Apparent viscosity for non-Newtonian fermentation media in bioreactors

The apparent viscosity of non-Newtonian fermentation media is examined. The present state of this subject is discussed. The energy dissipation rate concept is used for a new evaluation of the apparent viscosity in bioreactors, i.e. stirred tank and bubble column bioreactors. The proposed definition of the apparent viscosity is compared with the definitions available in the literature.List of Symbols A _d m ² downcomer cross-sectional area - A _r m ² riser cross-sectional area - a m^–1 specific surface area - C constant in eq. (13) - D m column diameter - D _I m impeller diameter - g m s^–2 gravitational acceleration - h J m^–2 s^–1 K^–1 heat transfer coefficient - K Pa s ⁿ consistency index in a power-law model - k constant in eq. (3) - k _L m s ^–1 liquid-phase mass transfer coefficient - N s^–1 impeller speed - n flow index in a power-law model - P W power input - Re Reynolds number ND _I ^/2 /(/) - U _sg m s ^–1 superficial gas velocity - (U _sg ) _r m s^–1 superficial gas velocity based on riser - V-m³ liquid volume - v ₀ m s^–1 friction velocity Greek Symbols s^–1 shear rate - _c s^–1 characteristic shear rate - W kg^–1 energy dissipation rate per unit mass - W kg^–1 characteristic energy dissipation rate per unit mass - Pa s viscosity - _app Pa s apparent viscosity - kg m^–3 density - Pa shear stress