Effects of asynchronous fluctuations in DOC supply and bacterial growth on biodegradation efficiency

Abstract

We present a model of the biodegradation system in which dissolved organic carbon (DOC) is supplied by a continuous flow of wastewater, aerobically decomposed by heterotrophic bacteria, and continuously discharged downstream. In this model, the rate at which DOC is supplied to the system ( u) and the maximum growth rate of bacteria ( k) fluctuate periodically. We demonstrate analytically how temporal patterns (amplitude, period, and phase difference) in these two fluctuations influence the average DOC concentration and bacterial biomass. These patterns affect: (i) the temporal variability of DOC concentration and (ii) correlations among the fluctuating DOC concentration, the maximum bacterial growth rate, and bacterial biomass. The temporal variability of DOC tends to increase as the relative amplitude of u to k and the fluctuation period increase, leading to a decrease in the average bacterial biomass and biodegradation efficiency. On the other hand, a higher positive (or negative) correlation among fluctuations leads to higher (lower) bacterial biomass and biodegradation efficiency. The sign of the correlations depends on the phase difference between u and k, and tends to be negative at longer periods. The temporal variability of DOC and the effects of correlations among fluctuations determine whether the average DOC concentration is higher or lower than the equilibrium DOC concentration when u and k are temporally constant. Furthermore, the patterns of the fluctuations determine whether the bacterial community is maintained or washed out. In addition, we evaluate numerically the magnitude of the effect of fluctuations. In particular, the dependence on the phase difference can generate a greater than two-fold difference in the average DOC concentration. These results imply that the temporal control of the DOC supply rate, synchronized with the fluctuations of the bacterial community, can improve the efficiency of biodegradation and reduce the DOC concentration in the outflow from a system, even if the total load of DOC delivered to the system is not reduced.