Meissner effect and Coanda effect

Question

1) I've come up with the Meissner effect in my job recently:

(Magnetic field lines through a conductor vs. field lines through a superconductor)

2) And today I saw a video of Mark Rober explaining the Coanda effect.

(Fluid flow curving with the friction of a solid)

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And despite both effects coming from totally different processes, I've seen several similarities such as:

• how the flux lines in both cases curve around the object (fluid or magnetic)
• the absurdly good stability both of these effects give when levitating objects

And since I know that in the Coanda effect, this curvature is the responsible for giving the stability for the levitation, I was just curious to know if their corresponding levitating behavior could be similar, described maybe by similar equations.

Do you know if the comparison has been made before? Thanks!

Answer 1

Hey Guillermo Abad Lopéz, I can not speak much about the equations of fluid dynamics and how they apply to the Coanda effect but I think what you are more observing is that in both the flux lines just following the path of least resistance and and that you might be looking for a pattern as they do arise from different physical phenomena, but I guess the field lines are similar. In the case of the Meissner effect you might have heard of an Arago's disk where a changing magnetic flux induces Eddy currents in the disk which in turn produce there own magnetic fields which are able to attract and repel like a magnet (https://www.youtube.com/watch?v=g0eA5L79PIc). Now for a type 1 superconductor you can literally apply this idea to it and imagine how the eddy currents will be able to flow without any resistance, so if you had a magnet above a superconductor the change in magnetic flux of dropping this magnet on the superconductor will induce eddy currents in the superconductor that will oppose the magnet and for our intents and purposes it would be like two north and north poles of magnet pressing against each other so they repel and the magnet levitates. This is the explanation taught in basic undergrad and high schools but is only for type 1 and is quite simplistic. There is also some penetration of magnetic field in this case into the superconductor down to the London Pentration depth and the magnetic field in the superconductor decays exponentially. This is related to the skin effect where current travels close to the surface and in the case of a superconductor they are called screening currents which travel around the surface of it and are induced by a magnetic flux. This is also known as superdiamagnitism too. With the air around the ball, like the magnetic field around the superconductor the air and magnetic field lines can not penetrate so they just go around the objects, so for the ball the air can't get through the plastic and the magnetic field can't get through the superconductor so they just go around it. So I guess they are similar if you had fan blowing air from the ground to the ceiling and a ball would levitate and a superconductor directly above a large magnet in the ground that would levitate in the same scenario.

I do want to leave you wanting to learn more about this so, in a type two superconductor magnetic flux actually penetrates all the way through the superconductor but only in discrete Abrikosov Vortices with a flux equal to the quantum flux. Now here is the fun part if you have a magnetic track like a train track and put a superconductor above it it will levitate like the Meissner effect except this time if you flip the track upside down so the superconductor is below it, the superconductor will still be the same distance from the track!!!! This is known as flux pinning and our toy model of just having two north poles facing each other causing the levitation in the Meisnner effect breaks down as if it was two north poles they should repel and the superconductor should drop to the ground but it does not. Here is more about it https://www.nature.com/scitable/blog/student-voices/a_closer_look_at_quantum/