The rationale? At the anode chlorine ions are oxidized to chlorine gas creating a local "ion depletion zone" and a electric field gradient motivating ionic species to move away from it.
Entirely happy? What is the "ion depletion zone" exactly. As chlorine ions get oxidized, sodium ions accumulate causing all incoming ions to reroute. You might as well call it an accumulation zone. Another matter: the bipolar electrode was at one time a distinct research interest of Martin Fleischmann, you know the guy we are supposed ridicule for 20 years to come and then revere as a genius. This Daniell cell without a bridge also has the look and feel of electrolysed water. More explanations are in order but the paper does not provide them. Finally, being a microfluidic device the output is only 0.04 microliter per minute. So there is some way to go.