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The present paper focuses on the development of a population balance model (PBM) accounting for microbial population dynamics in a fluctuating environment. Heterogeneity within the cell population has two origins: extrinsic/intrinsic noises (cell to cell variability due to biological processes) and external noise (due to fluctuations in the cell environment). Modelling the effects of concentration gradients on the population heterogeneity was addressed in previous works using a population balance model based on the specific growth rate. However that model was unable to predict the distribution of specific growth rates experimentally observed at steady state. Using recent experimental data, we now propose a suitable law for the probability that cells growing at a given specific rate produce daughter cells with a different growth rate. Characteristic times of substrate assimilation and mixing at the cell scale are then …