The explanation for this movement of the water hinges on the properties of individual water molecules and ions (see figure below). The first thing to observe is that the fluid within the cell seems to separate/stratify into two distinct layers. One layer which surrounds the electrodes and extends to directly below them. The second layer is below and extends to the bottom of the cell. The layer between the two liquids looks like the line separating a layer of oil from a layer of water. A strong light source shining down into the cell facilitates being able to observe the separation. The stratification does not appear until the electric current flows.
This apparent separation is due to the upper layer consisting
of both normal water molecules and the ions of the electrolyte which are
in the liquid. The reason that the ions are drawn into this upper layer
is that they are more electrically charged than water molecules and so
are more strongly attracted to the electrodes and the electric field than
are the water molecules. In addition, the greater portion of the molecules
which make up the solution are water molecules and so the balance of them
must remain in the bottom portion of the cell to fill in the space. The
lighter, more electrically charged ions are drawn up toward the electrodes
creating a layer of water and ions which is less dense than the predominately
water only layer beneath. So this layer of less dense solution forms
around the electrodes and any heating that occurs as a result of the electrolytic
conduction of electricity across the cell is then concentrated in the less
dense, upper layer and causes that layer to become even less dense due
to heating of the solution. This creates a sort of thermocline between
the less dense and more dense layers.
The water molecules in the predominately water solution below
the above mentioned lower density layer, being dipoles, are also affected
by the electric field between the electrodes above them. It causes them
to orient themselves so that the positively charged hydrogen side of the
water molecule is attracted to and so pointing toward the electric field
of the cell.
In the upper layer the water molecules nearer the negatively charged cathode would aim their positively charged hydrogen side at that electrode and those nearer the positively charged anode would aim their negatively charged oxygen side toward that electrode.
Once the water molecules below the ion layer are all oriented in relation to the electric field they also orient in relation to the permanent magnetic field ( not necessarily in that order). They do this because hydrogen has a very large magnetic moment and because of this the hydrogen portion of the water molecules will force the whole molecule to orient into the direction of the magnetic field. This is a normal and well documented behavior, perhaps most readily available for further study in papers relating to the MRI (Magnetic resonance Imaging) device. The main difference being the addition of the electric field in the cells which orients all of the water molecules in the same direction (as described above). Once the water molecules are oriented on these two axes; the electric and the magnetic, the normal kinetic energy of every molecule, which would otherwise be observed as random movement of individual molecules through the solution, in effect join together and the net result is that the molecules all begin to move in the same direction at the same time and the water starts to spin.
The molecules within the ion layer would also orient according to the magnetic field around each electrode and since the fields oppose they would rotate in opposite directions. this effect can easily be observed in an operating cell once one knows what one is looking for.
An increase in the strength of either the permanent magnetic field or the electric current /field between the electrodes could be seen then to be able to increase the speed with which the water is rotating around the inside of the cell by simply increasing the strength of the attraction between the water molecules and either of the fields. The energy which powers the movement of the water must then be considered to come from the water itself as it's own kinetic energy. without the presence of the electric and magnetic fields this kinetic energy would be spent in the individual, random movement of the water molecules through the solution. So this otherwise unavailable energy could potentially be harnessed to provide additional work energy in some way without decreasing the energy being otherwise used or produced by the cell.
After I determined the most probable mechanism responsible for the motion of the water below the electrodes I considered the effects that the magnetic fields of the electrodes might have on each other and how the permanent magnetic field might fit in. I thought that if the permanent magnetic field could link with the magnetic field(s) of one or both of the electrodes then perhaps this could serve to further reduce the voltage drop in the cell by strengthening the electrode field and thereby it's resistance to the drop in voltage. I had already determined the orientation of the magnetic field around each electrode (see figure above) and I realized that in a "normal" cell, one in which the electrodes are at opposite sides of the cell and inserted from the top, that the magnetic fields of the electrodes would actually oppose each other. This realization explained one more reason why the voltage would drop across the cell. This is because the current at the anode must travel "up and out" of the cell and it's movement is being opposed by the field of the cathode where the current flows "down", into the cell. This effect is commonly known and understood between two current carrying metallic conductors when current is flowing in opposite directions and the two conductors are in close proximity to each other.