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

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Abstract

A method for evaluating the average shear rate (\( \dot \gamma _{{\text{av}}} \)) in a stirred and aerated tank bioreactor has been proposed for non-Newtonian fluids. The volumetric oxygen transfer coefficient (k L a) was chosen as the appropriate characteristic parameter to evaluate the average shear rate (\( \dot \gamma _{{\text{av}}} \)). 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 \( \dot \gamma _{{\text{av}}} \) 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 (\( \dot \gamma _{{\text{av}}} \)) varied from 437 to 2,693 s−1 by increasing with N and flow index (n) and decreasing with the fluid consistency index (K).

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Abbreviations

a, b, c :

parameters of Eq. 10

d, e, f :

parameters of Eq. 12

Ce:

dissolved oxygen concentration (mmol L−1)

Ce0 :

dissolved oxygen concentration at t = t 0 (mmol L−1)

Ces :

saturation concentration of dissolved oxygen with air (mmol L−1)

d i :

impeller diameter (m)

k e :

constant of the oxygen probe (s−1)

k :

proportionality constant

k L a :

volumetric oxygen transfer coefficient (s−1)

K :

consistency index (Pa sn)

n :

flow index

N :

rotational impeller speed (rpm)

Q :

volumetric flow rate (m3 s−1)

P :

power input (W)

t :

time (“s” in the equation 6 and “h” in the Fig. 4)

U GR :

superficial gas velocity in the riser region (m s−1)

V :

working volume (m3)

ϕair :

specific air flow rate (vvm)

\( \dot \gamma \) :

shear rate (s−1)

\( \dot \gamma _{{{\text{av}}}} \) :

average shear rate (s−1)

\( \dot \gamma _{{\max }} \) :

maximum shear rate (s−1)

μ :

dynamic viscosity (Pa s)

μ app :

apparent viscosity (Pa s)

μ L :

dynamic viscosity of liquid (Pa s)

σ:

surface tension of fluid (N m−1)

τ :

shear stress (Pa)

τ e :

response time (s)

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Acknowledgments

The authors thank the financial support of FAPESP (Grant Proc. 05/55079-4) and CNPq.

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Authors and Affiliations

  1. Department of Chemical Engineering, Federal University of S. Carlos, CP 676, CEP 13565-905, Sao Carlos, SP, Brazil

    Alexandre Campesi, Marcel O. Cerri, Carlos O. Hokka & Alberto C. Badino

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  1. Alexandre Campesi
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  2. Marcel O. Cerri
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  3. Carlos O. Hokka
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  4. Alberto C. Badino
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Correspondence to Alberto C. Badino.

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Campesi, A., Cerri, M.O., Hokka, C.O. et al. Determination of the average shear rate in a stirred and aerated tank bioreactor. Bioprocess Biosyst Eng 32, 241–248 (2009). https://doi.org/10.1007/s00449-008-0242-4

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