Take a cup of coffee and walk. Why did the coffee spill? the funny Nobel Prize in fluid Mechanics.

If you walk with a cup of coffee, why is it easy to spill?

Although this is a common phenomenon, it is not a simple problem. Because the two units involved in this mechanical system are biology (coffee holder) and fluid (coffee), the motion pattern of biology is not as stable as machinery, and fluid mechanics is also notoriously difficult to do. Create more uncertain variables.

However, perhaps angered by the spilled coffee, Mayer and Krechetnikov of the Department of Mechanics at the University of California, Santa Barbara decided to look for the answer to this question. They filmed a number of experimental participants walking with a cup of coffee. Through the image analysis software and the sensors on the coffee cup, they could get the motion state of the person and the coffee cup up and down, left and right, forward and backward, and oblique. The mechanical model of nonlinear simple pendulum was used to compare the coffee liquid level, and the model was solved by computer. Through actual measurement and computer simulation, we have finally figured out the appearance of the system.

Through the experiment, it is observed that after people pick up the coffee cup and start to walk, the coffee is most likely to spill between the seventh step and the tenth step.

Of course, this problem has something to do with the geometric size of the coffee cup. The material and shape of the liquid affect the natural frequency of its oscillation. Coffee in a common mug has a natural frequency of about 2.6 to 4.3 hertz, while people walk at a frequency of about 1 to 2.5 hertz, which is of the same order of magnitude, so the oscillation of coffee in the cup is easily affected by the pace of the cup holder. In addition, the smooth inner edge of the coffee cup makes the oscillation of the coffee almost unhindered.

Further analysis, when people start from the static state, there is usually a small period of accelerated motion between the first step and the fourth step. The coffee in the cup, like the passengers on the bus, will tilt the liquid level due to the influence of the starting acceleration, providing the initial potential energy for subsequent sloshing. After the fourth step, most people move forward at a fixed speed, but there is still a slight speed difference between each step, which puts the coffee in the cup under a swaying acceleration force field, which encourages the coffee to get out of the cup.

Reducing the initial potential energy and reducing the subsequent swing is the only way to prevent coffee spillage, but this experiment reveals a paradoxical phenomenon: people who walk fast usually start to accelerate violently, resulting in a large initial potential energy of the liquid surface, while those who walk slowly, on the contrary, the pace is not as stable as the fast walker, constantly strengthening the shaking of the liquid surface. So, whether you walk fast or slowly, there is a good reason to spill coffee.

Of course, as long as people can focus on the shaking of the coffee liquid, they can naturally have a moderate acceleration and steady pace. In addition, the researchers also recommend the use of an elastic material or a cup with a ring around it to absorb the force of liquid sloshing or increase resistance, which can effectively avoid spilling coffee.

In addition to preventing coffee from spilling, this study has the value of engineering applications. In building pipelines or large machines, we can often see string with liquid surface, such as sewage pipe, hydraulic pipe and so on. The mathematical model established by this study can simulate the impulse motion (sloshing dynamics) caused by vibration, which is beneficial to the development of anti-spatter design.

But putting aside the value of engineering applications, using such a "hard work" experimental framework to see this sesame and mung bean-like thing of spilling coffee is like killing a chicken with a cow knife, which made the two scientists wear the title of the 2012 Ig Nobel "fluid Mechanics Prize".

Besides, wouldn't it be nice to put a lid on the coffee cup?