CFD Modeling of Stirred-Tank Bioreactors: Multiphase Hydrodynamics, Bubble Dispersion, and Shear Stress

Where $alpha_k$ is the phase volume fraction, and $M_{ik}$ represents interphase momentum exchange including drag (Grace or Ishii-Zuber models), turbulent lift, virtual mass, and turbulent dispersion forces.

2. Turbulent Shear Stress and Kolmogorov Microscales

Cell damage occurs when the smallest turbulent eddies (the Kolmogorov microscale, $eta$) approach or become smaller than the cell diameter ($d_{cell} sim 15 ext{–}25 mu ext{m}$ for CHO cells):

η = (ν³ / ε)^1/4

Where $ u$ is kinematic viscosity and $epsilon$ is local turbulent dissipation rate (W/kg). Because local $epsilon$ near impeller blade tips can exceed the average tank dissipation rate ($ar{epsilon}$) by 15 to 40 times, CFD enables engineers to optimize blade camber, rounded trailing edges, and lower rotational speeds to maintain $eta > d_{cell}$.

Empirical correlations provide a starting estimate, but only Computational Fluid Dynamics (CFD) can resolve the internal 3D spatial velocity, shear rate, and gas-holdup fields inside an industrial bioreactor. Physical sampling cannot measure turbulent energy dissipation at the impeller blade tip, yet this parameter dictates whether shear-sensitive mammalian cells survive or lyse during high-power agitation.

1. Multiphase Hydrodynamic Formulations

Accurate bioprocess CFD requires solving the Eulerian-Eulerian two-fluid model, where continuous broth and dispersed gas bubbles are treated as interpenetrating continua:

∂(α_k ρ_k u_k) / ∂t + ∇ · (α_k ρ_k u_k u_k) = -α_k ∇p + ∇ · τ_k + α_k ρ_k g + M_ik

Where $alpha_k$ is the phase volume fraction, and $M_{ik}$ represents interphase momentum exchange including drag (Grace or Ishii-Zuber models), turbulent lift, virtual mass, and turbulent dispersion forces.

2. Turbulent Shear Stress and Kolmogorov Microscales

Cell damage occurs when the smallest turbulent eddies (the Kolmogorov microscale, $eta$) approach or become smaller than the cell diameter ($d_{cell} sim 15 ext{–}25 mu ext{m}$ for CHO cells):

η = (ν³ / ε)^1/4

Where $ u$ is kinematic viscosity and $epsilon$ is local turbulent dissipation rate (W/kg). Because local $epsilon$ near impeller blade tips can exceed the average tank dissipation rate ($ar{epsilon}$) by 15 to 40 times, CFD enables engineers to optimize blade camber, rounded trailing edges, and lower rotational speeds to maintain $eta > d_{cell}$.