A stirred tank bioreactor of 2.7 m^3 is agitated using a Rushton turbine with diameter 0.5 m and stirrer speed of 1 s^{-1} . If the fermentation…
A stirred tank bioreactor of 2.7m3is agitated using a Rushton turbine with diameter 0.5 m and stirrer speed of 1s−1. If the fermentation broth has viscosity and density of10−2Pa.s and 1000kg.m−3respectively, the mixing time (in seconds) for the bioreactor will be
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Correct Answer: Option C
Explanation
For a stirred tank bioreactor with a Rushton turbine: Given: VolumeV=2.7 m3, Impeller diameterDi=0.5 m, Stirrer speedN=1 s−1, Viscosityμ=10−2 Pa⋅s, Densityρ=1000 kg⋅m−3. Reynolds number:Re=μNDi2ρ=0.011×0.25×1000=25,000(turbulent regime). Tank diameterDT=(πH4V)1/3, assumingH=DT:DT≈1.5 m. Using the empirical mixing time correlation for turbulent stirred tanks:tm≈N5.9(DT/Di)2=15.9×(1.5/0.5)2=15.9×9≈33.3 s.