Figure 1

Non-autonomous pH oscillations in the acid–base neutralization reaction by using various time-dependent inflow rate functions (waveforms) of the reagents, acid and alkaline solutions, with the phase difference of π (a). The time periods of the various inflow rate functions (triangular, sawtooth, square and sinusoidal) were identical, \(T_{{{\text{acid}}}} = T_{{{\text{base}}}} = 300\, {\text{s}}\) (b), \(T_{{{\text{acid}}}} = T_{{{\text{base}}}} = 200\, {\text{s}}\) (c), and \(T_{{{\text{acid}}}} = T_{{{\text{base}}}} = 100 \,{\text{s}}\) (d). The concentrations of the acid and alkaline solutions in the input feed were 0.1 M (\(c_{{{\text{H}}^{ + } }}^{0} = c_{{{\text{OH}}^{ - } }}^{0} = 0.1 \,{\text{M}})\), respectively.