Fluid mixing is normally deemed to be complete when the different fluid matters are uniformly distributed through the whole system. In a mixing system where a spontaneous and periodic reaction such as the Belousov-Zhabotinskii reaction (BZ reaction) takes place, however, all small fluid elements in the system can possess not only material characteristics such as the amount of reactants, but also information characterizing the dynamical mode, such as the period and the phase in the periodic concentration change. Moreover, this information can propagate to surroundings through short-range interactions without any fluid motion. In the fluid mixing operations accompanied by the BZ reaction, therefore, we can observe a different space-temporal concentration distribution from that in the usual fluid mixing system. In this study, by comparing the differences in the space-temporal concentration pattern change among a decolorizing reaction, a reversible color reaction, and a BZ periodic reaction, we consider the necessity of reconsidering the normal concept of fluid mixing.