On a hot summer day, the most pleasant thing is to have a glass of cold beer to cool your heart. Open the beer and the beer bubbles coming straight up look cool. But you know what? Some beer bubbles can sing the Divine Comedy "Anxious"-not only can they be drunk, but also can be heavy. The phenomenon that beer bubbles go down is not a miracle, but it is not common. The most famous example is probably the Guinness stout in Ireland, which is not only delicious, but also talked about because of the bubbles sinking against the sky in the wine. Why does this beer bubble sink? Irish affairs are settled by the Irish themselves. Mathematicians there have recently solved the mystery of bubble sinking.

Why do bubbles sink

In fact, people discovered this phenomenon a long time ago. These sinking beer bubbles are not optical illusions, but real actions against the sky. Beer like Guinness not only holds a stream of carbon dioxide like ordinary beer, but also suffocates nitrogen. The secret of bubble sinking comes from these nitrogen bubbles: once the beer is opened, the air pressure in the beer bottle decreases, and carbon dioxide and nitrogen will no longer dissolve in water and become saturated to form bubbles and foams.

In order to simplify the discussion, we assume that the bubble diameter is constant and only consider the buoyancy and resistance acting on the bubble. The motion of a single bubble depends on the balance between these two forces. Applying Newton's second law, that is, the mass of an object multiplied by the acceleration is equal to the resultant force acting on the object, and taking bubbles as the research object, we can get:

Among them, the first term on the right side of the equation is Archimedes buoyancy of bathtub, the second term is spherical resistance formula, ρ is fluid density, V is bubble volume, and C? d？ It's the drag coefficient, S. p？ Is the projected area of the bubble in the flow direction, U is the bubble velocity, and M is the bubble mass.

From the dimensional analysis, it can be estimated that the time for bubbles to move at a constant speed from rest is very short, about 4 × 10? -7? In other words, most of the time the bubbles we see are moving at a constant speed. At this time, the force of the bubble is balanced, and the left side of the above formula is zero. According to the experiment, the empirical formula of resistance coefficient under different flow conditions is obtained by fluid mechanics, and the bubble rising speed can be obtained by bringing it to the right of the equation:

Where re is the Reynolds number of the bubble, ν is the kinematic viscosity coefficient of the fluid, d is the bubble diameter, and g is the acceleration of gravity. We know that nitrogen bubbles are small and carbon dioxide bubbles are large, so nitrogen rises slowly and carbon dioxide rises quickly. The rising carbon dioxide bubbles are also subject to great resistance in water, so the acceleration brought to beer in turn is also great. Once the supersaturated bubble is formed, it will dominate the flow in the cup, making the beer in the center of the beer cup form an upward flow. After this flow reaches the surface of beer, it can't get rid of the gravity of the earth and has nowhere to go, so it spreads around and flows down the glass wall. This downward flow meets tiny nitrogen bubbles near the cup wall, and if it exceeds the rising speed of the bubbles, it will make them sink.

On the other hand, Guinness beer is a famous dark beer. A big feature of dark beer is black, which makes it easier to observe the movement of bubbles on the surface, rather than the movement of bubbles in the middle like transparent beer. In this way, only the bubbles near the cup wall are noticed, and this bubble sinking phenomenon becomes particularly obvious.

Is this the whole truth?

Nitrogen bubbles are indeed the key to bubble sinking, but the central flow driven by carbon dioxide bubbles is very weak, and it will also disperse energy on the beer surface and be blocked by the wall. Is it strong enough to hedge the rise of nitrogen bubbles?

This problem has been ignored for a long time. Until recently, Irish mathematicians made a computer numerical simulation of the beer glass that had just been filled, thus showing another malignant effect that can not be ignored in the sinking and flow of dry beer-beer glass.

Through Comsol, a computational fluid dynamics software based on MATLAB, Irish mathematicians assume that bubbles in beer are randomly distributed inside beer, and the bubbles remain spherical in the simulation process, with a diameter of 122 micron (from the formula deduced above, we can know that the speed of bubbles is about 4 mm per second). Because of the low flow rate, they further assumed that the flow was smooth laminar. After rough measurement, it is estimated that the total volume of bubbles in a beer glass accounts for 2% of the glass. Finally, and most importantly, they measured the circumference of this elegant beer glass (the left picture below) and applied it to their simulation.

Based on these data and the characteristics of bubbles and beer, they started numerical simulation. The simulation results not only confirm the previous speculation that the bubbles in the middle of the beer cup mainly rise, but also drive the liquid in the center of the cup to form an upward flow in the center, spread around the surface and flow down along the cup wall (bottom left); They further found that the shape design of this beer cup will add icing on the cake and make the downward beer flow stronger.

Further, scientists found that when bubbles formed and then floated, although the bubbles rose vertically, the bubbles would be relatively far away from the wall due to the outward expansion slope of the glass, thus forming a center rich in bubbles and a periphery with sparse bubbles. The average density of the center is small, so the liquid will rise, while the average density of the surrounding liquid is large, so it will sink, just like lighting a bonfire in the middle of a closed big warehouse, forming a cycle of "rising in the middle and falling around". The bonfire heats the fluid in the middle, so it forms a stronger updraft. When the airflow hits the ceiling, it spreads, then it is accelerated by the surrounding cold air and attracted by the low pressure near the ground bonfire, thus strengthening this cycle. In order to confirm this speculation, they also simulated the inverted beer cup and found that the cycle was very weak, even forming a reverse cycle (above). In this case, the bubble may not sink so permanently.

Data from: Shell Network "Beer Bubble Physics: Why does the bubble sink?" 》

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