Vortex in a magnetic stirrer

Added: 2026-05-09

[00:00:00][music] >> Hello to all fans of physics and physical experiments.

[00:00:11]This is Alexey Colchin with you, and today in our video we'll be experimenting with water vortices. In front of me is a magnetic stirrer.

[00:00:19]Inside it there's an electric motor with a permanent magnet attached to it. Now I'm dropping another magnet into the glass and it gets attracted to the permanent magnet inside the stirrer. I carefully turn on the magnetic stirrer and the water gradually starts spinning faster until a deep water vortex forms on the surface slowly descending downward into the container. And this vortex resembles the ones we see when we drain water from a bathtub. It also looks similar to giant destructive tornadoes. And we need to explain how it forms here since the water isn't draining anywhere.

[00:00:56]>> [sighs] >> I'll start by looking at the movement of water inside the glass. First of all, the rotating magnet sets all the water in motion making it spin as a whole. But there's another effect. It pushes the water toward the walls of the glass. The water rises up along the walls, then descends down along the axis of the glass, thus creating a second vortex motion. And all the water as a whole participates in both of these movements at the same time. And to observe this vortex motion, I'll perform an experiment that our colleague Valery Filippov from Izhevsk recently demonstrated.

[00:01:29]Right here we can observe a small plastic ring floating steadily on the surface of the water inside this tube.

[00:01:36]Now, I am going to slowly increase the rotation speed of the magnetic stirrer at the bottom.

[00:01:41]As you can see, a deep water vortex gradually begins to form in the center.

[00:01:46]Consequently, the ring not only starts spinning rapidly around the tube, but it also begins to slide all the way down toward the base. And if you add a few particles to the glass whose density is close to that of water, you can see how they rotate away from the vortex.

[00:02:00]Sometimes they rise up, then get pulled into the vortex and spiral down it at a furious speed, after which this motion repeats again.

[00:02:10]When the liquid rotates as a whole, its surface takes the shape of a paraboloid, and we need to understand how the superposition of vortex motion transforms the paraboloid into a funnel.

[00:02:22]Due to the vortex motion, the law of conservation of angular momentum applies to any small volume of water. So, the product of the azimuthal component of velocity and the radius of rotation remains constant.

[00:02:36]On the other hand, let's consider an element of liquid that is on its surface, and if it is far from the axis, its speed is low. One can consider it practically zero. Then this element spirals down into the center of the vortex, gaining speed, which is calculated using the standard formula, V squared equals 2gh. And now, it would be good to combine these two formulas, but in one of them, we see the total velocity V, while in the other, we have its azimuthal component VP.

[00:03:06]Let's place a small piece of plastic on the surface of the water, record its movement with a high-speed camera, and trace its path. And we can see that the pitch of the spiral is much smaller than the length of one loop, which means that the total velocity and the azimuthal velocity are practically equal.

[00:03:23]And now, let's replace the azimuthal velocity VP with the total velocity V, substitute one equation into the other, and we get the equation for the surface of the vortex, h * r squared equals a constant.

[00:03:38]Let's overlay the graph of this function onto a photograph of the vortex, and we can see how well they match each other.

[00:03:43]According to the first formula, a water particle cannot reach the axis of rotation, otherwise its azimuthal velocity would approach infinity. And the second formula is consistent with this statement and tells us that the vortex should always reach the bottom of the vessel.

[00:04:00]But in real experiments at low stir speeds, the tip of the vortex does not reach the bottom of the vessel. The point is that in the simplified model of an ideal fluid, surface tension forces were not taken into account, and these forces tend to reduce the surface area and smooth out the tip of the vortex.

[00:04:17]Moreover, at the center of any vortex, there is a vortex filament for which the equations of motion for an ideal fluid are no longer applicable because viscosity plays a significant role there. This vortex filament is clearly visible when there are many tiny air bubbles in the water. But why do these bubbles remain on the axis of the vortex and not float to the surface? We already know that the azimuthal velocity of water particles is inversely proportional to the radius of rotation.

[00:04:47]Then the centripetal acceleration, which equals the square of the azimuthal velocity divided by the radius, is inversely proportional to the cube of the radius and increases rapidly as you approach the axis of rotation.

[00:05:00]This centripetal acceleration is provided by the difference in pressure on the inner and outer sides of the particle. And this means that the pressure drops rapidly toward the axis of rotation, and that's where air bubbles rise to the surface.

[00:05:14]And to measure the pressure across the diameter of the glass, we assemble this setup. Here, a thin plastic tube is submerged in the water and connected to a relative pressure sensor. And this entire upper structure serves only one purpose, to allow the tube to be slowly moved across the diameter of the glass.

[00:05:34]Right now, the stirrer is turned off.

[00:05:37]Let's move the tube through the glass and record the hydrostatic pressure at a depth of 9 cm. It is constant and equals 0.9 kPa, of course, not counting atmospheric pressure. Now, let's turn on the stirrer and repeat the experiment slowly moving the tube through the very center of the vortex.

[00:05:55]The closer to the axis of rotation, the more the pressure decreases. And at the center of the vortex, it drops almost to zero, then rises again approaching the hydrostatic value. In another similar experiment, we'll lower a tube open at the top into the center of the whirlpool. The pressure under the tube is lower than atmospheric, so an air column is drawn through the tube into the water, which sometimes breaks up into separate bubbles.

[00:06:21]The air bubbles strung along the vortex filament are especially visible in a tall cylinder. Here, the funnel descends to half the height of the cylinder, and beyond that, we can see the vortex filament extending all the way to the bottom.

[00:06:37]And now, before we move on to our traditional final question, I want to thank everyone who supports our educational projects. You can find out how to do this in the description below this video.

[00:06:49]Now, let's pour a thin layer of sunflower oil onto the surface of the water and turn on the stirrer at a very low speed.

[00:06:57]And if you wait a little, an oil funnel will form at the boundary between the water and the oil. And the question is, why does it appear even at such low stirrer speeds?

[00:07:09]Share your thoughts on this in the comments to this video on YouTube.

[00:07:17]>> [music]