We study the aqueous solution of vanadium pentoxide by using topology methods. The experiments by Zocher, Kaznacheev, and Dogic exhibited that in the sol phases of V2O5–H2O, the tactoid droplets of V2O5 can coalesce. In the magnetic field, this effect is associated with a gauge field action, viz. we consider coalescence (“junction,” in the topologically more convenient term) of droplets as annihilation of topological defects, concerning with the tactoid geometry. We have shown, that in the magnetic field, the tactoid junction is mainly caused by non-Abelian monopoles (vortons), whereas the Abelian defects almost do not annihilate. Taking into account this annihilation mechanism, the estimations of time-aging of the V2O5–H2O sols may be specified.