Bioreactor scale-up is complicated by dynamic interactions between mixing, reaction, mass transfer, and biological phenomena, the effects of which are usually predicted with simple correlations or case-specific simulations. This two-part study investigated whether axial diffusion equations could be used to calculate mixing times and to model and characterize large-scale stirred bioreactors in a general and predictive manner without fitting the diffusivity parameter. In this first part, a resistances-in-series model analogous to basic heat transfer theory was developed to estimate the diffusivity such that only available hydrodynamic numbers and literature data were needed in calculations. For model validation, over 800 previously published experimentally determined mixing times were predicted with the transient axial diffusion equation. The collected data covered reactor sizes up to 160 m ³, single- and multi-impeller configurations, aerated and non-aerated operation in turbulent and transition flow regimes, and various mixing time quantification methods. The model performed excellently for typical multi-impeller configurations as long as flooding conditions were avoided. Mixing times for single-impeller and few non-standard bioreactors were not predicted equally well. The transient diffusion equation together with the developed transfer resistance analogy proved to be a convenient and predictive model of mixing in typical large-scale bioreactors.