[hamdani yusuf (OP)]

We can consider this experiment as a variation of Marinov motor. In the original version, the magnet is in toroidal form, which makes the magnetic field around it is close to 0. In this video, the conductive liquid is used instead of metal ring which act as rotor.
Which part of Maxwell's equations applies here? Does it have anything to do with Lorentz' force? Does it involve another electromagnetic interaction? 

[alancalverd]

Fleming's Left-hand Motor Rule. The effective field in this case is vertical i.e. perpendicular to the plane of the liquid.

[RD]

If one of the electrodes was dangling it would be a Faraday motor ...

Further reading ... https://wikipedia.org/wiki/Magnetohydrodynamic_converter

[hamdani yusuf (OP)]

The effective field in this case is vertical i.e. perpendicular to the plane of the liquid.

What makes the effective field different than measured magnetic field?
In the original setup, the magnet being used is a toroid. It means the B field around it is close to 0.

[alancalverd]

The lines of force run from N to S both vertically and horizontally. If there were no field, there would be no movement.

[hamdani yusuf (OP)]

The lines of force run from N to S both vertically and horizontally. If there were no field, there would be no movement.

How do the lines of force distributed? It should explain the observation that the direction of liquid movement is counter clockwise when the electrodes are located outside of the liquid ring. But it reverses when they are placed inside of liquid ring.

[alancalverd]

There has to be some initial asymmetry to determine the direction of the current flow: if the electrodes and magnetic field were perfectly symmetrical the current would flow equally in both directions and there would be no movement! Once the liquid flow has started, that pretty well determines the current direction depending on whether the positive or negative ions are more mobile.

Experiments with bath water (does it spin the other way south of the equator?) have shown that micro-flow persists for hours after the bath is filled. In this case if the bulk of the conductive liquid is flowing, say, clockwise, that will persist when the electrodes are removed, but turbulence at the surfaces may produce local countercurrent eddies that will start the flow in the opposite direction when you move the electrodes.

Some old electric clocks had symmetric synchronous motors, and in the days when we had frequent power outages I recall my grandmother's clock sometimes stationary and often running backwards when the power was restored!

[hamdani yusuf (OP)]

There has to be some initial asymmetry to determine the direction of the current flow: if the electrodes and magnetic field were perfectly symmetrical the current would flow equally in both directions and there would be no movement! Once the liquid flow has started, that pretty well determines the current direction depending on whether the positive or negative ions are more mobile.

Experiments with bath water (does it spin the other way south of the equator?) have shown that micro-flow persists for hours after the bath is filled. In this case if the bulk of the conductive liquid is flowing, say, clockwise, that will persist when the electrodes are removed, but turbulence at the surfaces may produce local countercurrent eddies that will start the flow in the opposite direction when you move the electrodes.

Some old electric clocks had symmetric synchronous motors, and in the days when we had frequent power outages I recall my grandmother's clock sometimes stationary and often running backwards when the power was restored!

The experiment shows that the effect is consistent by repeatedly switching direction, thus it's not just an artefact.
The question would be, what kind of asymmetry could explain the observed result?

[alancalverd]

Two separate questions.

First, there must be an initial asymmetry in order for there to be any movement. Your diagram shows "i"  in both directions, so no gross motion is possible without an asymmetric trigger.

Second, once movement has been established, the inevitable turbulence (you can see it in the video) provides the trigger to reverse the flow.

Or it's magic.

[hamdani yusuf (OP)]

The diagram in #3 is the original setup. The brush connected to the ring rotor on the outside only.
The video shows some modifications. It uses liquid conductor. The electrodes can be placed anywhere on the liquid ring.
The asymmetry seems to come from the radial electric current in the toroid plane.
The flow direction is consistently determined by the position of the electrodes. No turbulence is required.

[alancalverd]

If the system is completely symmetrical, nothing will move. It is the principle used in residual current magnetic circuit breakers.

[hamdani yusuf (OP)]

If the system is completely symmetrical, nothing will move. It is the principle used in residual current magnetic circuit breakers.

The problem is, the B field around the toroid supposed to be 0. But still we find that some electromagnetic force is generated.

[alancalverd]

Supposed by whom? If you take the magnet away, you certainly will have zero field. Does the motor work then? I suspect not, so B_ext≠0.

[hamdani yusuf (OP)]

The absence of circumferential current [4] (the path of circumferential current is indicated by the red arrow in figure 3 of this section) and the axially symmetric layout of the conductors and magnetic materials [4][5][6] are sufficient conditions for total internal confinement of the B field. (Some authors prefer to use the H field). Because of the symmetry, the lines of B flux must form circles of constant intensity centered on the axis of symmetry. The only lines of B flux that encircle any current are those that are inside the toroidal winding. Therefore, from Ampere's circuital law, the intensity of the B field must be zero outside the windings.

https://en.wikipedia.org/wiki/Toroidal_inductors_and_transformers#Sufficient_conditions_for_total_internal_confinement_of_the_B_field

[alancalverd]

I say again, if B= 0 it will work without the magnet.

[Bored chemist]

I say again, if B= 0 it will work without the magnet.

He's not wrong.