the reactor ia a nano-TiO2-membrane coupling system where the chemical adsorption of virus phage F2 (by nanosized TiO2) was the main mechanism. In this context, a system that uses biosorption or adsorption for removing general contaminants, could be defined reactor or dynamic continuous-fiow system.
Lastly, the acronym MAR (Membrane Adsorption Reactor) sounds very good ;-) !!!