Determination of the average shear rate in a stirred and aerated tank bioreactor

A method for evaluating the average shear rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma _{{\text{av}}} $$\end{document}) in a stirred and aerated tank bioreactor has been proposed for non-Newtonian fluids. The volumetric oxygen transfer coefficient (kLa) was chosen as the appropriate characteristic parameter to evaluate the average shear rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma _{{\text{av}}} $$\end{document}). The correlations for the average shear rate as a function of N and rheological properties of the fluid (K and n) were obtained for two airflow rate conditions (ϕair). The shear rate values estimated by the proposed methodology lay within the range of the values calculated by classical correlations. The proposed correlations were utilized to predict the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma _{{\text{av}}} $$\end{document} during the Streptomyces clavuligerus cultivations carried out at 0.5 vvm and four different rotational impeller speeds. The results show that the values of the average shear rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma _{{\text{av}}} $$\end{document}) varied from 437 to 2,693 s−1 by increasing with N and flow index (n) and decreasing with the fluid consistency index (K).