repeated hammering of millions of microjets erodes even hardened steel. Ship propellers, pump impellers, and concrete dam spillways are all vulnerable to cavitation damage.

Nature has weaponised cavitation. The pistol shrimp (Alpheus) snaps its oversized claw so fast (within 0.5 ms) that the rushing water creates a cavitation bubble in its wake. The bubble’s collapse produces:

A pressure wave of ~80 atmospheres at 4 cm distance A sound exceeding 200 dB (one of the loudest biological sounds in the ocean) A brief flash of light (shrimpoluminescence) A temperature at the collapse centre estimated at 4,700°C

The shrimp uses this to stun prey. The physics is the same as what damages ship propellers — just deployed as a hunting strategy.

Sonoluminescence: Light From Sound

And then there is sonoluminescence — arguably the most surprising thing a bubble can do.

Place a small gas bubble (about 5 µm radius) in water. Drive it with ultrasound at about 25–40 kHz. The oscillating pressure field causes the bubble to expand during the low-pressure phase (to about 50 µm) and collapse during the high-pressure phase (back to less than 1 µm). At the moment of maximum compression, the bubble emits a flash of light.

Not a vague glow. A sharp, brief, blue-white flash — lasting about 50–200 picoseconds — so short and so precisely timed that the bubble can flash with perfect regularity, once per acoustic cycle, tens of thousands of times per second. A single bubble, pulsating in a sound field, becomes a tiny light source visible to the naked eye in a darkened room.

The phenomenon was first noticed by Frenzel and Schultes in 1934 (they observed fogging of photographic plates in ultrasonically irradiated water) but was not controlled and studied as single-bubble sonoluminescence (SBSL) until Felipe Gaitan achieved stable SBSL in 1989.

The conditions at the moment of light emission are extreme:

Gas temperature: 10,000–20,000 K (some models predict much higher) Pressure: ~10,000 atmospheres Compression ratio: ~10⁶ (from maximum to minimum radius) Flash duration: 50–200 ps

The light emission is broadband — roughly a blackbody spectrum peaking in the ultraviolet, with a tail extending into the visible (hence the blue-white colour). The number of photons per flash is about 10⁵–10⁶.

The exact mechanism of light emission is still debated. Leading candidates include:

Thermal bremsstrahlung — radiation from free electrons in a transiently ionised gas (a plasma) at the moment of maximum compression.

Adiabatic compression heating — the gas is compressed so rapidly that heat cannot escape, reaching temperatures sufficient for thermal radiation.

Plasma emission — the collapsing bubble briefly creates a hot, dense plasma.

What makes sonoluminescence remarkable is the energy concentration. Sound waves at modest amplitude (about 1 atmosphere of acoustic pressure variation) drive a macroscopic oscillation of a bubble, which concentrates the acoustic energy into a volume about a billion times smaller at the moment of collapse. The energy density amplification — from a gentle sound wave to conditions approximating a stellar surface — is extraordinary.

Some early speculations even proposed that sonoluminescence might produce conditions sufficient for nuclear fusion (bubble fusion or sonofusion), but these claims have not been confirmed and remain highly controversial.

Bubble Acoustics: The Sound of Pop

When a bubble pops at a liquid surface, it produces a characteristic sound — a brief, sharp click. The frequency of the sound depends on the bubble size. Large bubbles produce low pops; small bubbles produce high pings.

Minnaert’s formula (1933) gives the resonant frequency of a gas bubble in liquid:

f = (1/2πR) × √(3γP₀/ρ)

where R is the bubble radius, γ is the ratio of specific heats of the gas (1.4 for air), P₀ is the ambient pressure, and ρ is the liquid density.

For a 3 mm bubble in water: f ≈ 1,100 Hz (about two octaves above middle C). For a 1 mm bubble: f ≈ 3,300 Hz. For a 0.3 mm bubble: f ≈ 11,000 Hz.

This formula explains the sound of rain falling on water (different raindrop sizes produce different bubble sizes, each ringing at its Minnaert frequency), the sound of a brook (turbulence entrains bubbles of various sizes), and even the sound of boiling water (the rumbling comes from collapsing steam bubbles resonating at their natural frequencies).

The babbling brook is, from a physics perspective, a random ensemble of Minnaert oscillators.

Anti-Bubbles and Beyond

An anti-bubble is the inverse of a soap bubble: a thin shell of air enclosing a droplet of liquid, suspended in the same liquid. Where a soap bubble is air surrounded by a thin liquid film in air, an anti-bubble is liquid surrounded by a thin air film in liquid. They’re surprisingly stable (lasting several seconds to minutes) and can be produced by gently dripping soapy water into a pool of the same solution.

Anti-bubbles illustrate a general principle: the physics of thin films, Laplace pressure, and surface tension applies equally regardless of which phase is the film and which is the bulk. The equations don’t care.

From soap bubbles to cavitation to sonoluminescence, the physics of bubbles spans an astonishing range — from the gentlest demonstrations of surface tension to some of the most extreme transient conditions achievable in a laboratory. A soap bubble is among the simplest structures in physics. A sonoluminescent bubble is among the most energetically concentrated.

Both are just air enclosed by water, shaped by the same equation: ΔP = 2γ/R.

Sometimes the simplest equation produces the widest range of phenomena.