Theory of Water Ionisation

A water ionizer uses the principle of electrolysis, first recorded in 1800 when William Nicholson and Johann Ritter decomposed water into hydrogen and 

The Electrolytic cell, the 'heart' of the water ionizer.

Michael Faraday defined the cathode as the electrode to which cations flow (positively charged ions, like silver ions Ag+), to be reduced by reacting with (negatively-charged) electrons on the cathode. Likewise he defined the anode as the electrode to which anions flow (negatively charged ions, like chloride ions Cl-), to be oxidized by depositing electrons on the anode. Thus positive electric current flows from the cathode to the anode. To an external wire connected to the electrodes of a battery, thus forming an electric circuit, the cathode is positive and the anode is negative.

Consider two voltaic cells, A and B, with the voltage of A greater than the voltage of B. Mark the positive and negative electrodes as anode and cathode. Place them in a circuit with anode near anode and cathode near cathode, so the cells will tend to drive current in opposite directions. The cell with the larger voltage discharges, making it a voltaic cell. Likewise the cell with the smaller voltage charges, making it an electrolytic cell. For the electrolytic cell, the external markings of anode and cathode are opposite the chemical definition. That is, the electrode marked as anode for discharge acts as the cathode while charging and the electrode marked as cathode acts as the anode while charging.

A modern water ionizer uses the very same technology. Here is a diagram of a typical water ionizer flow: