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\begin{document}

\title{Modeling large-scale bioreactors with diffusion equations. Part I:
Predicting axial diffusivity and mixing times}



\author[1]{Pauli Losoi}%
\author[1]{Jukka Konttinen}%
\author[1]{Ville Santala}%
\affil[1]{Tampereen yliopisto - Hervannan kampus}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
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
\textsuperscript{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.%
\end{abstract}%



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