Shear rate in stirred tank and bubble column bioreactors

A rigorous theoretical analysis is used to show that for both Newtonian and non-Newtonian power law fluids agitated in stirred vessels, the average shear rate γ in the fluid is a function of the rotational speed N of the impeller, as follows:γ=constant⋅N (laminar flow)γ=constant⋅N (laminar flow)γ=constant⋅N3/2 (turbulent flow).γ=constant⋅N3/2 (turbulent flow).Only in turbulent flow, the proportionality constant in the above equation depends on the flow index and the consistency index of the power law fluid. The above equations derived by theoretical reasoning are in excellent agreement with the long established empirical art.In bubble columns, the average shear rate depends on the superficial gas velocity Ug, as follows:γ=constant⋅Ug1/(n+1)where n is the flow index of the power law fluid. The proportionality constant in the above equation for bubble columns is a function of the flow index, consistency index and the density of the liquid.